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Full-Text Articles in Social and Behavioral Sciences
Uniform Nonparametric Inference For Time Series Using Stata, Jia Li, Zhipeng Liao, Mengsi Gao
Uniform Nonparametric Inference For Time Series Using Stata, Jia Li, Zhipeng Liao, Mengsi Gao
Research Collection School Of Economics
In this article, we introduce a command, tssreg, that conducts nonparametric series estimation and uniform inference for time-series data, including the case with independent data as a special case. This command can be used to nonparametrically estimate the conditional expectation function and the uniform confidence band at a user-specified confidence level, based on an econometric theory that accommodates general time-series dependence. The uniform inference tool can also be used to perform nonparametric specification tests for conditional moment restrictions commonly seen in dynamic equilibrium models.
The Regression Smoother Lowess: A Confidence Band That Allows Heteroscedasticity And Has Some Specified Simultaneous Probability Coverage, Rand Wilcox
Journal of Modern Applied Statistical Methods
Many nonparametric regression estimators (smoothers) have been proposed that provide a more flexible method for estimating the true regression line compared to using some of the more obvious parametric models. A basic goal when using any smoother is computing a confidence band for the true regression line. Let M(Y|X) be some conditional measure of location associated with the random variable Y, given X and let x be some specific value of the covariate. When using the LOWESS estimator, an extant method that assumes homoscedasticity can be used to compute a confidence interval for M(Y|X = x). A trivial way of …
Testing Conditional Independence Via Empirical Likelihood, Liangjun Su, Halbert White
Testing Conditional Independence Via Empirical Likelihood, Liangjun Su, Halbert White
Liangjun Su
We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time …
Estimating Smooth Structural Change In Cointegration Models, Peter C. B. Phillips, Degui Li, Jiti Gao
Estimating Smooth Structural Change In Cointegration Models, Peter C. B. Phillips, Degui Li, Jiti Gao
Research Collection School Of Economics
This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to reorient coordinates and …
Nonparametric Predictive Regression, Ioannis Kasparis, Elena Andreou, Peter C. B. Phillips
Nonparametric Predictive Regression, Ioannis Kasparis, Elena Andreou, Peter C. B. Phillips
Research Collection School Of Economics
A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The limit distribution of these predictive tests is nuisance parameter free and holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. Asymptotic theory and simulations show that the proposed tests are more powerful than existing parametric predictability tests when deviations from unity are large or the predictive regression is nonlinear. Empirical illustrations to monthly SP500 stock returns data are provided. …
Testing Conditional Independence Via Empirical Likelihood, Liangjun Su, Halbert White
Testing Conditional Independence Via Empirical Likelihood, Liangjun Su, Halbert White
Research Collection School Of Economics
We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time …
A Smooth Test For The Equality Of Distributions, Anil Bera, Aurobindo Ghosh, Zhijie Xiao
A Smooth Test For The Equality Of Distributions, Anil Bera, Aurobindo Ghosh, Zhijie Xiao
Research Collection School Of Economics
The two-sample version of the celebrated Pearson goodness-of-fit problem has been a topic of extensive research, and several tests like the Kolmogorov-Smirnov and Cramer-von Mises have been suggested. Although these tests perform fairly well ´ as omnibus tests for comparing two probability density functions (PDFs), they may have poor power against specific departures such as in location, scale, skewness, and kurtosis. We propose a new test for the equality of two PDFs based on a modified version of the Neyman smooth test using empirical distribution functions minimizing size distortion in finite samples. The suggested test can detect the specific directions …
Testing Conditional Independence Via Empirical Likelihood, Liangjun Su, Halbert White
Testing Conditional Independence Via Empirical Likelihood, Liangjun Su, Halbert White
Research Collection School Of Economics
We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time …
Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang
Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang
Research Collection School Of Economics
This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD) or their variants, but restrict our attention to nonparametric and semiparametric regression models. In particular, we consider variable selection in additive models, partially linear models, functional/varying coefficient models, single index models, general nonparametric regression models, and semiparametric/nonparametric quantile regression models.
