Parametric Statistical Inference
Inference involves drawing conclusions about some general phenomenon from limited empirical observations in the face of random variability. In a scientific context, the general must include the completely unforeseen if all possibilities are to be considered. Many of the statistical models most used to describe such phenomena belong to one of a small number of families--the exponential, transformation, and stable families. In the past 25 years, the likelihood function has been recognized as the fundamental element of approach to drawing scientific conclusions. This book brings together for the first time these two components of statistics as the central themes of statistical inference. Chapters focus on model building, approximations, and examples. There are also appendices on the elements of measure theory, probability theory, and numerical methods. The discussions are appropriate for students of mathematical statistics.
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Exponential family of probability distributions
Goodness of fit
Factoring the likelihood function
ancillary statistic asymptotic Barndorff-Nielsen and Cox Bayes Bayesian binomial distribution canonical parameter Chapter Chi-squared distribution conditional distribution conjugate prior constant critical region data generating mechanism data of Table data set decision-making defined density depend Derive deviance statistic distribution of Equation dose expected information explanatory variables exponential dispersion exponential family factor Fisher fixed value frequentist given information orthogonal integral interval likelihood function likelihood ratio linear exponential family linear models location-scale family log likelihood martingale maximum likelihood estimate measure model function model selection modified profile likelihood normal distribution normed likelihood nuisance parameters observed data observed value obtained P-value parameter of interest parameter values parametrization invariant pivotal quantity plot point estimate Poisson distribution possible posterior distribution prior distribution probability distribution procedure random variables regression model residuals sample space saturated model Section stochastic sufficient statistic tion transformation usually variance zero