Asymptotic Theory of Nonlinear Regression / by Alexander V. Ivanov
(Mathematics and Its Applications ; 389)
| データ種別 | 電子ブック |
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| 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 |
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| 内容注記 | 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 |
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| 一般注記 | 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 () |
| 著者標目 | *Ivanov, Alexander V. author SpringerLink (Online service) |
| 件 名 | LCSH:Statistics LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:System theory LCSH:Mathematical models LCSH:Probabilities FREE:Statistics FREE:Statistics, general FREE:Probability Theory and Stochastic Processes FREE:Applications of Mathematics FREE:Mathematical Modeling and Industrial Mathematics FREE:Systems Theory, Control |
| 分 類 | DC23:519.5 |
| 巻冊次 | ISBN:9789401588775 
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| ISBN | 9789401588775 |
| URL | http://dx.doi.org/10.1007/978-94-015-8877-5 |
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