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＜電子ブック＞
Asymptotic Theory of Nonlinear Regression / by A.A. Ivanov
(Mathematics and Its Applications ; 389)

版	1st ed. 1997.
出版者	Dordrecht : Springer Netherlands : Imprint: Springer
出版年	1997
本文言語	英語
大きさ	VI, 330 p : online resource
著者標目	*Ivanov, A.A author SpringerLink (Online service)
件　名	LCSH:Statistics  LCSH:Probabilities LCSH:Mathematics LCSH:Mathematical models LCSH:System theory LCSH:Control theory FREE:Statistics FREE:Probability Theory FREE:Applications of Mathematics FREE:Mathematical Modeling and Industrial Mathematics FREE:Systems Theory, Control
一般注記	1 Consistency -- 2 Approximation by a Normal Distribution -- 3 Asymptotic Expansions Related to the Least Squares Estimator -- 4 Geometric Properties of Asymptotic Expansions -- I Subsidiary Facts -- II List of Principal Notations -- Commentary -- 1 -- 2 -- 3 -- 4 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 £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, 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 £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n 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 () HTTP:URL=https://doi.org/10.1007/978-94-015-8877-5

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