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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.

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