Asymptotic Theory of Nonlinear Regression
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Asymptotic Theory of Nonlinear Regression

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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 GBPi = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment GBPn = {lRn, 8 , P; ,() E e} is the product of the statistical experiments GBPi, 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 GBPn is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments GBPn 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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Product details

  • Hardback | 330 pages
  • 162 x 238 x 26mm | 621.42g
  • Dordrecht, Netherlands
  • English
  • 1997 ed.
  • VI, 330 p.
  • 0792343352
  • 9780792343356

Table of contents

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.
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