Approximations for the time of change and the power function in change-point models |
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| Institution: | 1. Department of Statistics and Applied Probability, University of Alberta, Edmonton, Alberta Canada T6G 2G1;2. Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA;1. Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan;2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia;3. Department of Statistics, Government College University Lahore, Lahore 54000, Pakistan |
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| Abstract: | Assuming that the observations are from an exponential family we obtain the asymptotic distribution of the maximum likelihood estimator of the time of change. We also prove that the maximum likelihood ratio test is asymptotically normal, if there is a change in the parameters at an unknown time. |
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