Three Tests for a Change-point in Variance of Normal Distribution

This paper considers the problem of testing for a change-point in variance of the sequence of normal random variables with unknown mean. We construct three tests, namely, L-test based on Lehmann’s （1951） non-parametric U-statistic, B-test based on Bayesian method and R-test derived from the maximum likelihood ratio method. The approximate critical values of L, B, R tests are calculated. Monte Carlo simulation studies were carried out to calculate power of these tests, the CUSUM of squares test （Brown et al, 1975） and the LM-test （Nyblom, 1989）. An empirical power comparison of the above tests suggests that when change-point is between the beginning and the mid portion, L and R tests are better, when changes-point is between the mid.portion and the end, CUSUM of squares and B tests are better.