Title page for ETD etd-02132009-171622

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
  • estimators
Date of Defense 1995-02-13
Availability restricted
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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