High-dimensional Newey-Powell Test via Approximate Message Passing
Statistics Seminar
18th October 2024, 1:00 pm – 2:00 pm
Fry Building, 2.04
In numerous high-dimensional regression models and theories, the assumption of homoscedastic regression error is commonly made. Despite the prevalence of heteroscedastic errors in real-world datasets, exploring heteroscedasticity testing in high-dimensional settings has yet to be addressed.
In this project, we focus on adapting the heteroscedasticity test introduced by Newey and Powell (1987) for low-dimensional settings to high-dimensional data. The proposed test aims to identify variables that are correlated with regression error, which hinders fitting and further constructing instrumental variables.The asymptotic theory for the Newey-Powell test has been well-established for low dimensions, but we extend its applicability to cases where the number of dimensions grows linearly with the sample size. The asymptotic analysis for the test statistic utilizes the Approximate Message Passing (AMP) algorithm, from which we obtain the limiting distribution of the test.
The numerical performance of the test is investigated by an extensive simulation study and two real datasets.
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