"A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test"

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We establish a joint central limit theorem for sums of squares and the fourth powers of residuals in a high-dimensional regression model. We then apply this CLT to detect the… Click to show full abstract

We establish a joint central limit theorem for sums of squares and the fourth powers of residuals in a high-dimensional regression model. We then apply this CLT to detect the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size n tends to infinity and the number of covariates p may be fixed or tend to infinity.

Keywords: high dimensional; regression; theorem sums; residuals high; central limit; limit theorem

Journal Title: TEST
Year Published: 2018

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