An Analog of the Bickel–Rosenblatt Test for Error Density in the Linear Regression Model

Fuxia Cheng (), Hira L. Koul (), Nao Mimoto () and Narayana Balakrishna ()
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Fuxia Cheng: Illinois State University
Hira L. Koul: Michigan State University
Nao Mimoto: The University of Akron
Narayana Balakrishna: Cochin University of Science and Technology

Chapter Chapter 11 in Research Papers in Statistical Inference for Time Series and Related Models, 2023, pp 291-323 from Springer

Abstract: Abstract This paper addresses the problem of testing the goodness-of-fit hypothesis pertaining to error density in multiple linear regression models with non-random and random predictors. The proposed tests are based on the integrated square difference between a nonparametric density estimator based on the residuals and its expected value under the null hypothesis when all regression parameters are known. We derive the asymptotic distributions of this sequence of test statistics under the null hypothesis and under certain global alternatives. The asymptotic null distribution of a suitably standardized test statistic based on the residuals is the same as in the case of known underlying regression parameters. Under the global $$L_2$$ L 2 alternatives of [2], the asymptotic distribution of this sequence of statistics is affected by not knowing the parameters and, in general, is different from the one obtained in [2] for the zero intercept linear autoregressive time series context.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-0803-5_11

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DOI: 10.1007/978-981-99-0803-5_11

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