A nonparametric hypothesis test for heteroscedasticity in multiple regression

Zambom, Adriano Zanin; Kim, Seon Jin

doi:10.1002/cjs.11333

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…Therefore, test statistics developed for MANOVA with unequal group covariance e.g., [19] could potentially be sensitive for detecting departure from the null hypothesis (2). These ideas of a moving window in a one-way layout were previously used for lack-of-fit test [10,11] and test of homogeneity of variance [12,20] in the univariate setting.…”

Section: Moving Window One-way Layoutmentioning

confidence: 99%

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Nonparametric Tests for Multivariate Association

Harrar

2022

Symmetry

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Testing the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matrix assumptions. Our test is motivated by recent results in MANOVA tests for a large number of groups. Two types of tests are proposed. While it is natural to consider the classical approach for constructing the test by jointly considering all the variables together, we also investigate a composite test where variable-by-variable univariate tests are combined to form a multivariate test. The asymptotic distributions of the test statistics are derived in a unified manner by deriving the asymptotic matrix variate normal distribution of random matrices involved in the construction of the statistics. The tests have good numerical performance in finite samples. The application of the methods is illustrated with gene expression profiling of bronchial airway brushings.

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Section: Moving Window One-way Layoutmentioning

confidence: 99%

“…The second approach is based on the idea of simultaneous inference where multiple univariate tests are combined to construct a composite multivariate test. A somewhat related idea to the latter was implemented in Zambom and Kim [20] to develop lack-of-fit test in univariate multiple regression.…”

Section: Test Statisticsmentioning

confidence: 99%

Nonparametric Tests for Multivariate Association

Harrar

2022

Symmetry

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Detection of marginal heteroscedasticity for partial linear single-index models

Zhang

Gai

Lin

2019

Communications in Statistics - Simulation and Computation

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Iterative Approaches to Handling Heteroscedasticity With Partially Known Error Variances

Marzjarani¹

2019

IJSP

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Heteroscedasticity plays an important role in data analysis. In this article, this issue along with a few different approaches for handling heteroscedasticity are presented. First, an iterative weighted least square (IRLS) and an iterative feasible generalized least square (IFGLS) are deployed and proper weights for reducing heteroscedasticity are determined. Next, a new approach for handling heteroscedasticity is introduced. In this approach, through fitting a multiple linear regression (MLR) model or a general linear model (GLM) to a sufficiently large data set, the data is divided into two parts through the inspection of the residuals based on the results of testing for heteroscedasticity, or via simulations. The first part contains the records where the absolute values of the residuals could be assumed small enough to the point that heteroscedasticity would be ignorable. Under this assumption, the error variances are small and close to their neighboring points. Such error variances could be assumed known (but, not necessarily equal).The second or the remaining portion of the said data is categorized as heteroscedastic. Through real data sets, it is concluded that this approach reduces the number of unusual (such as influential) data points suggested for further inspection and more importantly, it will lowers the root MSE (RMSE) resulting in a more robust set of parameter estimates.

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A nonparametric hypothesis test for heteroscedasticity in multiple regression

Cited by 3 publications

References 27 publications

Nonparametric Tests for Multivariate Association

Nonparametric Tests for Multivariate Association

Detection of marginal heteroscedasticity for partial linear single-index models

Iterative Approaches to Handling Heteroscedasticity With Partially Known Error Variances

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