تقرير
Consistency of M estimates for separable nonlinear regression models
| العنوان: | Consistency of M estimates for separable nonlinear regression models |
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| المؤلفون: | Victoria, Fasano María, Maronna, Ricardo A. |
| سنة النشر: | 2012 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory |
| الوصف: | Consider a nonlinear regression model : y_{i}=g(x_{i},{\theta})+e_{i}, i=1,...,n, where the x_{i} are random predictors x_{i} and {\theta} is the unknown parameter vector ranging in a set {\Theta}\subsetR^{p}. All known results on the consistency of the least squares estimator and in general of M estimators assume that either {\Theta} is compact or g is bounded, which excludes frequently employed models such as the Michaelis-Menten, logistic growth and exponential decay models. In this article we deal with the so-called separable models, where p=p_{1}+p_{2}, {\theta}=({\alpha},{\beta}) with {\alpha}\inA\subsetR^{p_{1}}, {\beta}\inB\subsetR^{p_{2},}and g has the form g(x,{\theta})={\beta}^{T}h(x,{\alpha}) where h is a function with values in R^{p_{2}}. We prove the strong consistency of M estimators under very general assumptions, assuming that h is a bounded function of {\alpha}, which includes the three models mentioned above. Key words and phrases: Nonlinear regression, separable models, consistency, robust estimation. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1207.0473 |
| رقم الأكسشن: | edsarx.1207.0473 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |