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UTILIZING AUXILIARY VARIABLES 'IN SEQUENTIAL RATIO AND REGRESSION ESTIMATION SCHEMES

IP.com Disclosure Number: IPCOM000128253D
Original Publication Date: 1976-Dec-31
Included in the Prior Art Database: 2005-Sep-15
Document File: 11 page(s) / 29K

Publishing Venue

Software Patent Institute

Related People

M.J Doviak: AUTHOR [+4]

Abstract

Ratio and regression estimators for a mean are considered In conjunction with certain sequential sampling schemes. An auxil-lary variable is assumed present and both fixed-cost and fixed--width confidence interval stopping rules are investigated. The asymptotic distributions of the estimators are derived as well as optimal probabilities pertinent to theschemes. Comparisons are nade with results of certain double sampling procedures. Esti-nation of the ratio of two means is also considered and the results of a Monte Carlo simulation are included.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

UTILIZING AUXILIARY VARIABLES 'IN SEQUENTIAL RATIO AND REGRESSION ESTIMATION SCHEMES

By M.J Doviak R. L. Scheaffer

Old Dominion University University of Florida

ABSTRACT

Ratio and regression estimators for a mean are considered In conjunction with certain sequential sampling schemes. An auxil-lary variable is assumed present and both fixed-cost and fixed--width confidence interval stopping rules are investigated. The asymptotic distributions of the estimators are derived as well as optimal probabilities pertinent to theschemes. Comparisons are nade with results of certain double sampling procedures. Esti-nation of the ratio of two means is also considered and the results of a Monte Carlo simulation are included.

INTRODUCTION

Let (X,Y) be a bivariate random variable with distribution fmctlon F* Denote the means of

(Equation Omitted)

respectivelyt

(Equation Omitted)

and let cr and ay, assumed finite, denote ti )orresponding vart- X ances. Also let a denote the coefficient of correlation between

X and Y. Let C and C be the costs incurred in measuring the 0 1 auxiliary variable X and the primary variable Y. respectivelys-on, any sample member. Deciding how to apportion a finite sum of money C between auxiliary variable measurement and primary variable measurement has been investigated by several authors including Cochran 11953]. Tenenbein [1974]jj and Rao [1973]. Optimal values are derived for the various sample sizes associated with these double sampling schemes.

In this paper it Is assumed that all samples are randomly selected from F and that X is measured on each sample member. The primary variable Y is then measured with probability q. That is, Y Is measured on only a subset of the sample. Thus the experimenter does not decide a priori on which sample members to measure Y, but measures Y with probability q after each deter-mination of X. The motivation for measuringX on all sampled units and Y on only a subset is that for many applications C is much less than 0 C1* For examplev X could be,information already available In a file$, such as weekly income for a householdp and Y could be information only obtainable by interviews:19- such as weekly expen- diture for food. Also, ratio and regression estimation of u Y depends upon knowledge of tiX. If LLX is unknowng it can be esti- mated from the larger sample of X's and the ratio or regression technique can still be employed.

Old Dominion University Page 1 Dec 31, 1976

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UTILIZING AUXILIARY VARIABLES 'IN SEQUENTIAL RATIO AND REGRESSION ESTIMATION SCHEMES

For the situation outlined abovep double sampling is often employed. The second samplep an which Y Is measured,, is either

dom sample or a random subsample of the firsto an Independent ran In pract-ice# the second sample is often systematically (or merely haphazardly) selected from the first due to practical convenience.

The sampling scheme outlined below has t...