TY - JOUR
AU - Finch, Stephen J.
AB -  Abstract Through simulation and regression, we study the alternative distribution of the likelihood ratio test in which the null hypothesis postulates that the data are from a normal distribution after a restricted Box–Cox transformation and the alternative hypothesis postulates that they are from a mixture of two normals after a restricted (possibly different) Box–Cox transformation. The number of observations in the sample is called N. The standardized distance between components (after transformation) is D = (μ2 − μ1)/σ, where μ1 and μ2 are the component means and σ2 is their common variance. One component contains the fraction π of observed, and the other 1 − π. The simulation results demonstrate a dependence of power on the mixing proportion, with power decreasing as the mixing proportion differs from 0.5. The alternative distribution appears to be a non-central chi-squared with approximately 2.48 + 10N −0.75 degrees of freedom and non-centrality parameter 0.174N(D − 1.4)2 × [π(1 − π)]. At least 900 observations are needed to have power 95% for a 5% test when D = 2. For fixed values of D, power, and significance level, substantially more observations are necessary when π ≥ 0.90 or π ≤ 0.10. We give the estimated powers for the alternatives studied and a table of sample sizes needed for 50%, 80%, 90%, and 95% power. 
TI - The Likelihood Ratio Test with the Box–Cox Transformation for the Normal Mixture Problem: Power and Sample Size Study
JF - Communications in Statistics: Simulation and Computation
DO - 10.1081/SAC-200033328
DA - 2004-01-02
UR - https://www.deepdyve.com/lp/taylor-francis/the-likelihood-ratio-test-with-the-box-cox-transformation-for-the-9G8Bbt3k4m
SP - 553
EP - 565
VL - 33
IS - 3
DP - DeepDyve
ER -