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題 名 | On the Calibration of Silverman's Test for Multimodality |
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作 者 | Hall,Peter; York,Matthew; | 書刊名 | Statistica Sinica |
卷 期 | 11:2 2001.04[民90.04] |
頁 次 | 頁515-536 |
分類號 | 319.5 |
關鍵詞 | Bandwidth; Bootstrap; Density estimation; Kernel methods; Mode; Monte Carlo methods; Smoothing parameter; |
語 文 | 英文(English) |
英文摘要 | It is known that Silverman's bootstrap test for multimodality tends towards conservatism, even in large samples, in the sense that the actual level tends to be less than the nominal one. In this paper, and in the context of testing for a single mode, we propose a means of calibrating Silverman's test so as to improve its level accuracy. The calibration takes two forms -- first, an asymptotic approach, which involves identifying the limiting distribution of the test statistic and adjusting for its departure from a hypothetical Uniform distribution; and second, a Monte Carlo technique, which enables a degree of correction for second-order effects to be incorporated. As an aid to applying Silverman's test to contexts rather different from those he envisaged, for example to the case of testing for the number of modes of a density in a compact interval, we show that the modes of the density estimator remain separated as the bandwidth is decreased, at least until a point is reached where the first three derivatives of the estimator vanish simultaneously. Theoretical and numerical properties of alternative forms of Silverman's test are addressed. |
本系統中英文摘要資訊取自各篇刊載內容。