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book chapter · Palgrave Macmillan UK eBooks · 1992

Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases

Anirudh L. Nagar, Charu Chandrika

Cited by 1Abstract and details only

Abstract

For testing the linear restrictions on regression coefficients in the classical linear regression model, it is a common practice to use Snedecor’s F-distribution. In Neyman-Pearson theory of testing of statistical hypotheses, the efficiency of a statistical test is to be judged by its power of detecting the departure from the null hypothesis ( H 0 ). Hence it is imperative that the distribution of any statistic be known both under the null and the alternative hypothesis ( H 1 ). Under the null hypothesis, H 0 (β = β 0 ), the test statistic z , follows the central F distribution, and therefore we may use the tables of the F distribution to obtain the points of significance. However, under the alternative hypothesis, the distribution of z is non-central F. For a fixed sample size, we must use this distribution to evaluate the power of the test. Tiku (1967) has computed the tables for the power of the F-test using incomplete Beta functions.

Cite this paper

APA 7

Nagar, A. L., & Chandrika, C. (1992). Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases. Palgrave Macmillan UK eBooks, 189–221. https://doi.org/10.1007/978-1-349-12221-9_11

MLA 9

Nagar, Anirudh L., and Charu Chandrika. “Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases.” Palgrave Macmillan UK eBooks, 1992, pp. 189–221, https://doi.org/10.1007/978-1-349-12221-9_11.

Chicago

Nagar, Anirudh L., and Charu Chandrika. 1992. “Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases.” Palgrave Macmillan UK eBooks: 189–221. https://doi.org/10.1007/978-1-349-12221-9_11.

Harvard

Nagar, A.L. and Chandrika, C. (1992) ‘Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases’, Palgrave Macmillan UK eBooks, pp. 189–221. Available at: https://doi.org/10.1007/978-1-349-12221-9_11.

BibTeX
@incollection{nagar1992edgeworth,
  title = {{Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases}},
  author = {Nagar, Anirudh L. and Chandrika, Charu},
  booktitle = {Palgrave Macmillan UK eBooks},
  pages = {189--221},
  year = {1992},
  doi = {10.1007/978-1-349-12221-9_11}
}

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