Department of Statistics Seminar
North Carolina State University

presents

Dr. Tommy Wright

U. S. Census Bureau

"Simple Proof of an Important Inequality for Probability Sampling"

ABSTRACT

The U. S. Census Bureau conducts many nationwide probability sample surveys to estimate monthly, quarterly, and annual characteristics about the economy and people of the United States. It is known that sampling and estimated results can be made more efficient by use of observed auxiliary information (variables) that are highly correlated with yet unobserved variables of interest. Simple examples will illustrate how gains in efficiency can be realized before sampling (e.g., stratification), during sampling (e.g., probability proportional to size sampling), and after sampling (e.g., ratio estimation). Thus correlation is an important and useful concept in probability sampling. Using an elementary but important identity associated with Lagrange, this talk presents a simple proof (Wright, 1992) that Pearson's correlation coefficient r is always between -1 and 1 and that all points (x,y) fall on a straight line if and only if the square of r is 1. Another application of the identity is given to the problem of optimal allocation when sampling from a finite universe. The last third of the talk will focus on mention of some problem areas and challenges in data collection and dissemination where correlated data may help (disclosure avoidance, small area estimation, imputation for missing data) and that deserve more attention from statisticians. The presentation is suitable for a wide audience with minimal background.

Friday, April, 29, 2005

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.