Date: 2022-09-30

Time: 15:30-16:30 (Montreal time)

HTTPS://US06WEB.ZOOM.US/J/84226701306?PWD=UEZ5NVPZAULLDW5QNU8VZZIVBEJXQT09

MEETING ID: 842 2670 1306

PASSCODE: 692788

Abstract:

Capture-recapture experiments are widely used to collect data needed to estimate the abundance of a closed population. To account for heterogeneity in the capture probabilities, Huggins (1989) and Alho (1990) proposed a semiparametric model in which the capture probabilities are modelled parametrically and the distribution of individual characteristics is left unspecified. A conditional likelihood method was then proposed to obtain point estimates and Wald-type confidence intervals for the abundance. Empirical studies show that the small-sample distribution of the maximum conditional likelihood estimator is strongly skewed to the right, which may produce Wald-type confidence intervals with lower limits that are less than the number of captured individuals or even negative.

In this talk, we present a full likelihood approach based on Huggins and Alho’s model. We show that the null distribution of the empirical likelihood ratio for the abundance is asymptotically chi-square with one degree of freedom, and the maximum empirical likelihood estimator achieves semiparametric efficiency. We further propose an expectation–maximization algorithm to numerically calculate the proposed point estimate and empirical likelihood ratio function. Simulation studies show that the empirical-likelihood-based method is superior to the conditional-likelihood-based method: its confidence interval has much better coverage, and the maximum empirical likelihood estimator has a smaller mean square error.

Speaker

Professor Li received his PhD in statistics in 2007 from the University of Waterloo, and then spent six months at the University of British Columbia as a postdoctoral fellow (2008). He worked as the assistant professor at the University of Alberta for three and half years (2008-2011). He joined the University of Waterloo in January 2012. He serves as an associate editor for the Canadian Journal of Statistics.

Professor Li’s research interests concern some areas of statistics, including finite mixture model, asymptotic theory, empirical likelihood, inference with constraints, experimental design, and smoothing technique.

McGill Statistics Seminar schedule: https://mcgillstat.github.io/