Read e-book online A Course in Large Sample Theory: Texts in Statistical PDF

By Thomas S. Ferguson

ISBN-10: 0412043718

ISBN-13: 9780412043710

A direction in huge pattern thought is gifted in 4 elements. the 1st treats simple probabilistic notions, the second one positive aspects the fundamental statistical instruments for increasing the speculation, the 3rd comprises unique issues as functions of the overall conception, and the fourth covers extra common statistical issues. approximately all themes are lined of their multivariate setting.The e-book is meant as a primary yr graduate path in huge pattern conception for statisticians. it's been utilized by graduate scholars in records, biostatistics, arithmetic, and comparable fields. through the booklet there are numerous examples and routines with ideas. it's an amazing textual content for self research.

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Extra resources for A Course in Large Sample Theory: Texts in Statistical Science

Example text

If a particular model (parametrization) does not make biological sense, this is reason to exclude it from the set of candidate models, particularly in the case where causation is of interest. In developing the set of candidate models, one must recognize a certain balance between keeping the set small and focused on plausible hypotheses, while making it big enough to guard against omitting a very good a priori model. While this balance should be considered, we advise the inclusion of all models that seem to have a reasonable justification, prior to data analysis.

The likelihood (a relative, not absolute, value) is a function of the unknown parameter p. Given this formalism, one might compute the likelihood of many values of the unknown parameter p and pick the most likely one as the best estimate of p, given the data and the model. ” This is Fisher’s concept of maximum likelihood estimation; he published this when he was 22 years old as a third-year undergraduate at Cambridge University! He reasoned that the best estimate of an unknown parameter (given data and a model) was that which was the most likely; thus the name maximum likelihood, ML.

Introduction vector of parameters. Thus, θ is generic and might represent parameters in a regression model (β0 , β1 , β2 ) or the probability of a head in penny flipping trials (p). The models gi are discrete or continuous probability distributions, and our focus will be on their associated likelihoods, L(θ|data, model) or log-likelihoods log(L(θ|data, model)). Notation for the log-likelihood will sometimes be shortened to log(L(θ|x, g)) or even log(L). Ideally, the set of R models will have been defined prior to data analysis.

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A Course in Large Sample Theory: Texts in Statistical Science by Thomas S. Ferguson

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