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.

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 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.

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang
Keyword(s):  
Null Distribution ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Hedonic Price ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Test ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

The Odd Log-Logistic Geometric Normal Regression Model with Applications

2019 ◽  
Vol 11 (01n02) ◽  
pp. 1950003
Author(s):  
Fábio Prataviera ◽  
Gauss M. Cordeiro ◽  
Edwin M. M. Ortega ◽  
Adriano K. Suzuki
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Regression Models ◽  
Empirical Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Standard Normal Distribution ◽  
Model Parameters ◽  
Diagnostic Measures ◽  
Standard Normal

In several applications, the distribution of the data is frequently unimodal, asymmetric or bimodal. The regression models commonly used for applications to data with real support are the normal, skew normal, beta normal and gamma normal, among others. We define a new regression model based on the odd log-logistic geometric normal distribution for modeling asymmetric or bimodal data with support in [Formula: see text], which generalizes some known regression models including the widely known heteroscedastic linear regression. We adopt the maximum likelihood method for estimating the model parameters and define diagnostic measures to detect influential observations. For some parameter settings, sample sizes and different systematic structures, various simulations are performed to verify the adequacy of the estimators of the model parameters. The empirical distribution of the quantile residuals is investigated and compared with the standard normal distribution. We prove empirically the usefulness of the proposed models by means of three applications to real data.

scholarly journals Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality

1990 ◽  
Vol 6 (4) ◽  
pp. 466-479 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Yoon-Jae Whang
Keyword(s):  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Regression Models ◽  
Regression Function ◽  
Curse Of Dimensionality ◽  
Finite Sample ◽  
Squared Error ◽  
Convergence Results ◽  
Additive Regression ◽  
Parametric Regression Models

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 non-parametric 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 that AIR models do circumvent the curse of dimensionality. A lower bound on the rate of convergence of these estimators is shown to depend on the order of the AIR model and the smoothness of the regression function, but not on the dimension of the regressor vector. Series estimators with fixed and data-dependent truncation parameters are considered.

Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications

1993 ◽  
Vol 9 (2) ◽  
pp. 263-282 ◽  
Author(s):  
In Choi
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Confidence Intervals ◽  
Unit Roots ◽  
Small Sample ◽  
Asymptotic Distributions ◽  
Standard Normal Distribution ◽  
Finite Sample ◽  
Standard Normal ◽  
Least Squares Estimates

Using the asymptotic normality of the least-squares estimates for the autoregressive (AR) process with real, positive unit roots and at least one stable root, we consider the asymptotic distributions of the Wald and t ratio tests on AR coefficients. In addition, we propose a method of constructing confidence intervals for the sum of AR coefficients possibly in the presence of a unit root. Using simulation methods, we compare the finite-sample cumulative distributions of the t ratios for individual autoregressive coefficients with those of standard normal distributions, and investigate the finite-sample performance of our confidence intervals and t ratios. Our simulation results show that the t ratios for nonstationary processes converge to a standard normal distribution more slowly than those for stationary processes. Further, the confidence intervals are shown to work reasonably well in moderately large samples, but they display unsatisfactory performance at small sample sizes.

A CONSISTENT NONPARAMETRIC TEST ON SEMIPARAMETRIC SMOOTH COEFFICIENT MODELS WITH INTEGRATED TIME SERIES

2015 ◽  
Vol 32 (4) ◽  
pp. 988-1022 ◽  
Author(s):  
Yiguo Sun ◽  
Zongwu Cai ◽  
Qi Li
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Asymptotic Distributions ◽  
Varying Coefficient Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Smooth Coefficients ◽  
Alternative Hypotheses ◽  
Constant Coefficients ◽  
Integrated Time Series

In this paper, we propose a simple nonparametric test for testing the null hypothesis of constant coefficients against nonparametric smooth coefficients in a semiparametric varying coefficient model with integrated time series. We establish the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Moreover, we derive a central limit theorem for a degenerate second order U-statistic, which contains a mixture of stationary and nonstationary variables and is weighted locally on a stationary variable. This result is of independent interest and useful in other applications. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed test.

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.

scholarly journals On Asymptotic Standard Normality of the Two Sample Pivot

2019 ◽  
Vol 71 (1) ◽  
pp. 49-61
Author(s):  
Rajeshwari Majumdar ◽  
Suman Majumdar
Keyword(s):  
Asymptotic Behavior ◽  
Finite Sample ◽  
Sample Sizes ◽  
Test Statistic ◽  
Random Samples ◽  
Two Samples ◽  
Spherically Symmetric Distribution ◽  
Standard Normal ◽  
Sample Approximation ◽  
Ams Classification

The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test statistic being asymptotically standard normal, which is known to happen if the two samples are independent and the ratio of the sample sizes converges to a finite positive number. This restriction on the asymptotic behavior of the ratio of the sample sizes carries the risk of rendering the asymptotic justification of the finite sample approximation invalid. It turns out that neither the restriction on the asymptotic behavior of the ratio of the sample sizes nor the assumption of cross sample independence is necessary for the pivotal convergence in question to take place. If the joint distribution of the standardized sample means converges to a spherically symmetric distribution, then that distribution must be bivariate standard normal (which can happen without the assumption of cross sample independence), and the aforesaid pivotal convergence holds. AMS Classification: 62E20, 62G20

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