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Nonparametric Statistics Theory and Methods

Jayant V. Deshpande, Uttara Naik-Nimbalkar, and Isha Dewan
Publisher: 
World Scientific
Publication Date: 
2018
Number of Pages: 
266
Format: 
Hardcover
Price: 
98.00
ISBN: 
9789814663571
Category: 
Textbook
[Reviewed by
Robert W. Hayden
, on
09/18/2018
]

Nonparametric statistical methods are used for drawing inferences about a population based on a sample. They make fewer assumptions about the nature of the population than do the parametric techniques usually taught in an introductory statistics course. Their main advantage is that they can be used in a wider range of situations where little is known about the population in advance. The most talked about disadvantage is that these methods generally have less power in situations where we know more about the population, meaning that we need larger samples to get the same level of accuracy. Proponents of nonparametrics argue that the loss in power is small while the gain in safety against incorrect assumptions is great. If that were the whole story, nonparametric methods would probably be what we teach in a first course. The rest of the story is too complicated to deal with here, but we can say that nonparametrics is a valid but niche branch of statistics that was more fashionable some decades ago than it is today.

There are a few textbooks in nonparametric statistics. Most of these assume as prerequisite knowledge just an introductory statistics course. The book at hand is at a more advanced level, perhaps assuming a year-long mathematical statistics course. It lies on the boundary between textbook and monograph. There are exercises throughout for the reader, but if this were used as a text one would probably want to assign all of them. A quick survey of a convenience sample of statisticians suggested that a course in nonparametrics at this level is fairly rare, so we might better think of this book as a resource for someone wanting to know more than is in the usual undergraduate textbooks, perhaps because they are teaching a course using one of those books and would like to be a step ahead of their students.

The opening chapter contains a spotty review of prerequisites, an introduction to the ideas of nonparametric inference, and extended treatments of data censoring and ranked set sampling that feel out of place. The next chapter deals with order statistics, on which many nonparametric methods are based. There follows a chapter on estimating the population distribution as a whole. Then there are a half dozen chapters devoted to common inference situations such as goodness of fit, regression, or comparing two groups. These chapters contain a large number of different methods. It might be useful to have had more guidance in choosing among these. Very little is said about how their performance compares to alternative parametric approaches. In particular, there is little emphasis on the kinds of simulation studies that have been used to evaluate inference methods since at least the 1960s. Tucked among the six chapters on broad inference problems are chapters on optimal nonparametric methods, Bayesian methods, and density estimates.

There are eight pages of references, not many of which are recent, but this probably reflects on the relative decrease of activity in this area in recent years. There is an index of a bit over three pages. Proofreading of the main text has been rather lax, especially as regards putting it into idiomatic English. The book is printed on unusually good paper, as judged by its ability to handle highlighters.

The number of people looking for a book at this level on this topic is probably quite small, and hence so is the number of such books available. Anyone seeking in this realm should be aware of this book.


After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He contributed the chapter on evaluating introductory statistics textbooks to the MAA’s Teaching Statistics.

  • Principles of Statistical Inference
  • Order Statistics
  • Empirical Distribution Function
  • The Goodness of Fit Problem
  • The One Sample Problem
  • Optimal Nonparametric Tests
  • The Two Sample Problem
  • The Several Sample Problem
  • Tests for Independence
  • Nonparametric Density Estimation
  • Regression Analysis
  • Nonparametric Bayesian Methods
  • Appendix