Dual System Estimation Research Articles

Model bias effects in small area coverage error estimation

For estimation of population totals, dual system estimation (d.s.e.) is often used. Such a procedure is known to suffer from bias under certain conditions. In the following, a simple model is proposed that combines three conditions under which bias of the DSE can result. The conditions relate to response correlation, classification and matching error. The resulting bias is termed model bias. The effects of model bias and synthetic bias in a small area estimation application are illustrated. The illustration uses simulated population data

Empirical Bayes Estimation of Undercount in the Decennial Census

Abstract On April 1, 1990, the decennial census for the United States will be conducted by the U.S. Bureau of the Census. By December 31, 1990, the Census Bureau is specified by law to submit state population counts for the purpose of reapportionment of the U.S. House of Representatives, and by March 31, 1991, to submit small-area population counts for the purpose of redistricting. Census counts are used in a variety of other ways: for revenue-sharing formulas between different levels of government, for demographic projections, as a base for morbidity and mortality statistics, and so forth. Inaccurate census counts should be cause for concern for the whole nation. It is universally acknowledged that certain groups of people (e.g., young black males, illegal aliens, etc.) are harder to count than others. If the hard-to-count groups are distributed in equal proportions throughout the United States, there would be far less controversy over what to do about the uncounted people. As it is, many large American cities such as Chicago, Detroit, New York, and Los Angeles feel they are losing federal funds because their cities contain larger numbers of the groups that are less well counted. And certain states such as New York and California feel they are underrepresented in Congress, to the benefit of Midwestern states such as Indiana and Iowa. Census undercount is defined simply as the difference between the true count and the census count, expressed as a percentage of the true count. Small-area estimation of this undercount is considered here, using empirical Bayes methods based on a new and, it is argued, more realistic model than has been used before. Grouping of like subareas from areas such as states, counties, and so on into strata is a useful way of reducing the variance of undercount estimators. By modeling the subareas within a stratum to have a common mean and variances inversely proportional to their census counts, and by taking into account sampling of the areas (e.g., by dual-system estimation), empirical Bayes estimators that compromise between the (weighted) stratum average and the sample value can be constructed. The amount of compromise is shown to depend on the relative importance of stratum variance to sampling variance. These estimators are evaluated at the state level (51 states, including Washington, D.C.) and stratified on race/ethnicity (3 strata) using data from the 1980 postenumeration survey (PEP 3–8, for the noninstitutional population).

Empirical Bayes Estimation of Undercount in the Decennial Census

Empirical Bayes methods are used to estimate the extent of the undercount at the local level in the 1980 U.S. census. "Grouping of like subareas from areas such as states, counties, and so on into strata is a useful way of reducing the variance of undercount estimators. By modeling the subareas within a stratum to have a common mean and variances inversely proportional to their census counts, and by taking into account sampling of the areas (e.g., by dual-system estimation), empirical Bayes estimators that compromise between the (weighted) stratum average and the sample value can be constructed. The amount of compromise is shown to depend on the relative importance of stratum variance to sampling variance. These estimators are evaluated at the state level (51 states, including Washington, D.C.) and stratified on race/ethnicity (3 strata) using data from the 1980 postenumeration survey (PEP 3-8, for the noninstitutional population)."

The effects of correlation and matching error on dual system estimation

In a previous paper, Isaki (1986), it was shown that the relative bias of the dual system estimator can be substantially reduced in the presence of correlation of responses. Two alternative estimators were compared with the usual dual system estimator assuming no matching error. In the following, a simple matching error model is used to compare the three dual system estimators with respect to bias and mean square error in the presence of correlation. For the parameter values used we found that the usual dual system estimator is competitive with that of the alternative estimators.

Mas of toe dual system estimator and some alternatives

A dual system estimator was used to estimate the coverage of the 1980 Census, The estimator assumes that the response of a randomly selected individual to one system is independent of its response to the other system. When this is not the case, the resulting correlation induces a bias in the estimator. Several alternative estimators are proposed to handle this situation under a simple model and their average absolute relative errors are compared under two frequency distributions.

Alternative Dual System Network Estimators

"When there are two or more data systems and none of them enumerates the population at an acceptable completeness level, concern about the bias due to underenumeration suggests an estimator which makes joint use of data compiled by the combined imperfect data systems. Conventional dual system estimators are based on the existence of two separate data collection systems. Dual system network estimators assume a main survey and a follow-up quality check survey. The main survey adopts a multiplicity counting rule that combines two mutually exclusive partial counting rules." Three dual system network estimators are presented. "One was previously proposed by Sirken (1979) and is the natural analogue of the conventional dual system estimator. The two other estimators are proposed as potential improvements, although neither of them is the natural analogue of the conventional dual system estimator. The design effects of the three estimators are compared analytically and empirically with one another, and with those of the single system conventional and network estimators." (summary in FRE)

