Statistics Seminar
| Date/Time: | Monday, 06 Oct 2014 from 4:10 pm to 5:00 pm |
|---|---|
| Location: | Snedecor 3105 |
| Cost: | Free |
| URL: | www.stat.iastate.edu |
| Contact: | Jeanette La Grange |
| Phone: | 515-294-3440 |
| Channel: | College of Liberal Arts and Sciences |
| Categories: | Lectures |
| Actions: | Download iCal/vCal | Email Reminder |
This talk describes an empirical likelihood (EL) methodology for irregularly located spatial data under a class of stochastic sampling designs. The purpose of the EL method is to allow likelihood-type inference about spatial covariance parameters without assumptions about the joint data distribution (e.g., Gaussian), the distribution of sampling locations (e.g., uniform), or the exact concentration of sampling sites (e.g., level of infill sampling).
Unlike frequency domain empirical likelihood (FDEL) for equi-spaced time series, the development of FDEL needs special care for such spatial data as the discrete Fourier transform lacks its usual orthogonality properties, the periodogram can exhibit non-trivial bias, and the domain of frequencies is unbounded. A new FDEL is formulated which accounts for the effects of these factors, and the main results show that log-ratio statistics have chi-square limits, similarly to parametric likelihood. As a result, the proposed FDEL method provides asymptotically correct confidence regions and tests for spatial covariance parameters under weak assumptions. As a major advantage, the EL method does not require explicit determination of standard errors, which is utterly difficult in this setting due to the fact that asymptotic variances of estimators often depend intricately on a combination of unknown quantities, including the process spectral density, the spatial sampling density, and the exact asymptotic structure. Some numerical results illustrate the finite sample properties of the method.