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Articles 1 - 12 of 12
Full-Text Articles in Social and Behavioral Sciences
Posterior-Based Wald-Type Statistic For Hypothesis Testing, Xiaobin Liu, Yong Li, Jun Yu, Tao Zeng
Posterior-Based Wald-Type Statistic For Hypothesis Testing, Xiaobin Liu, Yong Li, Jun Yu, Tao Zeng
Research Collection School Of Economics
A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as MCMC output) is available, …
Hypothesis Testing, Specification Testing And Model Selection Based On The Mcmc Output Using R, Yong Li, Jun Yu, Tao Zeng
Hypothesis Testing, Specification Testing And Model Selection Based On The Mcmc Output Using R, Yong Li, Jun Yu, Tao Zeng
Research Collection School Of Economics
This chapter overviews several MCMC-based test statistics for hypothesis testing andspecification testing and MCMC-based model selection criteria developed in recentyears. The statistics for hypothesis testing can be viewed as the MCMC version ofthe “trinity” of test statistics based in maximum likelihood (ML), namely, the likelihoodratio (LR) test, the Lagrange multiplier (LM) test, and the Wald test. The model selection criteria correspond to two predictive distributions. One of them can be viewed asthe MCMC version of widely used information criterion, AIC. The asymptotic distributions of the test statistics and model selection criteria are discussed. The test statisticsand model selection criteria are …
A Practical Test For Strict Exogeneity In Linear Panel Data Models With Fixed Effects, Liangjun Su, Yonghui Zhang, Jie Wei
A Practical Test For Strict Exogeneity In Linear Panel Data Models With Fixed Effects, Liangjun Su, Yonghui Zhang, Jie Wei
Research Collection School Of Economics
This paper provides a practical test for strict exogeneity in linear panel data models with fixed effects when the number of individuals N goes to infinity while the number of time periods T is fixed. The test is based on the supremum of a sequence of Wald test statistics. Under suitable conditions, we establish the asymptotic distribution of the test statistic and consistency of the test. A bootstrap procedure is proposed to improve the finite sample performance and the validity of the procedure is justified. We investigate the finite sample performance of the test via a small set of Monte …
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CS’s) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CS’s are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t , and quasi-likelihood ratio tests and CS’s whose critical values are designed to yield robustness …
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CS’s) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CS’s are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t; and quasi-likelihood ratio tests and CS’s whose critical values are designed to yield robustness to …
Essays On The Random Parameters Logit Model, Tong Zeng
Essays On The Random Parameters Logit Model, Tong Zeng
LSU Doctoral Dissertations
This research uses quasi-Monte Carlo sampling experiments to examine the properties of pretest and positive-part Stein-like estimators in the random parameters logit (RPL) model based on the Lagrange Multiplier (LM), likelihood ratio (LR) and Wald tests. First, we explore the properties of quasi-random numbers, which are generated by the Halton sequence, in estimating the random parameters logit model. We show that increases in the number of Halton draws influence the efficiency of the RPL model estimators only slightly. The maximum simulated likelihood estimator is consistent and it is not necessary to increase the number of Halton draws when the sample …
Two Sides Of The Same Coin: Bootstrapping The Restricted Vs. Unrestricted Model, Panagiotis Mantalos
Two Sides Of The Same Coin: Bootstrapping The Restricted Vs. Unrestricted Model, Panagiotis Mantalos
Journal of Modern Applied Statistical Methods
The properties of the bootstrap test for restrictions are studied in two versions: 1) bootstrapping under the null hypothesis, restricted, and 2) bootstrapping under the alternative hypothesis, unrestricted. This article demonstrates the equivalence of these two methods, and illustrates the small sample properties of the Wald test for testing Granger-Causality in a stable stationary VAR system by Monte Carlo methods. The analysis regarding the size of the test reveals that, as expected, both bootstrap tests have actual sizes that lie close to the nominal size. Regarding the power of the test, the Wald and bootstrap tests share the same power …
Testing When A Parameter Is On The Boundary Of The Maintained Hypothesis, Donald W.K. Andrews
Testing When A Parameter Is On The Boundary Of The Maintained Hypothesis, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the alternative hypothesis, but not under the null. The paper establishes the asymptotic null and local alternative distributions of quasi-likelihood ratio, rescaled quasi-likelihood ratio, Wald, and score tests in this case. The results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models. Examples …
Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers tests of nonlinear parametric restrictions in semiparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like test statistics are considered and are shown to have asymptotic chi-square distributions under the null and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. A number of examples are given to illustrate the testing results of this paper and the estimation and stochastic equicontinuity results of the antecedents to this paper, viz. Andrews (1989b, …
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators. The results apply in time series and cross-sectional modeling contexts. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The criterion function need not be differentiable. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes. This paper also considers tests …
Inference In Econometric Models With Structural Change, Donald W.K. Andrews, Ray C. Fair
Inference In Econometric Models With Structural Change, Donald W.K. Andrews, Ray C. Fair
Cowles Foundation Discussion Papers
This paper extends the classical Chow (1960) test for structural change in linear regression models to a wide variety of nonlinear models, estimated by a variety of different procedures. Wald, Lagrange multiplier-like, and likelihood ratio-like test statistics are introduced. The results allow for heterogeneity and temporal dependence of general unifying results for estimation and testing in nonlinear parametric econometric models.
Asymptotic Results For Generalized Wald Tests, Donald W.K. Andrews
Asymptotic Results For Generalized Wald Tests, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This note presents conditions under which a quadratic form based on a g-inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result is of interest, because it is needed to establish asymptotic significance levels and local power properties of generalized Wald tests (i.e., Wald tests with singular limiting covariance matrices). Included in this class of tests are Hausman specification tests and various goodness of fit tests, among others. The necessary and sufficient condition is relevant to procedures …