On the change-point problem
TL;DR: In this article, the problem of testing a shift in the level of a process occurring at an unknown time point given an intial sample of fixed size from the original unchanged process is considered.
Abstract: We consider the problem of testing a shift in the level of a process occurring at an unknown time point given an intial sample of fixed size from the original unchanged process. Various large sample results for the proposed test are formulated and examined.
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TL;DR: In this paper, a binary search procedure was proposed to detect the changepoints in the sequence of the ratios of probabilities and obtain the maximum likelihood estimators of two multinomial probability vectors under the assumption that the probability ratio sequence has a changepoint.
Abstract: This article studies the problem of testing and locating changepoints in likelihood ratios of two multinomial probability vectors. We propose a binary search procedure to detect the changepoints in the sequence of the ratios of probabilities and obtain the maximum likelihood estimators of two multinomial probability vectors under the assumption that the probability ratio sequence has a changepoint. We also give a strongly consistent estimator for the changepoint location. An information theoretic approach is used to test the equality of two discrete probability distributions against the alternative that their ratios have a changepoint. Approximate critical values of the test statistics are provided by simulation for several choices of model parameters. Finally, we examine a real life data set pertaining to average daily insulin dose from the Boston Collaborative Drug Surveillance Program and locate the changepoints in the probability ratios.
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TL;DR: Shoutir Kishore Chatterjee (SKC) as discussed by the authors was the National Lecturer in Statistics (1985-1986), the President of the Section of Statistics of the Indian Science Congress (1989) and an Emeritus Scientist (1997-2000) of the Council of Scientific and Industrial Research, India.
Abstract: Shoutir Kishore Chatterjee was born in Ranchi, a small hill station in India, on November 6, 1934. He received his B.Sc. in statistics from the Presidency College, Calcutta, in 1954, and M.Sc. and Ph.D. degrees in statistics from the University of Calcutta in 1956 and 1962, respectively. He was appointed a lecturer in the Department of Statistics, University of Calcutta, in 1960 and was a member of its faculty until his retirement as a professor in 1997. Indeed, from the 1970s he steered the teaching and research activities of the department for the next three decades. Professor Chatterjee was the National Lecturer in Statistics (1985–1986) of the University Grants Commission, India, the President of the Section of Statistics of the Indian Science Congress (1989) and an Emeritus Scientist (1997–2000) of the Council of Scientific and Industrial Research, India. Professor Chatterjee, affectionately known as SKC to his students and admirers, is a truly exceptional person who embodies the spirit of eternal India. He firmly believes that “fulfillment in man’s life does not come from amassing a lot of money, after the threshold of what is required for achieving a decent living is crossed. It does not come even from peer recognition for intellectual achievements. Of course, one has to work and toil a lot before one realizes these facts.”
1 citations
TL;DR: Shoutir Kishore Chatterjee (SKC) as mentioned in this paper was the National Lecturer in Statistics (1985--1986) of the University Grants Commission, India, the President of the Section of Statistics of the Indian Science Congress (1989) and an Emeritus Scientist (1997--2000) of Council of Scientific and Industrial Research, India.
Abstract: Shoutir Kishore Chatterjee was born in Ranchi, a small hill station in India, on November 6, 1934. He received his B.Sc. in statistics from the Presidency College, Calcutta, in 1954, and M.Sc. and Ph.D. degrees in statistics from the University of Calcutta in 1956 and 1962, respectively. He was appointed a lecturer in the Department of Statistics, University of Calcutta, in 1960 and was a member of its faculty until his retirement as a professor in 1997. Indeed, from the 1970s he steered the teaching and research activities of the department for the next three decades. Professor Chatterjee was the National Lecturer in Statistics (1985--1986) of the University Grants Commission, India, the President of the Section of Statistics of the Indian Science Congress (1989) and an Emeritus Scientist (1997--2000) of the Council of Scientific and Industrial Research, India. Professor Chatterjee, affectionately known as SKC to his students and admirers, is a truly exceptional person who embodies the spirit of eternal India. He firmly believes that ``fulfillment in man's life does not come from amassing a lot of money, after the threshold of what is required for achieving a decent living is crossed. It does not come even from peer recognition for intellectual achievements. Of course, one has to work and toil a lot before one realizes these facts.''