Nonparametric Goodness-of-fit Test for Heteroscedastic Regression Models
نویسندگان
چکیده
For the heteroscedastic nonparametric regression model Yni = m(xni)+σ(xni)2ni, i = 1, ..., n, a novel method is proposed for testing that the regression function m is constant. The test statistic is motivated by recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large. Its asymptotic normality is derived under the null hypothesis and suitable local alternatives. A key merit of this approach is its practicality. The similarity of the form of the test statistic to that of the classical F -statistic in regression with replicated observations allows easy and fast calculation. Recently, some adaptive, rate-optimal tests were proposed, including Fan and Huang (2001), Horowitz and Spokoiny (2001), among others. The critical values of these tests have to be obtained through resampling. Simulation studies reveal that the new test using critical values from the derived asymptotic normal distribution is very accurate in finite sample size, and surprisingly, the power is quite competitive with these optimal tests.
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