A Test for Functional Form Against Nonparametric Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 452-475 ◽  
Author(s):  
Jeffrey M. Wooldridge
Keyword(s):  
Alternative Model ◽  
Regression Models ◽  
Functional Form ◽  
Parametric Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Sieve Estimation ◽  
Finite Sample Properties ◽  
Standard Normal ◽  
Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

A CONSISTENT NONPARAMETRIC TEST OF PARAMETRIC REGRESSION MODELS UNDER CONDITIONAL QUANTILE RESTRICTIONS

1998 ◽  
Vol 14 (1) ◽  
pp. 123-138 ◽  
Author(s):  
John Xu Zheng
Keyword(s):  
Regression Models ◽  
Nonparametric Test ◽  
Standard Normal Distribution ◽  
Finite Sample ◽  
Test Statistic ◽  
Asymptotic Power ◽  
Conditional Quantile ◽  
Standard Normal ◽  
Nonparametric Kernel ◽  
Parametric Regression Models

This paper proposes a nonparametric, kernel-based test of parametric quantile regression models. The test statistic has a limiting standard normal distribution if the parametric quantile model is correctly specified and diverges to infinity for any misspecification of the parametric model. Thus the test is consistent against any fixed alternative. The test also has asymptotic power 1 against local alternatives converging to the null at proper rates. A simulation study is provided to evaluate the finite-sample performance of the test.

Cause-specific quantile residual life regression

2015 ◽  
Vol 26 (4) ◽  
pp. 1912-1924 ◽  
Author(s):  
Jeong Youn Lim ◽  
Jong-Hyeon Jeong
Keyword(s):  
Residual Life ◽  
Fixed Time ◽  
Estimating Equation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Test Statistic ◽  
Life Distribution ◽  
Finite Sample Properties ◽  
Quantile Residual Life ◽  
Log Linear

We propose a cause-specific quantile residual life regression where the cause-specific quantile residual life, defined as the inverse of the cumulative incidence function of the residual life distribution of a specific type of events of interest conditional on a fixed time point, is log-linear in observable covariates. The proposed test statistic for the effects of prognostic factors does not involve estimation of the improper probability density function of the cause-specific residual life distribution under competing risks. The asymptotic distribution of the test statistic is derived. Simulation studies are performed to assess the finite sample properties of the proposed estimating equation and the test statistic. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer.

scholarly journals Additive Nonparametric Instrumental Regressions: A Guide to Implementation

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Samuele Centorrino ◽  
Frederique Feve ◽  
Jean-Pierre Florens
Keyword(s):  
Instrumental Variables ◽  
Regularization Method ◽  
Regression Models ◽  
Regression Function ◽  
Data Driven ◽  
Finite Sample ◽  
Partially Linear ◽  
Regularization Parameters ◽  
Finite Sample Properties ◽  
Additive Nonparametric Regression

AbstractWe present a review on the implementation of regularization methods for the estimation of additive nonparametric regression models with instrumental variables. We consider various versions of Tikhonov, Landweber-Fridman and Sieve (Petrov-Galerkin) regularization. We review data-driven techniques for the sequential choice of the smoothing and the regularization parameters. Through Monte Carlo simulations, we discuss the finite sample properties of each regularization method for different smoothness properties of the regression function. Finally, we present an application to the estimation of the Engel curve for food in a sample of rural households in Pakistan, where a partially linear specification is described that allows one to embed other exogenous covariates.

Testing for a Functional Form of Mean Regression in a Fully Parametric Environment

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Stanislav Anatolyev
Keyword(s):  
Labor Market ◽  
Functional Form ◽  
Young Men ◽  
Parametric Model ◽  
Test Statistic ◽  
Typical Size ◽  
Using Data

Abstract We develop a test for a restricted functional form of a mean regression when a complex distributional model for all variables is estimated. The test statistic is an average squared deviation from the estimated hypothesized function of the form implied by the estimated parametric model, and is asymptotically distributed as a mixture of χ2 distributions. The test is easy to implement using numerical derivatives, and it performs well in samples of typical size. We illustrate the test using data on labor market characteristics of US young men.

scholarly journals Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model

Econometrics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 22 ◽  
Author(s):  
Pierre Perron ◽  
Yohei Yamamoto
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Structural Changes ◽  
Error Variance ◽  
Regression Coefficients ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Joint Approach ◽  
Size Distortions

In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients, possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the variance (or in the coefficients). In this note, we provide evidence that such procedures have poor finite sample properties when the changes in the first step are not correctly accounted for. In doing so, we show that testing for changes in the coefficients (or in the variance) ignoring changes in the variance (or in the coefficients) induces size distortions and loss of power. Our results illustrate a need for a joint approach to test for structural changes in both the coefficients and the variance of the errors. We provide some evidence that the procedures suggested by Perron et al. (2019) provide tests with good size and power.

