Markov normal discrimination and some classification problems with qualitative data.

For time ordered variables characterized by the Markov normal distribution, classification rules are derived for discriminating between two populations with unequal means and equal variance-covariance matrices. It is shown that the rules for the Markov normal data are simpler than classification rules for normal data due to the fact that only the latest observation in the series of measurements, X$\sb{\rm n}$ or Y$\sb{\rm n}$, is needed rather than the entire sets, $\{$X$\sb{\rm t}\}$ and $\{$Y$\sb{\rm t}\}$ for t = 1,$\...$,n. We examine the problem when the recording intervals are changed and when the observation to be classified is a vector at time point t = n + 1. Markov normal discrimination in which the variance-covariance matrices are not equal is also considered with known and estimated population parameters. To evaluate the performance of the classification rule, we calculate the probabilities of misclassification over a range of values of $\rho$ (the correlation between the new observation with the last time ordered observation). The second part of the dissertation looks at the relative discriminating power between normal data and qualitative data formed when the range of a continuous variable is divided into a number of intervals or states. The work of Cochran and Hopkins (1961) is extended from six states to k states and instead of transforming a normal variable, we transform a logistic variable. Alternatives such as symmetric and non-symmetric intervals, intervals of equal length and intervals having equal probability are examined.PhDBiological SciencesBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128273/2/8907096.pd