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
Abstract The 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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