Relevant, concrete, and thorough—the essential data-basedtext on statistical inference The ability to formulate abstract concepts and draw conclusionsfrom data is fundamental to mastering statistics. Aspects ofStatistical Inference equips advanced undergraduate and graduatestudents with a comprehensive grounding in statistical inference,including nonstandard topics such as robustness, randomization, andfinite population inference. A. H. Welsh goes beyond the standard texts and expertlysynthesizes broad, critical theory with concrete data and relevanttopics. The text follows a historical framework, uses real-datasets and statistical graphics, and treats multiparameter problems,yet is ultimately about the concepts themselves. Written with clarity and depth, Aspects of StatisticalInference: Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches Illustrates methods with real-data sets on diabeticretinopathy, the pharmacological effects of caffeine, stellarvelocity, and industrial experiments Considers multiparameter problems Develops large sample approximations and shows how to usethem Presents the philosophy and application of robustnesstheory Highlights the central role of randomization in statistics Uses simple proofs to illuminate foundational concepts Contains an appendix of useful facts concerning expansions,matrices, integrals, and distribution theory Here is the ultimate data-based text for comparing andpresenting the latest approaches to statistical inference.
Intended as a text for the postgraduate students of statistics, this well-written book gives a complete coverage of Estimation theory and Hypothesis testing, in an easy-to-understand style. It is the outcome of the authors’ teaching experience over the years. The text discusses absolutely continuous distributions and random sample which are the basic concepts on which Statistical Inference is built up, with examples that give a clear idea as to what a random sample is and how to draw one such sample from a distribution in real-life situations. It also discusses maximum-likelihood method of estimation, Neyman’s shortest confidence interval, classical and Bayesian approach. The difference between statistical inference and statistical decision theory is explained with plenty of illustrations that help students obtain the necessary results from the theory of probability and distributions, used in inference.
Statistics is a subject with a vast field of application, involving problems which vary widely in their character and complexity.However, in tackling these, we use a relatively small core of central ideas and methods. This book attempts to concentrateattention on these ideas: they are placed in a general settingand illustrated by relatively simple examples, avoidingwherever possible the extraneous difficulties of complicatedmathematical manipulation.In order to compress the central body of ideas into a smallvolume, it is necessary to assume a fair degree of mathematicalsophistication on the part of the reader, and the book is intendedfor students of mathematics who are already accustomed tothinking in rather general terms about spaces and functions
This volume focuses on the abuse of statistical inference in scientific and statistical literature, as well as in a variety of other sources, presenting examples of misused statistics to show that many scientists and statisticians are unaware of, or unwilling to challenge the chaotic state of statistical practices.;The book: provides examples of ubiquitous statistical tests taken from the biomedical and behavioural sciences, economics and the statistical literature; discusses conflicting views of randomization, emphasizing certain aspects of induction and epistemology; reveals fallacious practices in statistical causal inference, stressing the misuse of regression models and time-series analysis as instant formulas to draw causal relationships; treats constructive uses of statistics, such as a modern version of Fisher's puzzle, Bayesian analysis, Shewhart control chart, descriptive statistics, chi-square test, nonlinear modeling, spectral estimation and Markov processes in quality control.
Statistical inference is the foundation on which much of statistical practice is built. This book covers the topic at a level suitable for students and professionals who need to understand these foundations.
This excellent text emphasizes the inferential and decision-making aspects of statistics. The first chapter is mainly concerned with the elements of the calculus of probability. Additional chapters cover the general properties of distributions, testing hypotheses, and more.
Inference involves drawing conclusions about some general phenomenon from limited empirical observations in the face of random variability. Two central unifying components of statistics are the likelihood function and the exponential family. These are here brought together for the firsttime as the central themes of a book on statistical inference. This book is appropriate as an advanced undergraduate or graduate text in mathematical statistics.
A treatment of the problems of inference associated with experiments in science, with the emphasis on techniques for dividing the sample information into various parts, such that the diverse problems of inference that arise from repeatable experiments may be addressed. A particularly valuable feature is the large number of practical examples, many of which use data taken from experiments published in various scientific journals. This book evolved from the authors own courses on statistical inference, and assumes an introductory course in probability, including the calculation and manipulation of probability functions and density functions, transformation of variables and the use of Jacobians. While this is a suitable text book for advanced undergraduate, Masters, and Ph.D. statistics students, it may also be used as a reference book.
Priced very competitively compared with other textbooks at this level! This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. Beginning with an introduction to the basic ideas and techniques in probability theory and progressing to more rigorous topics, Probability and Statistical Inference studies the Helmert transformation for normal distributions and the waiting time between failures for exponential distributions develops notions of convergence in probability and distribution spotlights the central limit theorem (CLT) for the sample variance introduces sampling distributions and the Cornish-Fisher expansions concentrates on the fundamentals of sufficiency, information, completeness, and ancillarity explains Basu's Theorem as well as location, scale, and location-scale families of distributions covers moment estimators, maximum likelihood estimators (MLE), Rao-Blackwellization, and the Cramér-Rao inequality discusses uniformly minimum variance unbiased estimators (UMVUE) and Lehmann-Scheffé Theorems focuses on the Neyman-Pearson theory of most powerful (MP) and uniformly most powerful (UMP) tests of hypotheses, as well as confidence intervals includes the likelihood ratio (LR) tests for the mean, variance, and correlation coefficient summarizes Bayesian methods describes the monotone likelihood ratio (MLR) property handles variance stabilizing transformations provides a historical context for statistics and statistical discoveries showcases great statisticians through biographical notes Employing over 1400 equations to reinforce its subject matter, Probability and Statistical Inference is a groundbreaking text for first-year graduate and upper-level undergraduate courses in probability and statistical inference who have completed a calculus prerequisite, as well as a supplemental text for classes in Advanced Statistical Inference or Decision Theory.