Asymptotic Methods of Nonlinear Wave The
β Alan Jeffrey, T. Kawahara
π Library
π
1982
π Pitman Advanced Publishing Program
π English
β¦ LIBER β¦
π
Asymptotic Theory of Nonlinear Regression
β Scribed by Alexander V. Ivanov (auth.)
- Publisher
- Springer Netherlands
- Year
- 1997
- Tongue
- English
- Leaves
- 332
- Series
- Mathematics and Its Applications 389
- Edition
- 1
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
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 Β£i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment Β£n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments Β£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 Β£n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments Β£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 ().
β¦ Table of Contents
Front Matter....Pages i-vi
Introduction....Pages 1-3
Consistency....Pages 5-78
Approximation by a Normal Distribution....Pages 79-153
Asymptotic Expansions Related to the Least Squares Estimator....Pages 155-250
Geometric Properties of Asymptotic Expansions....Pages 251-288
Back Matter....Pages 289-330
β¦ Subjects
Statistics, general; Probability Theory and Stochastic Processes; Applications of Mathematics; Mathematical Modeling and Industrial Mathematics; Systems Theory, Control
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