scholarly journals A FLEXIBLE NONPARAMETRIC TEST FOR CONDITIONAL INDEPENDENCE

2015 ◽  
Vol 32 (6) ◽  
pp. 1434-1482 ◽  
Author(s):  
Meng Huang ◽  
Yixiao Sun ◽  
Halbert White
Keyword(s):  
Conditional Independence ◽  
Kernel Smoothing ◽  
Nonparametric Test ◽  
Nuisance Parameters ◽  
Local Power ◽  
Test Statistic ◽  
Conditional Moment ◽  
Finite Samples ◽  
Monte Carlo Experiments ◽  
Logistic Functions

This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n−1/2 local power. The test statistic is based on an estimator of the topological “distance” between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the exponential or logistic functions, which are indexed by nuisance parameters. The use of GCR functions makes the test able to detect any deviation from the null. We use a kernel smoothing method when estimating the distance. An integrated conditional moment (ICM) test statistic based on these estimates is obtained by integrating out the nuisance parameters. We simulate the critical values using a conditional simulation approach. Monte Carlo experiments show that the test performs well in finite samples. As an application, we test an implication of the key assumption of unconfoundedness in the context of estimating the returns to schooling.

scholarly journals A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE

2008 ◽  
Vol 24 (4) ◽  
pp. 829-864 ◽  
Author(s):  
Liangjun Su ◽  
Halbert White
Keyword(s):  
Monte Carlo Simulation ◽  
Exchange Rates ◽  
Conditional Independence ◽  
Nonparametric Test ◽  
Delta Method ◽  
Mixing Conditions ◽  
Test Statistic ◽  
Finite Samples ◽  
Functional Delta Method ◽  
Simulation Results

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f(y|x,z) and f(y|x), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n−1/2h−d/4. The cases for which not all random variables of interest are continuously valued or observable are also discussed. Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes. We apply our procedure to test for Granger noncausality in exchange rates.

On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity

1994 ◽  
Vol 10 (1) ◽  
pp. 70-90 ◽  
Author(s):  
R.M. de Jong ◽  
H.J. Bierens
Keyword(s):  
Infinite Number ◽  
Fixed Number ◽  
Model Specification ◽  
Test Statistic ◽  
Conditional Moment ◽  
Chi Square ◽  
Moment Conditions ◽  
Conditional Moments ◽  
Finite Samples ◽  
Consistent Model

In this paper, a consistent model specification test is proposed. Some consistent model specification tests have been discussed in econometrics literature. Those tests are consistent by randomization, display a discontinuity in sample size, or have an asymptotic distribution that depends on the data-generating process and on the model, whereas our test does not have one of those disadvantages. Our test can be viewed upon as a conditional moment test as proposed by Newey but instead of a fixed number of conditional moments, an asymptotically infinite number of moment conditions is employed. The use of an asymptotically infinite number of conditional moments will make it possible to obtain a consistent test. Computation of the test statistic is particularly simple, since in finite samples our statistic is equivalent to a chi-square conditional moment test of a finite number of conditional moments.

A TEST OF AUTOCORRELATION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM

1998 ◽  
Vol 14 (1) ◽  
pp. 87-122 ◽  
Author(s):  
Yoon-Jae Whang
Keyword(s):  
Nonlinear Regression Model ◽  
Local Power ◽  
Kernel Estimate ◽  
Finite Sample ◽  
Test Statistic ◽  
Chi Square ◽  
Monte Carlo Experiments ◽  
Consistency Results ◽  
Unknown Form ◽  
Nonparametric Kernel

This paper develops a test of autocorrelation in the presence of heteroskedasticity of unknown form in the nonlinear regression model. The test statistic is based on the sample autocovariance of the residuals standardized by a nonparametric kernel estimate of the unknown heteroskedasticity function. Under appropriate conditions, the test statistic is shown to have a limiting chi-square distribution. Local power and consistency results for the test are also established. Monte Carlo experiments show that the test has reasonable size performance and generally dominates some of the existing tests in terms of finite-sample power.

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.

A boundary crossing probability for the Bessel process

1998 ◽  
Vol 30 (3) ◽  
pp. 807-830 ◽  
Author(s):  
Rebecca A. Betensky
Keyword(s):  
Nonparametric Test ◽  
Bessel Process ◽  
Boundary Crossing ◽  
Test Statistic ◽  
Boundary Crossing Probability ◽  
Significance Level ◽  
Straight Line ◽  
Crossing Probability ◽  
Nonparametric Test Statistic ◽  
First Crossing Time

Analytic approximations are derived for the distribution of the first crossing time of a straight-line boundary by a d-dimensional Bessel process and its discrete time analogue. The main ingredient for the approximations is the conditional probability that the process crossed the boundary before time m, given its location beneath the boundary at time m. The boundary crossing probability is of interest as the significance level and power of a sequential test comparing d+1 treatments using an O'Brien-Fleming (1979) stopping boundary (see Betensky 1996). Also, it is shown by DeLong (1980) to be the limiting distribution of a nonparametric test statistic for multiple regression. The approximations are compared with exact values from the literature and with values from a Monte Carlo simulation.

