PARTITIONING-BASED ESTIMATORS OF REGRESSION FUNCTIONS IN THE PRESENCE OF IMCOMPLETE DATA

Includes bibliographical references (pages 51-52)One of the nonparametric approaches to estimate a regression function is the partitioning method. However, the situation could become complicated when there are missing data. In this research, partitioning-based methods are proposed to estimate the regression function in the presence of missing covariates in the data. Two methods of forming the partitoing-based estimators are considered, when: (i) the missing data probability is estimated by kernel method, or (ii) the missing data probability is estimated by least-squares method. Exponential performance bounds will be derived on the Lp norms of the resulting estimators. Such bounds, in conjunction with Borel-Cantelli lemma, provide various strong convergence results. The partitioning-based estimators can then be used to construct the classifiers in the statistical classification problems with missing covariates. Exponential performance bounds will also be derived for the resulting classifiers. Together with Borel-Cantelli lemma, the bounds will yield strong cosistency results