Asymptotic results for parametric estimation in inadequate two phases regression models

Benzekri, S; Brodeau, F.

doi:10.1080/02331889108802316

Cited by 2 publications

(3 citation statements)

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“…Observe ®nally, that this implies also the treatment of regression models with a ®nite number of singularities of the signal provided one of the growth conditions in de®nition 2 are satis®ed (cf. Benzekri & Brodeau (1991) for applications).…”

Section: Several Remarks and Extensionsmentioning

confidence: 99%

“…This allows avoidance of several technical assumptions, such as the assumption of fourth moments of the error t as it was required by Bunke & Schmidt (1980) or Zwanzig (1980) who assumed in addition to a modi®ed Lindeberg condition that lim n3I n t1 t À2 E 4 t < I in order to guarantee the applicability of Kolmogoro's SLLN for the strong consistency of the LSE. Benzekri & Brodeau (1991) treated the case of non-smooth signals g whereas Wu (1981), LaÈ uter (1989 and Richardson & Battacharya (1986) considered non-compact parameter spaces H. The case of random predictors was investigated by Hausman (1978) and White (1981) where the strong consistency is proved by a modi®cation of Mickey's theorem as given in Jennrich (1969). All these approaches, however, do not cover triangular schemes of the error distribution as in (3).…”

Section: Scand J Statist 29mentioning

confidence: 99%

“…Y i À f h t i 2 can be utilized in principle to detect deviations from U k in any non-parametric direction, see Schmidt (1979), Bunke & Schmidt (1980), Zwanzig (1980), Bunke (1981), White (1980White ( , 1981, Benzekri & Brodeau (1991). Tests which are directly based on the LSE, however, require knowledge of the variance r 2 t of et or of the ÔÔbest ®tting'' parameter random design assumption (Dette & Munk, 1998b) in the case of linear regression models.…”

Section: Introductionmentioning

confidence: 99%

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Testing the Goodness of Fit of Parametric Regression Models with Random Toeplitz Forms

Munk

2002

Scandinavian J Statistics

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We introduce a class of Toeplitz-band matrices for simple goodness of ®t 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 ®xed 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 con®dence 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 ®t and estimating the error variance is highlighted. As a by-product we obtain a much simpler proof of a result of concerning the optimality of an estimator for the variance. Our results unify and generalize recent results by Brodeau (1993) and Dette & Munk (1998a,b) 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 ®nite sample approximations.

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Section: Several Remarks and Extensionsmentioning

confidence: 99%