A consistent test for heteroscedasticity in semi-parametric regression with nonparametric variance function based on the kernel method

Lin, Jin-Guan

doi:10.1080/02331888.2010.543464

Cited by 11 publications

(8 citation statements)

References 25 publications

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“…The above theorem is a standard result and it is similar to Theorem 3.1 in Dette [4] and Theorem 1 in Lin and Qu [16], who studied the CT for heteroscedasticity in nonparametric regression and in semiparametric regression, respectively. We can find that the asymptotic distribution of T CT is mainly determined by σ 2 (·) and m 4 (·).…”

Section: Remark 23supporting

confidence: 56%

“…According to Dette [4] and Lin and Qu [16], we can obtain the asymptotic distribution of the statistic T CT defined in Equation (19) and establish consistency of the test, which rejects the hypothesis of homoscedasticity for large values of T CT . The following theorem shows that the statistic T CT defined in Equation (19) is asymptotically normal.…”

Section: Ct Statisticmentioning

confidence: 99%

“…But, with some additional technical difficulties in the asymptotic analysis, we can apply them to construct a test for heteroscedasticity. Similar to Dette [4] and Lin and Qu [16], a modified version of a test statistic introduced by Zheng [27] can be used,…”

Section: Ct Statisticmentioning

confidence: 99%

“…For the linear models, such as Eubank and Thomas [5], Galea et al [10], Cysneiros et al [3], Paula et al [21] and Lin et al [19]. For the nonlinear models, there are Wei et al [24], Dette [4], Lin and Wei [17,18], Galea et al [9], Cao et al [2], Lin and Qu [16] and the references therein.…”

Section: Introductionmentioning

confidence: 96%

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Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data

Lin

Zhao

Wang

2015

Journal of Applied Statistics

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It is important to detect the variance heterogeneity in regression model because efficient inference requires that heteroscedasticity is taken into consideration if it really exists. For the varying-coefficient partially linear regression models, however, the problem of detecting heteroscedasticity has received very little attention. In this paper, we present two classes of tests of heteroscedasticity for varying-coefficient partially linear regression models. The first test statistic is constructed based on the residuals, in which the error term is from a normal distribution. The second one is motivated by the idea that testing heteroscedasticity is equivalent to testing pseudo-residuals for a constant mean. Asymptotic normality is established with different rates corresponding to the null hypothesis of homoscedasticity and the alternative. Some Monte Carlo simulations are conducted to investigate the finite sample performance of the proposed tests. The test methodologies are illustrated with a real data set example.

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Section: Remark 23supporting

confidence: 56%

Section: Ct Statisticmentioning

confidence: 99%

Section: Ct Statisticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data

Lin

Zhao

Wang

2015

Journal of Applied Statistics

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“…The approach in Dette (2002) was extended to the case of a partially linear regression by You and Chen (2005) and Lin and Qu (2012). The same idea was also used in Zheng (2009), who proposed a local smoothing test for non-parametric regression, now with multivariate covariates, which is also our scenario.…”

Section: Introductionmentioning

confidence: 99%

Detecting Heteroscedasticity in Non-Parametric Regression Using Weighted Empirical Processes

Chown

Müller

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Heteroscedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroscedasticity for the non‐parametric regression model with multiple covariates. It is based on a suitable residual‐based empirical distribution function. The residuals are constructed by using local polynomial smoothing. Our test statistic involves a ‘detection function’ that can verify heteroscedasticity by exploiting just the independence–dependence structure between the detection function and model errors, i.e. we do not require a specific model of the variance function. The procedure is asymptotically distribution free: inferences made from it do not depend on unknown parameters. It is consistent at the parametric (root n) rate of convergence. Our results are extended to the case of missing responses and illustrated with simulations.

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Rank tests in heteroscedastic linear model with nuisance parameters

Jurečková

Navrátil

2013

Metrika

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A consistent test for heteroscedasticity in semi-parametric regression with nonparametric variance function based on the kernel method

Cited by 11 publications

References 25 publications

Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data

Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data

Detecting Heteroscedasticity in Non-Parametric Regression Using Weighted Empirical Processes

Rank tests in heteroscedastic linear model with nuisance parameters

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