Least squares mixture decomposition estimation

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/<i>n</i>) 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/<i>n</i> 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 <i>p</i> (< 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1995

Author dc:creator

• Kim, Donggeon

Chair dc:contributor.committeechair

• Terrell, George R.

Committee members dc:contributor.committeemember

• Good, Irving John
• Foutz, Robert
• Smith, Eric P.
• Coakley, Clint W.

• estimators

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-02132009-171622

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/37348