An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models

Wang, Lan; Akritas, Michaël G.; Keilegom, Ingrid Van

doi:10.1080/10485250802066112

Cited by 32 publications

(46 citation statements)

References 23 publications

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“…It has been observed in the literature that the effect of the choice of m has little influence on the performance of high‐dimensional ANOVA‐type tests (Wang, Akritas, & Van Keilegom, ; Zambom & Akritas, ; Kim & Zambom, ) as long as the value of m is neither too small nor too large. Choosing a very small m , such as

m < 5

, yields liberal levels; conversely, choosing large values of m yields conservative levels.…”

Section: The Test Statistic and Some Asymptotic Resultsmentioning

confidence: 99%

A nonparametric hypothesis test for heteroscedasticity in multiple regression

Zambom

Kim

2017

Can J Statistics

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This article presents a new method to test for heteroscedasticity in a general multiple nonparametric regression model. The test statistic is based on a high‐dimensional one‐way ANOVA constructed with the absolute value of the residuals, and its asymptotic distribution is derived under the null hypothesis of homoscedasticity and local alternative. The properties of the proposed test statistic are preserved when a correctly specified parametric mean function is used to obtain the residuals. Unlike most methods in the literature no parametric form is required for the multivariate variance function. Extensive simulations suggest that the proposed test detects heteroscedasticity in all models considered while classical methods fail in some cases. Two real data applications are examined. The Canadian Journal of Statistics 45: 425–441; 2017 © 2017 Statistical Society of Canada

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m < 5

, yields liberal levels; conversely, choosing large values of m yields conservative levels.…”

Section: The Test Statistic and Some Asymptotic Resultsmentioning

confidence: 99%

A nonparametric hypothesis test for heteroscedasticity in multiple regression

Zambom

Kim

2017

Can J Statistics

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“…() to ( and , whereas Wang and Van Keilegom () and Wang et al. () consider the cases for noise ε t following either a finite autoregressive model with a known order p or being unconditionally heteroscedastic. The key idea of the proposed local regression procedure for trend detection consists of the following three steps: Suppose that there exists no prior information on whether noise ε i satisfies or .…”

Section: Testing For Parametric Trendsmentioning

confidence: 99%

“…Hence, the trend test statistic (named WAVK after the first letters of authors' surnames who first proposed the procedure, that is, Wang et al , ) takes the form

WAVK MathClass-rel= F_{n} MathClass-rel= \frac{MST}{MSE} MathClass-rel= \frac{k_{n}}{n MathClass-bin- 1} {MathClass-op\sum}_{i MathClass-rel= 1}^{n} {((), {\overset{V}{true}}_{i.} MathClass-bin- {\overset{V}{true}}_{..})}^{2} 1.61em / \frac{1}{n (k_{n} MathClass-bin- 1)} {MathClass-op\sum}_{i MathClass-rel= 1}^{n} {MathClass-op\sum}_{j MathClass-rel= 1}^{k_{n}} {((), V_{i MathClass-punc, j} MathClass-bin- {\overset{V}{true}}_{i.})}^{2}

where

V_{i 1} MathClass-punc, MathClass-op\dots MathClass-punc, V_{i k_{n}}

denote the k n pre‐filtered observations in the I th group, that is,

{V_{i 1} MathClass-punc, MathClass-op\dots MathClass-punc, V_{i k_{n}}} MathClass-rel= {Z_{j} MathClass-punc: j MathClass-rel\in W_{i}}

{\overset{V}{true}}_{i.}

and

{\overset{V}{true}}_{..}

are the mean of the I th group and grand mean, respectively. In turn, treatment sum of squares

(MST) MathClass-rel= k_{n}

…”

Section: Testing For Parametric Trendsmentioning

confidence: 99%

“…In this paper, we extend the flexible local regression method of Wang and Van Keilegom () and Wang et al. () to a more general case of linear time series that do not degenerate to a finite‐dimensional representation and conditionally heteroscedastic processes. In contrast to the methodology of Wang and Van Keilegom () and Wang et al.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to the methodology of Wang and Van Keilegom () and Wang et al. (), we impose no conditions on a prior knowledge of the underlying process, that is, we perform trend testing under the assumption that neither dependence structure nor order of the hypothesized model for the observed environmental data are known, which is the typical situation in the vast majority of environmental studies. Moreover, to improve finite‐sample performance of the trend test, we propose to employ a computationally efficient and robust hybrid of sieve and parametric resampling schemes, following the recent results of Kreiss et al.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On detecting non‐monotonic trends in environmental time series: a fusion of local regression and bootstrap

2013

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In this paper, we propose a new testing procedure for detecting smooth (non)monotonic trends embedded into a linear noise that possibly does not degenerate to a finite‐dimensional representation or into a conditionally heteroscedastic (autoregressive conditionally heteroscedastic/generalized autoregressive conditionally heteroscedastic (ARCH/GARCH)) noise. The proposed nonparametric trend test is local regression‐based, and we develop a flexible and computationally efficient hybrid bootstrap procedure to approximate its finite sample behavior. Because the proposed trend test does not assume prior knowledge on the dependence structure and probability distribution of the observed process, the new testing procedure is fully data‐driven and robust to misspecification of dependence structure and distributional assumptions, which is of particular importance for noisy environmental measurements. Moreover, because the proposed methodology allows to test for monotonic versus non‐monotonic trends and hence, to assess existence of extremums in the hypothesized trend function, the developed approach may be also employed for preliminary detection of regime shifts and change points in the observed environmental data series. Our simulation studies indicate competitive performance of the proposed nonparametric procedure for detection of (non)monotonic trends against conventional trend tests. Copyright © 2013 John Wiley & Sons, Ltd.

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A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects

2010

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In this paper, we present a test of independence between the response variable, which can be discrete or continuous, and a continuous covariate after adjusting for heteroscedastic treatment effects. The method involves first augmenting each pair of the data for all treatments with a fixed number of nearest neighbours as pseudo‐replicates. Then a test statistic is constructed by taking the difference of two quadratic forms. The statistic is equivalent to the average lagged correlations between the response and nearest neighbour local estimates of the conditional mean of response given the covariate for each treatment group. This approach effectively eliminates the need to estimate the nonlinear regression function. The asymptotic distribution of the proposed test statistic is obtained under the null and local alternatives. Although using a fixed number of nearest neighbours pose significant difficulty in the inference compared to that allowing the number of nearest neighbours to go to infinity, the parametric standardizing rate for our test statistics is obtained. Numerical studies show that the new test procedure has robust power to detect nonlinear dependency in the presence of outliers that might result from highly skewed distributions. The Canadian Journal of Statistics 38: 408–433; 2010 © 2010 Statistical Society of Canada

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An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models

Cited by 32 publications

References 23 publications

A nonparametric hypothesis test for heteroscedasticity in multiple regression

A nonparametric hypothesis test for heteroscedasticity in multiple regression

On detecting non‐monotonic trends in environmental time series: a fusion of local regression and bootstrap

A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects

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