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A Power Approximation for the Chi-Square Goodness-of-Fit Test: Simple Hypothesis Case
- Source :
- Journal of the American Statistical Association. 72:604-607
- Publication Year :
- 1977
- Publisher :
- Informa UK Limited, 1977.
-
Abstract
- The limiting distribution of the chi-square goodness-of-fit statistic Tn under alternatives is noncentral chi-square if the alternative probabilities approach the null probabilities at an appropriate rate as n → ∞. It is shown that for fixed alternative probabilities, the limiting distribution of (Tn − μ n )/σ n is standard normal. Both of these asymptotic results can be used to approximate the power of the goodness-of-fit test. Numerical comparisons between these two approximations indicate that for large values of the true power, the normal approximation is best, but for moderate values of power, the chi-square approximation is best.
Details
- ISSN :
- 1537274X and 01621459
- Volume :
- 72
- Database :
- OpenAIRE
- Journal :
- Journal of the American Statistical Association
- Accession number :
- edsair.doi...........6c82e598b5e35f808407f4a264ccd651