JSM 2005 Online Program

Abstract #303756

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	451
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
Sponsor:	IMS
Abstract - #303756
Title:	Local Likelihood Estimation of the Intensity Function for Spike Trains Observed on Overlapping, Nonidentical Intervals
Author(s):	Matt Gregas*+
Companies:	University of Minnesota
Address:	5800 4th Street NE Apt 2, Fridley, MN, 55432, United States
Keywords:	Poisson Process ; Intensity Estimation ; Local Linear Smoothing ; Local Likelihood
Abstract:	Motivated by a neuroscience experiment that observes spike trains from the primary motor cortex of the rhesus monkey, we develop methods for estimating the intensity function of a Poisson point process corresponding to a single spike train and for estimating families of intensity functions with a common (unknown) shape or amplitude. Additionally, we provide tests for a breakpoint in an intensity function at a given location. These methods are based on local likelihood smoothing. We discuss asymptotic properties of the intensity estimate and test statistics for breakpoints and present results from simulation studies that describe the power and actual significance levels of our tests. Estimates for families of intensity functions build on Functional Data Analysis methodology, but extend beyond the current procedures. In particular, our methods do not require the point process be observed on the full support of the intensity function for each member of the family. We show that for this case, local likelihood methodology corresponds to using a local polynomial fit with adjusted kernel weights.

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