Type of Document Dissertation Author Kim, Donggeon URN etd-02132009-171622 Title Least squares mixture decomposition estimation Degree PhD Department Statistics Advisory Committee

Advisor Name Title Terrell, George R. Committee Chair Coakley, Clint W. Committee Member Foutz, Robert Committee Member Good, I. J. Committee Member Smith, Eric P. Committee Member Keywords

- estimators
Date of Defense 1995-02-13 Availability restricted AbstractThe Least Squares Mixture Decomposition Estimator (LSMDE) is a newnonparametric density estimation technique developed by modifying the ordinary kernel

density estimators. While the ordinary kernel density estimator assumes equal weight

(l/

n) for each data point, LSMDE assigns the optimized weight to each data point via thequadratic programming under the Mean Integrated Squared Error (MISE) criterion. As

results, we find out that the optimized weights for a given data set are far different from

l/

nfor a reasonable smoothing parameter and, furthermore, many data points areassigned to zero weights after the optimization. This implies that LSMDE decomposes

the underlying density function to a finite mixture distribution of

p(< n) kernelfunctions. LSMDE turns out to be more informative, especially in multi-dimensional

cases when the visualization of the density function is difficult, than the ordinary kernel

density estimator by suggesting the underlying structure of a given data set.

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