Nonparametric Predictive Regression, Ioannis Kasparis, Elena Andreou, Peter C.B. Phillips
Nonparametric Predictive Regression, Ioannis Kasparis, Elena Andreou, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The test statistics are related to those of Kasparis and Phillips (2012) and are obtained by kernel regression. The limit distribution of these predictive tests holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. In this sense the proposed tests provide a unifying framework for predictive inference, allowing for possibly nonlinear relationships of unknown form, and offering robustness to integration …
Dynamic Misspecification In Nonparametric Cointegrating Regression, Ioannis Kasparis, Peter C. B. Phillips
Dynamic Misspecification In Nonparametric Cointegrating Regression, Ioannis Kasparis, Peter C. B. Phillips
Research Collection School Of Economics
Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a "pseudo-true function" limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-true function and appropriately scaled, the NW estimator still has a mixed …
Comparing The Strength Of Association Of Two Predictors Via Smoothers Or Robust Regression Estimators, Rand R. Wilcox
Comparing The Strength Of Association Of Two Predictors Via Smoothers Or Robust Regression Estimators, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Consider three random variables, Y , X1 and X2, having some unknown trivariate distribution and let n2j (j = 1, 2) be some measure of the strength of association between Y and Xj. When n2j is taken to be Pearson’s correlation numerous methods for testing Ho : n21 = n22 have been proposed. However, Pearson’s correlation is not robust and the methods for testing H0 are not level robust in general. This article examines methods for testing H0 based on a robust fit. The …
Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications, Qiying Wang, Peter C. B. Phillips
Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications, Qiying Wang, Peter C. B. Phillips
Research Collection School Of Economics
A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya-Watson estimator has the same limit distribution (to the second order including bias) as the local linear …
Dynamic Misspecification In Nonparametric Cointegrating Regression, Ioannis Kasparis, Peter C.B. Phillips
Dynamic Misspecification In Nonparametric Cointegrating Regression, Ioannis Kasparis, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression …
Asymptotic Theory For Zero Energy Density Estimation With Nonparametric Regression Applications, Qiying Wang, Peter C.B. Phillips
Asymptotic Theory For Zero Energy Density Estimation With Nonparametric Regression Applications, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya-Watson estimator has the same limit distribution (to the second order including bias) as the local linear …
Structural Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Structural Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional cointegrating regressions where the regressor is an integrated time series, it is shown here that inverse and ill-posed inverse problems do not arise. Remarkably, nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution …
Local Limit Theory And Spurious Nonparametric Regression, Peter C.B. Phillips
Local Limit Theory And Spurious Nonparametric Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated processes that includes the important practical case of spurious regressions. Some local regression diagnostics are suggested for forensic analysis of such regresssions, including a local R² and a local Durbin Watson (DW) ratio, and their asymptotic behavior is investigated. The most immediate findings extend the earlier work on linear spurious regression (Phillips, 1986), showing that the key behavioral characteristics of …
Testing Structural Change In Time-Series Nonparametric Regression Models, Liangjun Su, Zhijie Xiao
Testing Structural Change In Time-Series Nonparametric Regression Models, Liangjun Su, Zhijie Xiao
Research Collection School Of Economics
We propose a CUSUM type of test for structural change in dynamic nonparametric regression models. It is based upon the cumulative sums of weighted residuals from a single nonparametric regression and complements the conventional parameter instability tests in parametric models. We derive the limiting distributions of the test under both the null hypothesis and sequences of local alternatives. A boot-strap procedure is also proposed and its validity is justified. Finally, simulation experiments are conducted to investigate the finite sample properties of our test.
A Consistent Characteristic Function-Based Test For Conditional Independence, Liangjun Su, Halbert White
A Consistent Characteristic Function-Based Test For Conditional Independence, Liangjun Su, Halbert White
Research Collection School Of Economics
Y is conditionally independent of Z given X if Pr{f(y|X,Z)=f(y|X)}=1 for all y on its support, where f(·|·) denotes the conditional density of Y given (X,Z) or X. This paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal. We extend the test of Su and White (2005. A Hellinger-metric nonparametric test for conditional independence. Discussion Paper, Department of Economics, UCSD) in two directions: (1) our test is less sensitive to the choice of bandwidth sequences; (2) our test has power …
Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly involves the density function of the processes under consideration and avoids Fourier integral representations and Markov process theory which have been used in earlier research on this type of problem. The approach provides results of wide applicability to important practical cases and involves rather simple derivations that should make the limit theory more accessible and useable in econometric applications. …
Whose Money? Whose Time? A Nonparametric Approach To Modeling Time Spent On Housework, Sanjiv Gupta, Michael Ash
Whose Money? Whose Time? A Nonparametric Approach To Modeling Time Spent On Housework, Sanjiv Gupta, Michael Ash
Economics Department Working Paper Series
We argue that earlier quantitative research on the relationship between heterosexual partners’ earnings and time spent on housework has two basic flaws. First, it has focused on the effects of women’s shares of couples’ total earnings on their housework, and has not considered the simpler possibility of an association between women’s absolute earnings and housework. Consequently it has relied on unsupported theoretical restrictions in the modeling. We adopt a flexible, nonparametric approach that does not impose the polynomial specifications on the data that characterize the two dominant models of the relationship between earnings and housework, the “economic exchange” and “gender …
Inferences About The Components Of A Generalized Additive Model, Rand R. Wilcox
Inferences About The Components Of A Generalized Additive Model, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
A method for making inferences about the components of a generalized additive model is described. It is found that a variation of the method, based on means, performs well in simulations. Unlike many other inferential methods, switching from a mean to a 20% trimmed mean was found to offer little or no advantage in terms of both power and controlling the probability of a Type I error.