Book Reviews

Abstract Abstract The Costs of Higher Education: How Much Do Colleges and Universities Spend Per Student and How Much Should They Spend?: Howard R. Buwen. San Francisco, Calif.: Jossey-Bass, 1980, xxiii + 287 pp. $15.95 (paperback). Reviewed by: Werner Z. Hirsch A Summary of Reports and Recommendations: The Carnegie Council on Policy Studies in Higher Education. San Francisco, Calif.: Jossey-Bass, 1980, x + 489 pp. $27.95 (paperback). Reviewed by: Charles S. Benson Sampling Methods for Censuses and Surveys (4th ed.): Frank Yates. New York: Macmillan, 1981. xvi + 458 pp. $55.00. Reviewed by: Charles H. Proctor Developments in Dual System Estimation of Population Size and Growth: Karol J. Krotki (ed.). Edmonton, Alberta, Canada: The University of Alberta Press, 1978. xviii + 260 pp. $17.50 (paperback). Reviewed by: Charles D. Cowan An Introduction to Mathematical Risk Theory: Hans U. Gerber. Philadelphia: S. S. Huebner Foundation for Insurance Education, 1979. xv + 164 pp. $15.95 (paperback). Reviewed by: E. Benton Cobb Mathematical Programming for Operations Researchers and Computer Scientists: Albert G. Holzman (ed.). New York: Marcel Dekker, 1981. xii + 373 pp. $45.00. Reviewed by: Patrick L. Brockett Techniques in Operational Research Vol. 2: Models, Search and Randomization.: Brian Conolly. New York: Ellis Horwood Limited Publishers (Division of John Wiley & Sons), 1981. 338 pp. $77.95. Reviewed by: Patrick L. Brockett Linear Programming: Algorithms and Applications.: S. Vajda. London, New York: Chapman and Hall, 1981. vii + 150 pp. $9.95 (paperback). Reviewed by: Salih O. Duffua Probabilistic Mechanical Design.: Edward B. Haugen. New York: John Wiley, 1980. 630 pp. $42.50. Reviewed by: Emil H. Jebe Engineering Applications of Correlation and Spectral Analysis.: Julius S. Bendat and Allan G. Piersol. New York: John Wiley, 1980. xiv + 302 pp. $29.95. Reviewed by: H. Dennis Tolley Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach.: Marcel F. Neuts. Baltimore, The Johns Hopkins University Press, 1981. xiii + 322 pp. $32.50. Reviewed by: C. C. Heyde Probability Inequalities in Multivariate Distributions.: Y. L. Tong. New York: Academic Press, 1980. xiii + 239 pp. $29.50. Reviewed by: Morris L. Eaton Applied Probability.: Frank A. Haight. New York: Plenum Press, 1981. xi + 290 pp. $35.00. Reviewed by: Luke Tierney Multinomial Probit: The Theory and Its Application to Demand Forecasting.: Carlos Daganzo. New York: Academic Press, 1979. xiv + 222 pp. $24.50. Reviewed by: B. B. Bhattacharyya Finite Mixture Distributions.: B. S. Everitt and D. J. Hand. New York: Methuen, 1981. xi + 143 pp. $14.95. Reviewed by: Stephen Vardeman Computational Probability.: P.M. Kahn (ed.). New York: Academic Press, 1980. xi + 340 pp. $21.00. Reviewed by: William F. Eddy Data Reduction: Analysing & Interpreting Statistical Data (revised reprint).: A.S.C. Ehrenberg. New York: John Wiley, 1978. xvii + 391 pp. Reviewed by: Brian L. Joiner Introductory Statistics for the Behavioral Sciences (4th ed.): Robert K. Young and Donald J. Veldman. New York: Holt, Rinehart and Winston, 1981. x + 687 pp. $19.95. Reviewed by: M. C. Shelley Basic Statistics for the Behavioral Sciences.: Kenneth Pfeiffer and James N. Olson. New York: Holt, Rinehart and Winston, 1981. xv + 444 pp. $19.95. Selltiz, Wrightsmαn and Cook's Research Methods in Social Relations (4th ed.): Louise H. Kidder. New York: Holt, Rinehart and Winston, 1981. xii + 483 pp. $14.95. Regression: A Second Course in Statistics.: Thomas H. Wonnacott and Ronald J. Wonnacott. New York: John Wiley, 1981. xix + 556 pp. $26.95. Reviewed by: Michael C. Costanza Intermediate Statistical Methods: G. Barrie Wetherill. London: Chapman and Hall, 1981. xv + 390 pp. $25.00. Reviewed by: Peter C. O'Brien Quantitive Methods for Decision Making in Business.: Richard E. Trueman. New York: Holt, Rinehart and Winston, 1981. 733 pp. Reviewed by: Anne B. Koehler Applied Statistical Techniques.: K.D.C. Stoodley, T. Lewis, and C.L.S. Stainton. New York: Halsted Press, 1980. 310 pp. $56.95. Reviewed by: George Thomas

Developments in Dual System Estimation of Population Size and Growth.

Developments in Dual System Estimation of Population Size and Growth.

Developments in Dual System Estimation of Population Size and Growth.

Developments in Dual System Estimation of Population Size and Growth.

Developments in Dual System Estimation of Population Size and Growth.

Developments in Dual System Estimation of Population Size and Growth.

Book reviews/Comptes rendus

Book reviewed in this article:DANIELGLENDAY, HUBERTGUINDON, and ALLAN TUROWETZ (eds.), Modernization and the Canadian State.GORDON BOWKER and JOHN CARRIER. Race and Ethnic Relations: Sociological Readings.JOSEPH F. KRAUTER and MORRIS DAVIS. Minority Canadians: Ethnic Group.PAT ARMSTRONG and HUGH ARMSTRONG. The Double Ghetto: Canadian Women and Their Segregated Work.LEROY O. STONE and CLAUDE MARCEAU. Canadian Population Trends and Public Policy Through the 1980's.KAROL KROTKI (ed.). Developments in Dual System Estimation of Population Size and Growth.MARTIN RULMER (ed.). Mining and Social Change.M. SILVERMAN and R.F. SALISBURY. A House Divided.? anthropological Studies of Factionalism: Social and Economic Papers No. 9. Institute of Social and Economic Research.RENEE G. KASINSKY. Refugees From Militarism: Draft‐age Americans in Canada.

Development in Dual System Estimation of Population Size and Growth

Development in Dual System Estimation of Population Size and Growth