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Minimum distance estimations in a switching regression model. (English) Zbl 0728.62065

Summary: We propose minimum distance estimators of parameters in a switching regression model under parametric error distributions with Cramér-von Mises type discrepancy. The main results of the proposed minimum distance estimator \({\hat \eta}=({\hat \beta}_ 1,{\hat \beta}_ 2,\hat p,{\hat \theta}_ 1,{\hat \theta}_ 2)\) of \(\eta =(\beta_ 1,\beta_ 2,p,\theta_ 1,\theta_ 2)\) show that (i) \({\hat \eta}\) is a strongly consistent estimator of \(\eta\), (ii) the limiting distribution of \(\sqrt{n}({\hat \eta}-\eta)\) is 5-variate normal.

MSC:

62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
62F12 Asymptotic properties of parametric estimators
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