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Journal of Statistical Theory and Practice

, Volume 3, Issue 3, pp 587–612 | Cite as

Testing for a Constant Coefficient of Variation in Nonparametric Regression

  • Holger DetteEmail author
  • Gabriele Wieczorek
Article

Abstract

In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the L2-distance between the square of the regression function and the variance function. We prove asymptotic normality of a standardized estimate of this distance under the null hypothesis and fixed alternatives. The finite sample properties of a corresponding bootstrap test are investigated by means of a simulation study. The results are applicable to stationary processes with the common mixing conditions and are used to construct tests for ARCH assumptions in financial time series.

Key-words

Stationary processes Multiplicative error structure Generalized nonparametric regression models 

AMS Subject Classification

62G08 62G10 62G20 

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Copyright information

© Grace Scientific Publishing 2009

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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