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Asymptotic Theory of Nonlinear Regression by A. A. Ivanov

Asymptotic Theory of Nonlinear Regression

by A. A. Ivanov
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Book cover type: Paperback
  • ISBN13: 9789048147755
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 330
  • Original Price: EUR 99.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 514 grams
  • BISAC Subject(s): Probability & Statistics / General, Applied, and System Theory

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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