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期刊名称: Applications of Mathematics
Volume:44    Issue:4        Page:245-270
ISSN:0862-7940

M-estimators of structural parameters in pseudolinear models期刊论文

作者: Liese Friedrich Vajda Igor
DOI:10.1023/A:1023027929079

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页码: 245-270
出版者: Kluwer Academic Publishers-Plenum Publishers,Springer,Springer Nature B.V
期刊名称: Applications of Mathematics
ISSN: 0862-7940
卷期: Volume:44    Issue:4
语言: English
摘要: Real valued M-estimators $$\hat \theta _n : = \min \sum\limits_1^n {\varrho \left( {Y_i - \tau \left(\theta \right)} \right)} $$ in a statistical model 1 with observations $$Y_i \sim F_{{\theta }_0 }$$ are replaced by $$\mathbb{R}^p $$ -valued M-estimators $$\hat \beta _n : = \min \sum\limits_1^n {\varrho \left( {Y_i - \tau \left( {u\left( {z_i^T \beta } \right)} \right)} \right)} $$ in a new model with observations $$Y_i \sim F_{u\left( {z_i^t {\beta }}_{0} \right)}$$ where $$z_i \in \mathbb{R}^p $$ are regressors, $${\beta }_{0} \in \mathbb{R}^p $$ is a structural parameter and $$u:\mathbb{R} \to \mathbb{R}$$ a structural function of the new model. Sufficient conditions for the consistency of $$\hat \beta _n $$ are derived, motivated by the sufficiency conditions for the simpler “parent estimator” $$\hat \theta _n $$ The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If F θ has a natural exponential density eθx−b( x ) then our pseudolinear model with u = (g o μ)−1 reduces to the well known generalized linear model, provided μ(θ) = db(θ)/dθ and g is the so-called link function of the generalized linear model. General results are illustrated for special pairs ϱ and τ leading to some classical M-estimators of mathematical statistics, as well as to a new class of generalized α-quantile estimators.
相关主题: generalized linear models, Fluids, Mathematics, Applications of Mathematics, M -estimator, pseudolinear models, Pseudolinear models, Generalized linear models, M-estimator, Linear models (Statistics), Usage, Analysis, Information theory, Studies, Mathematical models,

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