Asymptotic Theory of Nonlinear Regression Tapa dura - 1996 - 1997th Edición

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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 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 ().