McMaster University

Graduate Program in Statistics



STATISTICS SEMINAR



SPEAKER:
James E. Stafford,
Department of Public Health Science
University of Toronto
Date :Wednesday March 27, 2002.
Time : 3:30pm
Address Burke Science Building
Room: 138
TITLE:
A kernel density estimate for interval censored data
ABSTRACT:
We propose a method for kernel smoothing data that is either interval-censored or has been aggregated into bins. The method relies on weights computed using a proposed kernel density estimate for such data. This estimate retains the simplicity and intuitive appeal of the usual kernel density estimate for complete data and is easy to compute. It results from an algorithm where conditional expectations of a kernel are computed at each iteration. These conditional expectations are computed with respect to the density estimate from the previous iteration, allowing the estimator to extract more information from the data at each step. The estimator is applied to HIV data where interval censoring is common and to the Ontario health survey where data has been aggregated into bins.

In terms of the cumulative distribution function the algorithm is shown to coincide with the self-consistency algorithms of Efron (1967), Turnbull (1976), and Li et al. (1997), as the window size of the kernel shrinks to zero. It modifies these algorithms by introducing kernel smoothing at each iteration. Viewing the iterative scheme as a generalized EM algorithm permits a natural interpretation of the estimator as being close to the ideal kernel density estimate where the data is not censored in any way. Simulation results support the conjecture that kernel smoothing at every iteration does not effect convergence. In addition, comparison to the standard kernel density estimate, based on smoothing Turnbull's estimator, reflect favourably on the proposed estimator for all criteria considered. Use of the estimator for smoothing histograms, hazard estimation and scatterplot smoothing is also considered.

This is joint work with Thierry Duchesne of the Department of Statistics at University of Toronto.

About the Speaker
Jamie Stafford obtained his PhD from the University of Toronto in 1992. His doctoral work was done under the supervision of Rob Tibshirani. After graduation, Jamie was awarded an NSERC post-doctoral scholarship which he used to work at the University of Oxford and Stanford University. Returning to Canada in 1994 he joined the faculty at the University of Western Ontario where he remnained until 1999 when he returned to the University of Toronto. He currently holds a joint appointment in the Department of Public Health Sciences and Department of Statistics at University of Toronto. Jamies major research interests are in the area of statistical computing and symbolic computation. His doctoral thesis dealt with symbolic computation for asymptotic statistics and he has also worked (with David Bellhouse) on the application of symbolic computation to survey data. In 2000, Jamie and David Andrews published the book Symbolic Computation for Statistical Inference which details this important field of computational statistics. In recent years he has become very interested in smoothing and density estimation techniques particularly as they relate to survey data and survival data.
References
A preprint of the paper on which this talk is based is available here in PDF and postscript formats. See the references cited in the paper for more information.


Department of Mathematics and Statistics
Graduate Program in Statistics

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Last updated on November 13, 2001