This book offers a comprehensive guide to large sample techniques in statistics. More importantly, it focuses on thinking skills rather than just what formulae to use; it provides motivations, and intuition, rather than detailed proofs.

In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 standard situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson's? -testthe asymptotic distri- 2 2 bution of Pearson's? -test is not always? (e.g., Moore 1978).

Focuses on thinking skills rather than just what formulae to use Provides motivations, and intuition, rather than detailed proofs Begins with very simple and basic techniques, and connects theory and applications in entertaining ways Includes supplementary material: sn.pub/extras

Autorentext

Jiming Jiang is Professor of Statistics and a former Director of Statistical Laboratory at the University of California, Davis. He is a prominent researcher in the fields of mixed effects models, small area estimation, model selection, and statistical genetics. He is the author of Linear and Generalized Linear Mixed Models and Their Applications, 2nd Edition (Springer 2021), Robust Mixed Model Analysis (2019), Asymptotic Analysis of Mixed Effects Models: Theory, Applications, and Open Problems (2017), and The Fence Methods (with T. Ngyuen, 2016). Jiming Jiang has been editorial board member of The Annals of Statistics and Journal of the American Statistical Association, among others. He is a Fellow of the American Association for the Advancement of Science, the American Statistical Association, and the Institute of Mathematical Statistics; an elected member of the International Statistical Institute; and a Yangtze River Scholar (Chaired Professor, 2017-2020).

Inhalt
The ?-? Arguments.- Modes of Convergence.- Big O, Small o, and the Unspecified c.- Asymptotic Expansions.- Inequalities.- Sums of Independent Random Variables.- Empirical Processes.- Martingales.- Time and Spatial Series.- Stochastic Processes.- Nonparametric Statistics.- Mixed Effects Models.- Small-Area Estimation.- Jackknife and Bootstrap.- Markov-Chain Monte Carlo.