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140122 ||| eng |
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|a 9789401588775
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|a Ivanov, A.A.
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| 245 |
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|a Asymptotic Theory of Nonlinear Regression
|h Elektronische Ressource
|c by A.A. Ivanov
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| 250 |
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|a 1st ed. 1997
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 1997, 1997
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| 300 |
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|a VI, 330 p
|b online resource
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| 505 |
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|a 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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| 653 |
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|a Statistics
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| 653 |
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|a Control theory
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| 653 |
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|a Systems Theory, Control
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| 653 |
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|a Probability Theory
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| 653 |
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|a System theory
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| 653 |
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|a Mathematical Modeling and Industrial Mathematics
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| 653 |
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|a Applications of Mathematics
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| 653 |
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|a Statistics
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| 653 |
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|a Mathematics
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| 653 |
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|a Probabilities
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| 653 |
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|a Mathematical models
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Mathematics and Its Applications
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| 028 |
5 |
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|a 10.1007/978-94-015-8877-5
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| 856 |
4 |
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|u https://doi.org/10.1007/978-94-015-8877-5?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 519.5
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| 520 |
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|a 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 ()
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