| Abstract: | Testing the heteroscedasticity of the errors is a traditional and important problem for linear regressions. There are in the literature several well- established procedures for this problem such as the White test and the Breusch-Pagan test. However, in a high-dimensional scenario where the number of covariates p is large compared to the sample size n, these procedures become severely biased. In this paper, we propose two new test statistics to detect the existence of heteroscedasticity. The asymptotic normality of both statistics is obtained under the assumption that the degree of freedom k = n − p tends to infinity. This encompasses in particular two popular settings (i) the classical low-dimensional setting where the number of variables p is fixed while the sample size n tends to infinity; (ii) the proportional high-dimensional setting where p and n grow to infinity proportionally such that p/n → c ∈ (0,1). This dimension-proof property of the new test procedures guarantees a wide applicability of the proposed procedures to different combinations of the pair (p, n). Extensive Monte-Carlo experiments demonstrate the superiority of our proposed tests over popular existing methods in terms of size and power. The good performance of our tests is also confirmed by several real data analyses. |
| Date: | 25 February 2016 |
| Time: | 11:00am - 12:00noon |
| Speaker: | Ms Zhaoyuan LI |
| Venue: | Room 14-221, 14/F, Academic 3 |
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