Breakthroughs in Statistics: Volume 2: Methodology and Distribution Samuel Kotz (Editor), Norman L. Johnson
一套三本书, 收集了统计学中最经典的论文。
This is the second of a two volume collection of seminal papers in the statistical sciences written during the past 100 years. These papers have each had an outstanding influence on the development of statistical theory and practice over the last century. Each paper is preceded by an introduction written by an authority in the field providing background information and assessing its influence. Readers will enjoy a fresh outlook on now well-established features of statistical techniques and philosophy by becoming acquainted with the ways they have been developed. It is hoped that some readers will be stimulated to study some of the references provided in the Introduction (and also in the papers themselves) and so attain a deeper background knowledge of the basis of their work.

This volume is as praiseworthy as volume 1. However it covers a number of papers from the late 19th century and most of the twentieth century that dealt with distribution theory and statistical methodology rather than the foundational issues. Like volume 1 it was published in 1992 and includes an introduction by an expert that puts the article in contexts and explains why it is a breakthrough. All the articles are worthy of be designated as breakthrough seminal papers on the topic they cover. I will concentrate on my favorites to give the reader a flavor for the content. As with volume 1 I recommend this to any statistician or researcher interested in a deeper understanding of the history and key developments of statistics, a field developed primarily in the 20th Century.

The first paper in this collection is an article by Karl Pearson where his famous chi-square statistic is first introduced. Pearson's chi square was used by him as a way to evaluate the goodness of fit of a probability model to data. The chi square distribution that is the asymptotic distribution for Pearson's test statistic is one of the most important distributions in statistics. It is used in a variety of applications in biostatistics especially where contingency tables are involved and relationships between categorical or binary variables need to be tested.

The next paper is Gosset's (pen name Student) famous paper "The Probable Error of the Mean" published in 1908. This was the paper that guessed the central t distribution to be the exact sampling distribution of the t statistic used to estimate the mean of a distribution. Prior to Gosset's paper the standard normal distribution which is asymptotically correct for normally distributed samples was used. But Gosset dealt with small samples (perhaps in the range of 5 to 20) where the normal approximation is not good. Later R. A. Fisher mathematically proved the t distribution with n-1 degrees of freedom is the exact distribution for the t statistic from a sample of n independent identically distributed observations under the null hypothesis confirming Gosset's result.

Other papers among my favorites are Kolmogorov's 1933 paper on the empirical distribution function and the statistic that became known as the Kolmogorov-Smirnov statistic for goodness of fit testing based on the empirical distribution, the Kaplan and Meier paper of 1958 establishing a nonparametric estimator of the survival function based on right censored time to event data, D. R. Cox's 1972 paper on the proportional hazards model for survival functions, Box and Jenkins 1962 paper on adaptive optimization and stochastic control that spawned their book on time series monitoring and feedback control systems, Nelder and Wedderburn's paper in 1972 on generalized linear models that led to the software product GLIM and later to the application in another breakthrough paper (in volume III) by Liang and Zeger to longitudinal data, and last but certainly not least Efron's 1979 Annals of Statistics paper on the bootstrap and its relationship to the jackknife which spawned a multitude of applications utilizing bootstrap estimates of standard error, confidence intervals and the application of the bootstrap principle to do Monte Carlo bootstrap approximations in a wide variety of complex and previously intractable problems.