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
Date of Defense 1995-02-13 Availability restricted AbstractThe Least Squares Mixture Decomposition Estimator (LSMDE) is a new
nonparametric 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 the
quadratic 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/n for a reasonable smoothing parameter and, furthermore, many data points are
assigned to zero weights after the optimization. This implies that LSMDE decomposes
the underlying density function to a finite mixture distribution of p (< n) kernel
functions. 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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