Cross-Validation In Nonparametric Regression With Outliers, Denis H. Y. Leung
Cross-Validation In Nonparametric Regression With Outliers, Denis H. Y. Leung
Research Collection School Of Economics
A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers ill the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26 163-184]. However, Under these Circumstances Standard cross-validation is no longer a satisfactory bandwidth selector because it is unduly influenced by extreme prediction errors caused by the existence of these Outliers. A more robust method proposed here is a cross-validation method that discounts the extreme prediction errors. In large samples the robust method chooses consistent …
More Efficient Kernel Estimation In Nonparametric Regression With Autocorrelated Errors, Zhijie Xiao, Oliver B. Linton, Raymond J. Carroll, E. Mammen
More Efficient Kernel Estimation In Nonparametric Regression With Autocorrelated Errors, Zhijie Xiao, Oliver B. Linton, Raymond J. Carroll, E. Mammen
Cowles Foundation Discussion Papers
We propose a modification of kernel time series regression estimators that improves efficiency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent variable that has to be estimated from the data. We establish the asymptotic distribution of our estimator under weak dependence conditions. It is shown that the proposed estimation procedure is more efficient than the conventional kernel method. We also provide simulation evidence to suggest that gains can be achieved in moderate sized samples.
The Limiting Behavior Of Kernel Estimates Of The Lyapunov Exponent For Stochastic Time Series, Yoon-Jae Whang, Oliver B. Linton
The Limiting Behavior Of Kernel Estimates Of The Lyapunov Exponent For Stochastic Time Series, Yoon-Jae Whang, Oliver B. Linton
Cowles Foundation Discussion Papers
This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root-T consistency and asymptotic normality, while in the second case, which is more relevant for chaotic processes, we are only able to establish asymptotic normality at a slower rate of convergence. We provide consistent confidence intervals for both cases. We apply our procedures to simulated data.
Testing Additivity In Generalized Nonparametric Regression Models, Pedro Gozalo, Oliver B. Linton
Testing Additivity In Generalized Nonparametric Regression Models, Pedro Gozalo, Oliver B. Linton
Cowles Foundation Discussion Papers
We develop kernel-based consistent tests of an hypothesis of additivity in nonparametric regression extending recent work on testing parametric null hypotheses against nonparametric alternatives. The additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for standard estimators. The asymptotic distributions of the tests under a sequence of local alternatives are found and compared: in fact, we give a ranking of the different tests based on local asymptotic power. The practical performance is investigated via simulations and an application to the German migration data of Linton and Härdle (1996).
Additive Interactive Regression Models: Circumvention Of The Curse Of Dimensionality, Donald W.K. Andrews, Yoon-Jae Whang
Additive Interactive Regression Models: Circumvention Of The Curse Of Dimensionality, Donald W.K. Andrews, Yoon-Jae Whang
Cowles Foundation Discussion Papers
This paper considers series estimators of additive interactive regression (AIR) models. AIR models are nonparametric regression models that generalize additive regression models by allowing interactions between different regressor variables. They place more restrictions on the regression function, however, than do fully nonparametric regression models. By doing so, they attempt to circumvent the curse of dimensionality that afflicts the estimation of fully nonparametric regression models. In this paper, we present a finite sample bound and asymptotic rate of convergence results for the mean average squared error of series estimators that show the AIR models do circumvent the curse of dimensionality. The …
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Cowles Foundation Discussion Papers
The problem considered here is that of using a data-driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter. In contrast to other papers on this subject, we consider models with heteroskedastic errors. The results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators, nearest neighbor estimators, and local regression estimators, among others. Generalized C L , cross-validation, and generalized cross-validation procedures are analyzed.
The Macroeconomics Of Government Finance, Michael Haliassos, James Tobin
The Macroeconomics Of Government Finance, Michael Haliassos, James Tobin
Cowles Foundation Discussion Papers
This paper establishes the asymptotic normality of series estimators for nonparametric regression models. Gallant’s Fourier flexible form estimators, trigonometric series estimators, and polynomial series estimators are prime examples of the estimators covered by the results. The results apply to a wide variety of estimands in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic or heteroskeclastic. The paper also considers series estimators for additive interactive regression (AIR), seimparametric regression, and semiparametric index regression models and shows them to be consistent and asymptotically normal. All of the consistency and …
Asymptotic Normality Of Series Estimators For Nonparametric And Semiparametric Regression Models, Donald W.K. Andrews
Asymptotic Normality Of Series Estimators For Nonparametric And Semiparametric Regression Models, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper establishes the asymptotic normality of series estimators for nonparametric regression models. Gallant’s Fourier flexible form estimators, trigonometric series estimators, and polynomial series estimators are prime examples of the estimators covered by the results. The results apply to a wide variety of estimands in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic or heteroskeclastic. The paper also considers series estimators for additive interactive regression (AIR), seimparametric regression, and semiparametric index regression models and shows them to be consistent and asymptotically normal. All of the consistency and …