Use of composite outcomes to assess risk–benefit in clinical trials

2018 ◽  
Vol 15 (4) ◽  
pp. 352-358 ◽  
Author(s):  
Pamela A Shaw
Keyword(s):  
Clinical Success ◽  
Clinical Status ◽  
Data Safety Monitoring Board ◽  
Nuisance Parameters ◽  
Decision Tool ◽  
Test Statistic ◽  
Treatment Groups ◽  
Novel Treatment ◽  
Composite Outcomes ◽  
Net Clinical Benefit

Before a novel treatment can be deemed a clinical success, an assessment of its risk–benefit profile must be made. One of the inherent challenges for this assessment comes from the multiplicity that arises from comparing treatment groups across multiple outcomes. Composite outcomes that summarize a patient’s clinical status, or severity, across a prioritized list of safety and efficacy outcomes have become increasing popular. In this article, we review these approaches and illustrate through examples some of the challenges and complexities of a composite derived from prioritized outcomes, such as the win ratio. These challenges include the difficult tension between the analytical validity that comes from choosing a pre-specified outcome and an evaluation that is responsive to unexpected safety events that arise during the course of a trial. Other challenges include a sensitivity of the resulting test statistic to the underlying censoring distribution and other nuisance parameters. Approaches that resolve some of the difficulties of the analytical challenges associated with prioritized outcomes are then discussed. Ultimately, a composite outcome of net clinical benefit is another decision tool, but one to be used alongside more traditional analyses of efficacy and safety, and with the broader perspective that investigators, the data safety monitoring board, and regulators bring to an evaluation of risk–benefit.

Factor-augmented forecasting regressions with threshold effects

2021 ◽  
Author(s):  
Yayi Yan ◽  
Tingting Cheng
Keyword(s):  
Likelihood Ratio Statistic ◽  
Estimation Method ◽  
Wald Test ◽  
Threshold Effects ◽  
Threshold Parameter ◽  
Test Statistic ◽  
Stock Market Returns ◽  
Testing Procedures ◽  
Finite Samples ◽  
Regression Parameters

Abstract This paper introduces a factor-augmented forecasting regression model in the presence of threshold effects. We consider least squares estimation of the regression parameters, and establish asymptotic theories for estimators of both slope coefficients and the threshold parameter. Prediction intervals are also constructed for factor-augmented forecasts. Moreover, we develop a likelihood ratio statistic for tests on the threshold parameter and a sup-Wald test statistic for tests on the presence of threshold effects, respectively. Simulation results show that the proposed estimation method and testing procedures work very well in finite samples. Finally, we demonstrate the usefulness of the proposed model through an application to forecasting stock market returns.

scholarly journals A robust method for shift detection in time series

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 647-660
Author(s):  
H Dehling ◽  
R Fried ◽  
M Wendler
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Test Statistic ◽  
Moment Conditions ◽  
Limit Theory ◽  
Dependent Observations ◽  
U Statistics ◽  
Shift Detection ◽  
Heavy Tailed ◽  
The Stability

Summary We present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges–Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.

scholarly journals EXPLOITING INFINITE VARIANCE THROUGH DUMMY VARIABLES IN NONSTATIONARY AUTOREGRESSIONS

2013 ◽  
Vol 29 (6) ◽  
pp. 1162-1195 ◽  
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Unit Root ◽  
Asymptotic Properties ◽  
Ordinary Least Squares ◽  
Infinite Variance ◽  
Local Power ◽  
Test Statistic ◽  
Asymptotically Normal ◽  
Normal Test ◽  
Order Of Magnitude ◽  
Near Unit Root

We consider estimation and testing in finite-order autoregressive models with a (near) unit root and infinite-variance innovations. We study the asymptotic properties of estimators obtained by dummying out “large” innovations, i.e., those exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterative versions of the dummy-variable estimator are also discussed. We provide conditions on the preliminary parameter estimator and on the threshold that ensure that (i) the dummy-based estimator is consistent at higher rates than the ordinary least squares estimator, (ii) an asymptotically normal test statistic for the unit root hypothesis can be derived, and (iii) order of magnitude gains of local power are obtained.

scholarly journals AN ADAPTIVE TEST OF STOCHASTIC MONOTONICITY

2020 ◽  
pp. 1-42
Author(s):  
Denis Chetverikov ◽  
Daniel Wilhelm ◽  
Dongwoo Kim
Keyword(s):  
Monte Carlo ◽  
Conditional Distribution ◽  
Asymptotic Properties ◽  
Nonparametric Test ◽  
Critical Value ◽  
Data Driven ◽  
Local Alternatives ◽  
Stochastic Monotonicity ◽  
Adaptive Test ◽  
Finite Samples

We propose a new nonparametric test of stochastic monotonicity which adapts to the unknown smoothness of the conditional distribution of interest, possesses desirable asymptotic properties, is conceptually easy to implement, and computationally attractive. In particular, we show that the test asymptotically controls size at a polynomial rate, is nonconservative, and detects certain smooth local alternatives that converge to the null with the fastest possible rate. Our test is based on a data-driven bandwidth value and the critical value for the test takes this randomness into account. Monte Carlo simulations indicate that the test performs well in finite samples. In particular, the simulations show that the test controls size and, under some alternatives, is significantly more powerful than existing procedures.

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