2015/08/14 by Chris A. J. Klaassen, Klaassen, Chris A. J., Nanang Susyanto +1
Mathematics · #62F10 #62F12 #62F30 #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1508.03416
openalex publication_date 2015/08/14 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28
Consider a quite arbitrary (semi)parametric model with a Euclidean parameter\nof interest and assume that an asymptotically (semi)parametrically efficient\nestimator of it is given. If the parameter of interest is known to lie on a\ngeneral surface (image of a continuously differentiable vector valued\nfunction), we have a submodel in which this constrained Euclidean parameter may\nbe rewritten in terms of a lower-dimensional Euclidean parameter of interest.\nAn estimator of this underlying parameter is constructed based on the original\nestimator, and it is shown to be (semi)parametrically efficient. It is proved\nthat the efficient score function for the underlying parameter is determined by\nthe efficient score function for the original parameter and the Jacobian of the\nfunction defining the general surface, via a chain rule for score functions.\nEfficient estimation of the constrained Euclidean parameter itself is\nconsidered as well.\n Our general estimation method is applied to location-scale, Gaussian copula\nand semiparametric regression models, and to parametric models under linear\nrestrictions.\n