Exploring the variance of the sample variance through estimation and simulation

Author

Christina StradwickFollow

Date of Award

2019

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Dr. Laura Adkins, Committee Chairperson

Second Advisor

Dr. Avishek Mallick

Third Advisor

Dr. Alaa Elkadry

Abstract

In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S ² ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, V^ˆ (S ² ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.

Subject(s)

Mathematical statistics.

Sampling (Statistics)

Recommended Citation

Stradwick, Christina, "Exploring the variance of the sample variance through estimation and simulation" (2019). Theses, Dissertations and Capstones. 1236.
https://mds.marshall.edu/etd/1236