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Full-Text Articles in Social and Behavioral Sciences
Second Order Approximation In A Linear Regression With Heteroskedasticity For Unknown Form, Oliver B. Linton
Second Order Approximation In A Linear Regression With Heteroskedasticity For Unknown Form, Oliver B. Linton
Cowles Foundation Discussion Papers
We develop stochastic expansions with remainder o P ( n –2µ ), where 0 < µ < 1/2, for a standardised semiparametric GLS estimator, a standard error, and a studentized statistic, in the linear regression model with heteroskedasticity of unknown form. We calculate the second moments of the truncated expansion, and use these approximations to compare two competing estimators and to define a method of bandwidth choice.
Second Order Approximation In The Partially Linear Regression Model, Oliver B. Linton
Second Order Approximation In The Partially Linear Regression Model, Oliver B. Linton
Cowles Foundation Discussion Papers
We examine the second order properties of various quantities of interest in the partially linear regression model. We obtain a stochastic expansion with remainder o P ( n -2µ ), where µ < 1/2, for the standardized semiparametric least squares estimator, a standard error estimator, and a studentized statistic. We use the second order expansions to correct the standard error estimates for second order effects, and to define a method of bandwidth choice. A Monte Carlo experiment provides favorable evidence on our method of bandwidth choice.
Operational Algebra And Regression T-Tests, Peter C.B. Phillips
Operational Algebra And Regression T-Tests, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Data reduction involves a physical transition from sample data to econometric estimator and test statistic. This transition induces a mapping on the probability law of the sample, whose image is the distribution of the statistic of interest. At a general level, the mapping can often be captured by means of an operational algebra. Some methods than employ nonlinear functions of differential operators are suggested which can perform this task. The methods are related to pseudodifferential operator techniques that are used in abstract mathematics to solve systems of partial differential equations. They also generalize the fractional calculus methods developed by the …
Fractional Matrix Calculus And The Distribution Of Multivariate Tests, Peter C.B. Phillips
Fractional Matrix Calculus And The Distribution Of Multivariate Tests, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Fractional matrix operator methods are introduced as a new tool of distribution theory for use in multivariate analysis and econometrics. Earlier work by the author on this operational calculus is reviewed and to illustrate the use of these methods we give an exact distribution theory for a general class of tests in the multivariate linear model. This distribution theory unifies and generalizes previously known results, including those for the standard F statistic in linear regression, for Hotelling’s T 2 test and for Hotelling’s generalized T -2 test. We also provide a simple and novel derivation of conventional asymptotic theory as …
Asymptotic Expansions In Nonstationary Vector Autoregressions, Peter C.B. Phillips
Asymptotic Expansions In Nonstationary Vector Autoregressions, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the statistical properties of vector autoregressions (VAR’s) for quite general multiple time series which are integrated of order one. Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to yield first order asymptotics in nonstationary VAR’s. Characteristic and cumulant functionals for generalized random processes are introduced as a means of developing a refinement of central limit theory on function spaces. The theory is used to find asymptotic expansions of the regression coefficients in nonstationary VAR’s under very general conditions. The results are specified to the scalar case and …