Friday, October 20, at 327 Yost
Refreshments: 3:30 - 4:00 p.m, Talk: 4:00
- 5:00 p.m.
In this talk, some results about the large sample behavior of the likelihood ratio statistic for testing homogeneity in the normal mixture in location parameters (with or without an unknown scale parameter) are presented. When the parameters are restricted to a compact space, the limiting distribution is the same as the maximum of a c_2 variable with 2 d.f. and supremum of the square of a truncated Gaussian process with mean 0 and variance 1.
We further point out that there are some technical difficulties in directly
applying the asymptotic results. A modified likelihood ratio test is
proposed and it is shown that the new statistic has the usual chi-square
limiting distribution under the null hypothesis. According to our
simulations it has superior power against a number of competitors,
including the ordinary likelihood ratio test.