### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

OCTOBER 7, 2016

**Speaker: **
Dan Naiman, Johns Hopkins University

**Title: ***
To Replace or Not to Replace in Finite Population Sampling
*

**Abstract:**
We revisit the classical result in finite population sampling which states that in equally-likely “simple” random sampling the sample mean
is more reliable when we do not replace after each draw. In this talk, we review a classical result for the equally likely sampling case. Then we investigate if and when the same is true for samples where it may no longer be true that each member of the population has an equal chance of being selected, and when the population mean is estimated using the Horvitz-Thompson inverse probability weighing to produce an unbiased estimator. For a certain class of sampling schemes, we are able to obtain convenient expressions for the variance of the sample mean and surprisingly, we find that for some selection distributions a more reliable estimate of the population mean will happen by replacing after each draw. We show for selection distributions lying in a certain polytope the classical result prevails.

This is joint work with Fred Torcaso.

**Time:** Friday, October 7, 2016, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491