Statistical Inference Based on the likelihood
The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood.
Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.
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algorithm analysis approximation asymptotic distribution binomial called components computed confidence interval consider constant corresponding criterion defined denote density function depends distribution function elements equal equivalent error estimate Example exists explanatory variables exponential family expression fact Figure frequency gamma gamma distribution given hence independent instance large number likelihood equations likelihood function likelihood principle linear models log-likelihood matrix mean value method minimal sufficient statistic multinomial distribution multivariate Newton–Raphson non-centrality normal null hypothesis observed obtain order statistics p-value parameter pivotal quantity plot Poisson population Pr(Y probability distribution problem properties quantity random variable ratio relationship relevant response variable sample space sample value sequence ſlo specific statistical model sufficient statistic Suppose Table term test procedure test statistic Theorem tion transformation treatment var(Y variance vector write
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Probability Theory and Statistical Inference: Econometric Modeling with ...
Limited preview - 1999