# Semiparametric Filtering in Speech Processing

Wednesday, September 20, 2000 - 2:00pm - 3:25pm

Keller 3-180

Benjamin Kedem (University of Maryland)

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.

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.