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Some asymptotic results for robust procedures for testing the constancy of regression models over time. (English) Zbl 0722.62024
For \(X_ 1,...,X_ n\) independent random variables, where \(X_ i\) is distributed according to \(F(x-c'_ i\theta_ i)\), with \(c_ i\) known regression p-vectors and \(\theta_ i\) unknown vector parameters, the problem of robust testing \(H_ 0:\theta_ 1=...=\theta_ n\) against \(H_ 1:\theta_ 1=...=\theta_ m\neq \theta_{m+1}=...=\theta_ n\) is considered. A recursive M-procedure used for the testing problem is based on a normalization of \[ \max_{p<k\leq n}\{k^{-1/2} | \sum^{k}_{j=p+1}\Psi [x_ i-c'_ i\theta_{i-1}(\Psi)]| \}, \] where \(\Psi\) is a score function and \(\theta_{i-1}(.)\) is the M- estimator based on \(X_ 1,...,X_{i-1}\). The author studies the asymptotics of the above statistics under the null hypotheses.

62F35 Robustness and adaptive procedures (parametric inference)
62F05 Asymptotic properties of parametric tests
62E20 Asymptotic distribution theory in statistics
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