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.

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

SPATIAL DEPENDENCE IN OPTION OBSERVATION ERRORS

2020 ◽  
pp. 1-43
Author(s):  
Torben G. Andersen ◽  
Nicola Fusari ◽  
Viktor Todorov ◽  
Rasmus T. Varneskov
Keyword(s):  
Spatial Dependence ◽  
Option Price ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Testing Procedure ◽  
Observation Error ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Observation Times ◽  
Index Option

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau test for the null hypothesis of no spatial autocorrelation in the observation error. The test makes use of the smoothness of the true (unobserved) option price as a function of its strike and is robust to the presence of heteroskedasticity of unknown form in the observation error. A Monte Carlo study shows good finite-sample properties of the developed testing procedure and an empirical application to S&P 500 index option data reveals mild spatial dependence in the observation error, which has been declining in recent years.

Local polynomial estimation of a conditional mean function with dependent truncated data

Test ◽  
2011 ◽  
Vol 20 (3) ◽  
pp. 653-677 ◽  
Author(s):  
Han-Ying Liang ◽  
Jacobo de Uña-Álvarez ◽  
María del Carmen Iglesias-Pérez
Keyword(s):  
Truncated Data ◽  
Conditional Mean ◽  
Local Polynomial ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

scholarly journals TESTING A PARAMETRIC TRANSFORMATION MODEL VERSUS A NONPARAMETRIC ALTERNATIVE

2020 ◽  
Vol 36 (5) ◽  
pp. 871-906
Author(s):  
Arkadiusz Szydłowski
Keyword(s):  
Monte Carlo Study ◽  
Transformation Model ◽  
Proportional Hazard ◽  
Finite Sample ◽  
Proportional Hazard Model ◽  
Bootstrap Test ◽  
Finite Dimensional ◽  
Parametric Specification ◽  
Model Versus ◽  
Special Case

Despite an abundance of semiparametric estimators of the transformation model, no procedure has been proposed yet to test the hypothesis that the transformation function belongs to a finite-dimensional parametric family against a nonparametric alternative. In this article, we introduce a bootstrap test based on integrated squared distance between a nonparametric estimator and a parametric null. As a special case, our procedure can be used to test the parametric specification of the integrated baseline hazard in a semiparametric mixed proportional hazard model. We investigate the finite sample performance of our test in a Monte Carlo study. Finally, we apply the proposed test to Kennan’s strike durations data.

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 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.

Variance Component Testing in Multilevel Models

2001 ◽  
Vol 26 (2) ◽  
pp. 133-152 ◽  
Author(s):  
Johannes Berkhof ◽  
Tom A. B. Snijders
Keyword(s):  
Variance Component ◽  
Multilevel Models ◽  
Score Test ◽  
Null Distribution ◽  
Monte Carlo Study ◽  
Test Statistic ◽  
Reference Distribution ◽  
Score Tests ◽  
Asymptotic Normal ◽  
Variance Component Testing

Available variance component tests are reviewed and three new score tests are presented. In the first score test, the asymptotic normal distribution of the test statistic is used as a reference distribution. In the other two score tests, a Satterthwaite approximation is used for the null distribution of the test statistic. We evaluate the performance of the score tests and other available tests by means of a Monte Carlo study. The new tests are computationally relatively cheap and have good power properties.

scholarly journals SPECIFICATION TESTING IN NONPARAMETRIC INSTRUMENTAL QUANTILE REGRESSION

2020 ◽  
Vol 36 (4) ◽  
pp. 583-625 ◽  
Author(s):  
Christoph Breunig
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Monte Carlo Study ◽  
Test Statistics ◽  
Finite Sample ◽  
Test Statistic ◽  
Specification Testing ◽  
Quantile Regression Model ◽  
Endogenous Regressors ◽  
Finite Sample Properties

There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This article develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.

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.

Sign in / Sign up

Export Citation Format

Share Document