Asymptotic Theory of Nonlinear Regression
(Sprache: Englisch)
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...
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Klappentext zu „Asymptotic Theory of Nonlinear Regression “
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 Pds. i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment Pds. n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments Pds. 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 Pds. n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments Pds. 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 ().
Inhaltsverzeichnis zu „Asymptotic Theory of Nonlinear Regression “
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.
Bibliographische Angaben
- Autor: A. A. Ivanov
- 2010, Softcover reprint of the original 1st ed. 1997., 330 Seiten, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer Netherlands
- ISBN-10: 9048147751
- ISBN-13: 9789048147755
Sprache:
Englisch
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