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• W2049998781 abstract "ABSTRACT: We introduce a class of Toeplitz-band matrices for simple goodness of fit tests for parametric regression models. For a given length r of the band matrix the asymptotic optimal solution is derived. Asymptotic normality of the corresponding test statistic is established under a fixed and random design assumption as well as for linear and non-linear models, respectively. This allows testing at any parametric assumption as well as the computation of confidence intervals for a quadratic measure of discrepancy between the parametric model and the true signal g;. Furthermore, the connection between testing the parametric goodness of fit and estimating the error variance is highlighted. As a by-product we obtain a much simpler proof of a result of 34) concerning the optimality of an estimator for the variance. Our results unify and generalize recent results by 9) and 15,16) in several directions. Extensions to multivariate predictors and unbounded signals are discussed. A simulation study shows that a simple jacknife correction of the proposed test statistics leads to reasonable finite sample approximations." @default.
• W2049998781 created "2016-06-24" @default.
• W2049998781 creator A5087767807 @default.
• W2049998781 date "2002-09-01" @default.
• W2049998781 modified "2023-10-03" @default.
• W2049998781 title "Testing the Goodness of Fit of Parametric Regression Models with Random Toeplitz Forms" @default.
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• W2049998781 doi "https://doi.org/10.1111/1467-9469.00303" @default.
• W2049998781 hasPublicationYear "2002" @default.
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