Bootstrap of residual processes in regression: to smooth or not to smooth?

Neumeyer, Natalie; Keilegom, Ingrid Van

doi:10.1093/biomet/asz009

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…, n}, N is an independently drawn mean-zero random variable and the value ν controls the smoothing. Recently, Neumeyer and Van Keilegom (2017) proved that the smoothed (ν > 0) and the non-smoothed (ν = 0) versions of this kind of bootstrap are asymptotically equivalent. Unreported simulations showed that a better level approximation for the test in DNV is obtained for the non-smoothed case, therefore only the case ν = 0 will be shown in the tables below.…”

Section: Numerical Resultsmentioning

confidence: 99%

A model specification test for the variance function in nonparametric regression

Pardo–Fernández

Jiménez-Gamero

2018

AStA Adv Stat Anal

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The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted L 2 -distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The null asymptotic distribution of the test statistic is obtained and employed to approximate the critical values. Finite sample properties of the proposed test are numerically investigated in several Monte Carlo experiments. The developed results assume independent data. Their extension to dependent observations is also discussed.is the conditional variance function and ε is the regression error, which is assumed to be independent of X. Note that, by construction, E(ε) = 0 and V ar(ε)=1. The covariate X is one-dimensional and continuous with probability density function (pdf) f and compact support R. The pdf f is assumed to be positive on R. The regression function, the variance function, the distribution of the error and the distribution of the covariate are unknown and no parametric models are assumed for them.Parametric specifications for either the regression function or the variance function are quite attractive among practitioners since they describe the relation between the response and the covariate in a concise way. Because of this reason, there are a number of papers dealing with the parametric modelling of the conditional mean and the conditional variance of Y , given X. This paper proposes a new goodness-of-fit test for the parametric form of the conditional variance. Specifically, on the basis of independent observations from (1), we wish to test the null hypothesiswhere σ 2 (·; θ) represents a parametric model for the conditional variance function, against the general alternative H 1 : H 0 is not true.Several tests for H 0 have been proposed in the specialised literature. Some of them were designed for testing homoscedasticity (see, for example, Liero, 2003, Dette andMarchlewski, 2010); others assume that the regression function has a known parametric form (see, for example, Koul and Song, 2010, Samarakoon and Song, 2011, 2012; others were built for fixed design points (see, for example, Dette and Hetzler, 2009a,b); others detect contiguous alternatives converging to the null at a rate slower that n −1/2 (see, for example, Wang and Zhou, 2007, Samarakoon and Song, 2011, 2012. Although initially the test in Koul and Song (2010) was designed for parametric regression functions, they also provide the theory for a version where the mean function is nonparametrically estimated.The test in Dette et al. (2007) (henceforth DNV) does not possess any of the above cited cons. The methodology that will be proposed in the present paper is, in a certain sense, close to that in DNV. Next, we describe our proposal and the precise meaning of such closeness. Let ε = {Y − m(X)}/σ(X) be the regression error and let ε 0 = {Y − m(X)}/σ(X; θ)

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Section: Numerical Resultsmentioning

confidence: 99%

A model specification test for the variance function in nonparametric regression

Pardo–Fernández

Jiménez-Gamero

2018

AStA Adv Stat Anal

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Tests for validity of the semiparametric heteroskedastic transformation model

Hušková

Meintanis

Pretorius

2020

Computational Statistics & Data Analysis

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There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional transformation on the response variable. Specifically we consider testing for independence between the regressors and the errors in a model where the transformed response is just a location/scale shift of the error. Our criteria use the familiar factorization property of the joint characteristic function of the covariates under independence. The difficulty is that the errors are unobserved and hence one needs to employ properly estimated residuals in their place. We study the limit distribution of the test statistics under the null hypothesis as well as under alternatives, and also suggest a resampling procedure in order to approximate the critical values of the tests. This resampling is subsequently employed in a series of Monte Carlo experiments that illustrate the finite-sample properties of the new test. We also investigate the performance of related test statistics for normality and symmetry of errors, and apply our methods on real data sets.

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Are Unobservables Separable?

Babii,

Florens

2024

Econom. Theory

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It is common to assume in empirical research that observables and unobservables are additively separable, especially when the former are endogenous. This is because it is widely recognized that identification and estimation challenges arise when interactions between the two are allowed for. Starting from a nonseparable IV model, where the instrumental variable is independent of unobservables, we develop a novel nonparametric test of separability of unobservables. The large-sample distribution of the test statistics is nonstandard and relies on a Donsker-type central limit theorem for the empirical distribution of nonparametric IV residuals, which may be of independent interest. Using a dataset drawn from the 2015 U.S. Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for some commodities.

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Bootstrap of residual processes in regression: to smooth or not to smooth?

Cited by 4 publications

References 33 publications

A model specification test for the variance function in nonparametric regression

A model specification test for the variance function in nonparametric regression

Tests for validity of the semiparametric heteroskedastic transformation model

Are Unobservables Separable?

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