Consider the following problem. You have m instruments, one "good" and m-1 "bad," all collecting samples from the same quantity; e.g. from a time series of the utterance "speech." We think of the "bad" as a distortion of the "good." Suppose we have data from all the instruments. How can we COMBINE ALL THE DATA "good" and "bad" to improve upon the "good?" To answer this, we turn to the following statistical formulation.

Consider m probability distributions where the first m-1 are obtained by multiplicative exponential distortions of the the mth distribution, it being the "good" reference or common factor. Given m corresponding samples, "good" and "bad," we solve the semiparametric large sample problem regarding the estimation from the COMBINED data of each distortion and the common factor, and testing the hypothesis that the distributions are identical. In retrospect, the approach is a generalization of the classical one way analysis of variance. A power comparison with the t and F tests obtained by simulation points to the merit of the present approach.

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Mathematical Foundations of Speech Processing and Recognition

2000-2001 Program: Mathematics in Multimedia