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Biometrika 1998 85(1):229-233; doi:10.1093/biomet/85.1.229
© 1998 by Biometrika Trust
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MISCELLANEA

Score tests for heteroscedasticity in wavelet regression

ZONGW CAI, CLIFFORD M. HURVICH and CHIH-LING TSAI

Department of Mathematics, Southwest Missouri State University Springfield, Missouri 65804, U.S.A. zoc429f{at}cnas.smsu.edu
Department of Statistics and Operations Research, New York University New York, New York 10012, U.S.A. churvich{at}stern.nyu.edu
Graduate School of Management, University of California Davis, California 95616, U.S.A. cltsai{at}ucdavis.edu

We consider two score tests for heteroscedasticity in the errors of a signal-plus-noise model, where the signal is estimated by wavelet thresholding methods. The error variances are assumed to depend on observed covariates, through a parametric relationship of known form. The tests are based on the approaches of Breusch & Pagan (1979) and Koenker (1981). We establish the asymp totic validity of the tests and examine their performance in a simulation study. The Koenker test is found to perform well, in terms of both size and power.

Key Words: De-noising • Signal extraction • Thersholding


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