SELECTED TOPICS IN MARKOV CHAIN THEORY, WITH AN APPLICATION TO MARKETING.
COLUMBIA UNIV NEW YORK
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Discrete time-parameter Markov chains with a finite state space are considered. After a discussion on estimation of the parameters, various aspects of statistical inference are presented relating to the order of the chain and the stationarity of the transition probabilities. The theory of ergodic and absorbing chains is then developed using matrix algebra techniques. These allow most of the interesting criteria to be written in closed form expressions. The paper concludes with an application to marketing based on data obtained from a consumer panel in England. These data are shown to fit fairly well to a first order chain in equilibrium with stationary transition probabilities. Author