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Working Papers 1998 – Abstracts

16/98 Bandwidth Selection for Kernel Conditional Density Estimation David M. Bashtannyk and Rob J. Hyndman: We consider bandwidth selection for the kernel estimator of conditional density with one explanatory variable. Several bandwidth selection methods are derived ranging from fast rules-of-thumb which assume the underlying densities are known to relatively slow procedures which use the bootstrap. The methods are compared and a practical bandwidth selection strategy which combines the methods is proposed. The methods are compared using two simulation studies and a real data set.

17/98 Nonparametric Estimation and Symmetry Tests for Conditional Density Functions Rob J. Hyndman and Qiwei Yao: We suggest two new methods for conditional density estimation. The first is based on locally fitting a log-linear model, and is in the spirit of recent work on locally parametric techniques in density estimation. The second method is a constrained local polynomial estimator. Both methods always produce non-negative estimators. We propose an algorithm suitable for selecting the two bandwidths for either estimator. We also develop a new bootstrap test for the symmetry of conditional density functions. The proposed methods are illustrated by both simulation and application to a real data set.

18/98 Institutional Characteristics And The Relationship Between Students' First-Year University And Final-Year Secondary School Academic Performance Merran Evans and Alan Farley: A study of academic results of a student cohort in a diverse faculty of a large multi-campus university indicates that students' first-year performance at university is related to their prior academic achievement at secondary school, both overall and discipline specific, but that the extent and form of the relationship can vary by subject area and institutional – secondary school and university – characteristics. This may have implications for university selection and specification of prerequisite subjects for courses.