Nonlinear statistical models
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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Univariate Nonlinear Regression
Taylors Theorem and Matters of Notation
Statistical Properties of Least Squares Estimators
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applications approximation argument assume bounded in probability Chapter compact confidence interval consider converges almost surely correctly specified defined degrees of freedom denote DEPENDENT VARIABLE derived dP(e epoch dependent equation EXAMPLE 1 Continued finite follows Gallant Gauss-Newton method illustrate implies inequality Jacobian Lagrange multiplier test least squares estimator LEAST SQUARES ITERATIVE Lemma Let Assumptions likelihood ratio test method of moments minimizes Monte Carlo multivariate NON-LINEAR LEAST SQUARES noncentral chi-square noncentral chi-square distribution noncentral F-distribution noncentrality parameter nonlinear regression normally distributed notation null hypothesis obtain Output PARAMETER ESTIMATE Pitman drift Problem PROC MATRIX PROC NLIN q degrees random variables Recall regularity conditions sample SAS Statements Section sequence Show shown in Figure SQUARES ITERATIVE PHASE stage least squares STATISTICAL ANALYSIS SYSTEM SUM OF SQUARES Table Taylor's theorem three stage least tion uniformly variance variance-covariance matrix Wald test Wald test statistic whence