Linear Regression of the Poisson Mean

Author

Duane Steven Brown, Utah State University

Date of Award:

5-1982

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Department name when degree awarded

Applied Statistics

Committee Chair(s)

Ronald V. Canfield

Committee

Ronald V. Canfield

Committee

Gregory Jones

Committee

David White

Abstract

The purpose of this thesis was to compare two estimation procedures, the method of least squares and the method of maximum likelihood, on sample data obtained from a Poisson distribution. Point estimates of the slope and intercept of the regression line and point estimates of the mean squared error for both the slope and intercept were obtained. It is shown that least squares, the preferred method due to its simplicity, does yield results as good as maximum likelihood.

Also, confidence intervals were computed by Monte Carlo techniques and then were tested for accuracy. For the method of least squares, confidence bands for the regression line were computed under two different assumptions concerning the variance. It is shown that the assumption of constant variance produces false confidence bands. However, the assumption of the variance equal to the mean yielded accurate results.

Checksum

d8f2c803da1d8822416dad44eb70433f

Recommended Citation

Brown, Duane Steven, "Linear Regression of the Poisson Mean" (1982). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 6987.
https://digitalcommons.usu.edu/etd/6987