Nonparametric Statistical Inference: A Comprehensive Guide

Nonparametric statistical inference is a branch of statistics that makes no assumptions about the underlying distribution of the data. This is in contrast to parametric statistical inference, which assumes that the data come from a known distribution, such as the normal distribution. Nonparametric statistical inference is often used when the sample size is small, when the data are not normally distributed, or when the underlying distribution is unknown.

Types of Nonparametric Tests

There are many different types of nonparametric tests available, each of which has its own strengths and weaknesses. Some of the most commonly used nonparametric tests include:

Nonparametric Statistical Inference

by John J. Donohue

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• Distribution-free tests: These tests make no assumptions about the underlying distribution of the data. They can be used to test hypotheses about the mean, median, or variance of a population.
• Ranks tests: These tests use the ranks of the data rather than the actual values. They can be used to test hypotheses about the median or other quantiles of a population.
• Bootstrap tests: These tests use resampling to estimate the sampling distribution of a statistic. They can be used to test hypotheses about any statistic, regardless of the underlying distribution of the data.
• Permutation tests: These tests use random permutations of the data to estimate the sampling distribution of a statistic. They can be used to test hypotheses about any statistic, regardless of the underlying distribution of the data.

Advantages of Nonparametric Statistical Inference

There are several advantages to using nonparametric statistical inference. First, nonparametric tests are more robust than parametric tests. This means that they are less likely to be affected by violations of the assumptions of the test. Second, nonparametric tests are often more powerful than parametric tests, especially when the sample size is small. Third, nonparametric tests can be used to test hypotheses about any statistic, regardless of the underlying distribution of the data.

Disadvantages of Nonparametric Statistical Inference

There are also some disadvantages to using nonparametric statistical inference. First, nonparametric tests can be less efficient than parametric tests when the assumptions of the parametric test are met. Second, nonparametric tests can be more difficult to interpret than parametric tests. Third, nonparametric tests can be more computationally intensive than parametric tests.

Nonparametric statistical inference is a powerful tool that can be used to test hypotheses about data that does not come from a known distribution. Nonparametric tests are more robust and powerful than parametric tests, and they can be used to test hypotheses about any statistic. However, nonparametric tests can be less efficient and more difficult to interpret than parametric tests.

About the Author

John Donohue is a professor of statistics at the University of California, Berkeley. He is the author of several books and articles on nonparametric statistical inference. Dr. Donohue's research interests include nonparametric methods for censored data, semiparametric methods for longitudinal data, and Bayesian nonparametric methods.

Nonparametric Statistical Inference

by John J. Donohue

5 out of 5

Language	:	English
File size	:	35636 KB
Screen Reader	:	Supported
Print length	:	694 pages

FREE