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

In: Contributions to Consumer Demand and Econometrics

Author

Listed:
  • A. L. Nagar
  • Charu Chandrika

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 (H0). Hence it is imperative that the distribution of any statistic be known both under the null and the alternative hypothesis (H1). Under the null hypothesis, H0 (β = β0), 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.

Suggested Citation

  • A. L. Nagar & Charu Chandrika, 1992. "Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases," Palgrave Macmillan Books, in: Ronald Bewley & Tran Hoa (ed.), Contributions to Consumer Demand and Econometrics, chapter 11, pages 189-221, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-1-349-12221-9_11
    DOI: 10.1007/978-1-349-12221-9_11
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    Cited by:

    1. Brown, Kenneth & Cribari-Neto, Francisco, 1992. "On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 12(2), November.

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