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Adaptive tests of regression functions via multiscale generalized likelihood ratios
Author(s) -
Zhang Chunming M.
Publication year - 2003
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316065
Subject(s) - smoothing , nonparametric statistics , mathematics , score test , likelihood ratio test , computer science , component (thermodynamics) , set (abstract data type) , nonparametric regression , simple (philosophy) , mathematical optimization , statistics , algorithm , philosophy , physics , epistemology , thermodynamics , programming language
Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.