Asymptotic Theory of Nonlinear Regression
This book presents up-to-date mathematical results in asymptotic theory on nonlinear regression on the basis of various asymptotic expansions of least squares, its characteristics, and its distribution functions of functionals of Least Squares Estimator. It is divided into four chapters. In Chapter 1 assertions on the probability of large deviation of normal Least Squares Estimator of regression function parameters are made. Chapter 2 indicates conditions for Least Moduli Estimator asymptotic normality. An asymptotic expansion of Least Squares Estimator as well as its distribution function are obtained and two initial terms of these asymptotic expansions are calculated. Separately, the Berry-Esseen inequality for Least Squares Estimator distribution is deduced. In the third chapter asymptotic expansions related to functionals of Least Squares Estimator are dealt with. Lastly, Chapter 4 offers a comparison of the powers of statistical tests based on Least Squares Estimators. The Appendix gives an overview of subsidiary facts and a list of principal notations. Additional background information, grouped per chapter, is presented in the Commentary section. The volume concludes with an extensive Bibliography. Audience: This book will be of interest to mathematicians and statisticians whose work involves stochastic analysis, probability theory, mathematics of engineering, mathematical modelling, systems theory or cybernetics.
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Approximation by a Normal Distribution
Asymptotic Expansions Related to the Least Squares
5 other sections not shown
analogous arithmetic mean assertion Asymptotic Expansion calculation Christoffel symbols coefficients uniformly bounded condition IIIm conditions of Lemma conditions of Theorem Consequently consistent estimator converges convex set Corollary corresponding criteria criterion curvature differential differential geometry distribution equality equation errors of observation exist constants following property function g(j Gaussian Gaussian distribution geometric inequality integral ISBN Lemma Let the conditions Let us assume Let us consider Let us denote Let us estimate Let us further Let us introduce Let us note Let us set Let us write measure of non-linearity metric tensor multi-index n-foo non-linear regression normalisation notation obtain the a.e. parameter proof of Theorem quantities random vector regression analysis regression function regression model relation remainder term reparametrisation result right hand side scalar scalar curvature Section sequence signed measure statistical experiment sup sup tensor Theorem 17 Theorem 24 Theorem A.5 uniformly bounded variables zero