Nonlinear Statistical Models
John Wiley & Sons, 25 sept. 2009 - 610 pages
A comprehensive text and reference bringing together advances in the theory of probability and statistics and relating them to applications. The three major categories of statistical models that relate dependent variables to explanatory variables are covered: univariate regression models, multivariate regression models, and simultaneous equations models. Methods are illustrated with worked examples, complete with figures that display code and output.
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applications approximation argument assume bounded in probability central limit theorem Chapter compact conﬁdence interval converges almost surely correctly speciﬁed deﬁned deﬁnition degrees of freedom denote derived dP(e epoch dependent equation errors EXAMPLE 1 Continued ﬁnd ﬁnite ﬁrst ﬁtted ﬁxed follows Gallant Gauss-Newton method hypothesis H illustrate implies independent variables inequality inﬁnite instrumental variables ITERATIVE Lagrange multiplier test least squares estimator Lemma Let Assumptions likelihood ratio test method of moments minimizes Monte Carlo multiplier test statistic multivariate noncentral chi-square noncentral chi-square distribution noncentrality parameter nonlinear regression normally distributed notation null hypothesis obtain Output Pitman drift Problem q degrees random variables Recall regularity conditions RESIDUAL sample satisﬁes Section sequence Show shown in Figure speciﬁcation stage least squares strong law sum of squares Table Taylor’s theorem three stage least tion uniformly variance variance-covariance matrix Wald test Wald test statistic whence