Asymptotic theory of nonlinear regression
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Bibliographic Information
Asymptotic theory of nonlinear regression
（Mathematics and its applications, v. 389）
Kluwer Academic Publishers, c1997
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Includes bibliographical references (p. 309-324) and index
Description and Table of Contents
Description
Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple GBPi = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment GBPn = {lRn, 8 , P; ,() E e} is the product of the statistical experiments GBPi, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment GBPn is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments GBPn generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().
Table of Contents
Introduction. 1. Consistency. 2. Approximation by a Normal Distribution. 3. Asymptotic Expansions Related to the Least Squares Estimator. 4. Geometric Properties of Asymptotic Expansions. Appendix: I: Subsidiary Facts. II: List of Principal Notations. Commentary. Bibliography. Index.
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