A Semi-Parametric Model for Longitudinal Count Data

2013 ◽  
Vol 805-806 ◽  
pp. 1921-1924
Author(s):  
Kang Yin ◽  
Tian Jin
Keyword(s):  
Data Analysis ◽  
Social Science ◽  
Count Data ◽  
Marginal Distribution ◽  
Estimation Procedure ◽  
Parametric Model ◽  
Local Likelihood ◽  
Finite Sample ◽  
Longitudinal Count Data ◽  
Finite Sample Properties

Longitudinal count data analysis has been widely used in various social science and nature science. In this paper, we proposed a semi-parametric negative multinomia model for longitudinal count data. Using local likelihood technique and marginal distribution, we proposed an estimation procedure for our new model. The finite-sample properties are studied with a simulation study.

A CONSISTENT TEST OF CONDITIONAL PARAMETRIC DISTRIBUTIONS

2000 ◽  
Vol 16 (5) ◽  
pp. 667-691 ◽  
Author(s):  
John Xu Zheng
Keyword(s):  
Linear Expansion ◽  
Kernel Estimation ◽  
Nonparametric Test ◽  
Distribution Functions ◽  
Finite Sample ◽  
Information Function ◽  
Test Statistic ◽  
First Order ◽  
Standard Normal ◽  
Leibler Information

This paper proposes a new nonparametric test for conditional parametric distribution functions based on the first-order linear expansion of the Kullback–Leibler information function and the kernel estimation of the underlying distributions. The test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric distribution is correctly specified, whereas asymptotically rejecting the null with probability one if the parametric distribution is misspecified. The test is also shown to have power against any local alternatives approaching the null at rates slower than the parametric rate n−1/2. The finite sample performance of the test is evaluated via a Monte Carlo simulation.

CONSISTENT SPECIFICATION TESTING FOR CONDITIONAL SYMMETRY

1998 ◽  
Vol 14 (1) ◽  
pp. 139-149 ◽  
Author(s):  
John Xu Zheng
Keyword(s):  
Null Hypothesis ◽  
Kernel Method ◽  
Asymmetric Distribution ◽  
Local Alternatives ◽  
Finite Sample ◽  
Conditional Symmetry ◽  
Specification Test ◽  
Test Statistic ◽  
Specification Testing ◽  
Standard Normal

This paper presents a consistent specification test of conditional symmetry using a kernel method. The test statistic is shown to be asymptotically distributed as standard normal under the null hypothesis of conditional symmetry and consistent against any conditional asymmetric distribution. Power against local alternatives is also investigated. A Monte Carlo simulation is provided to evaluate the finite-sample performance of the test.

Nested logistic regression models and ΔAUC applications: Change-point analysis

2021 ◽  
pp. 096228022110223
Author(s):  
Chun Yin Lee
Keyword(s):  
Logistic Regression ◽  
Change Point ◽  
Regression Models ◽  
Real Life ◽  
Change Point Analysis ◽  
Reduced Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Logistic Regression Models ◽  
Nested Models

The area under the receiver operating characteristic curve (AUC) is one of the most popular measures for evaluating the performance of a predictive model. In nested models, the change in AUC (ΔAUC) can be a discriminatory measure of whether the newly added predictors provide significant improvement in terms of predictive accuracy. Recently, several authors have shown rigorously that ΔAUC can be degenerate and its asymptotic distribution is no longer normal when the reduced model is true, but it could be the distribution of a linear combination of some [Formula: see text] random variables [ 1 , 2 ]. Hence, the normality assumption and existing variance estimate cannot be applied directly for developing a statistical test under the nested models. In this paper, we first provide a brief review on the use of ΔAUC for comparing nested logistic models and the difficulty of retrieving the reference distribution behind. Then, we present a special case of the nested logistic regression models that the newly added predictor to the reduced model contains a change-point in its effects. A new test statistic based on ΔAUC is proposed in this setting. A simple resampling scheme is proposed to approximate the critical values for the test statistic. The inference of the change-point parameter is done via m-out-of- n bootstrap. Large-scale simulation is conducted to evaluate the finite-sample performance of the ΔAUC test for the change-point model. The proposed method is applied to two real-life datasets for illustration.

Sign in / Sign up

Export Citation Format

Share Document