摘要:

A bivariate distribution functionH(x, y) with marginalsF(x) andG(y) is said to be generated by an Archimedean copula if it can be expressed in the formH(x, y) = ϕ–1[ϕ{F(x)} + ϕ{G(y)}] for some convex, decreasing function ϕ defined on [0, 1] in such a way that ϕ(1) = 0. Many well-known systems of bivariate distributions belong to this class, including those of Gumbel, Ali-Mikhail-Haq-Thélot, Clayton, Frank, and Hougaard. Frailty models also fall under that general prescription. This article examines the problem of selecting an Archimedean copula providing a suitable representation of the dependence structure between two variatesXandYin the light of a random sample (X1,Y1), …, (Xn,Yn). The key to the estimation procedure is a one-dimensional empirical distribution function that can be constructed whether the uniform representation ofXandYis Archimedean or not, and independently of their marginals. This semiparametric estimator, based on a decomposition of Kendall's tau statistic, is seen to be √n-consistent, and an explicit formula for its asymptotic variance is provided. This leads to a strategy for selecting the parametric family of Archimedean copulas that provides the best possible fit to a given set of data. To illustrate these procedures, a uranium exploration data set is reanalyzed. Although the presentation is restricted to problems involving a random sample from a bivariate distribution, extensions to situations involving multivariate or censored data could be envisaged.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476372

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476373

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The Census Bureau has struggled for decades with the problem of undercount in the population census. Although the net national undercount has been greatly reduced in recent censuses, it still tends to display important differences by race, ethnic origin, and geographic location. The 1990 Post-Enumeration Survey (PES) was designed to produce Census tabulation of states and local areas corrected for the undercount or overcount of population. The PES was the subject of litigation between the federal government and a coalition of states and local governments. Because of the litigation, the PES was conducted under specific guidelines concerning timing, prespecification, and quality. The PES measured Census omissions by independently interviewing a stratified sample of the population. It measured Census erroneous enumerations by a dependent reinterview of a sample of Census records and by searching the records for duplicates. A dual-system estimator (DSE) was used to prepare estimates of the population by post-strata. Adjustment factors were computed as the ratio of these estimates to the census count. These factors were smoothed using a generalized linear model and then applied to the census counts by block and post-strata to produce adjusted census estimates. Although the government decided not to release these numbers as the official census results, the Census Bureau has conducted further research to improve these estimates to incorporate them into the postcensal estimates program. The revisions have included new post-strata and corrections of errors found in the original estimates. The results of the PES show a differential undercount by race and ethnic group and by owner/nonowner status. They also demonstrate differences in undercount by geography.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476374

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This article presents estimates of net coverage of the national population in the 1990 census, based on the method of demographic analysis. The general techniques of demographic analysis as an analytic tool for coverage measurement are discussed, including use of the demographic accounting equation, data components, and strengths and limitations of the method. Patterns of coverage displayed by the 1990 estimates are described, along with similarities or differences from comparable demographic estimates for previous censuses. The estimated undercount in the 1990 census was 4.7 million, or 1.85%. The undercount of males (2.8%) was higher than for females (.9%), and the undercount of Blacks (5.7%) exceeded the undercount of Non-Blacks (1.3%). Black adult males were estimated to have the highest rate of undercounting of all groups. Race-sex-age patterns of net coverage in the 1990 census were broadly similar to patterns in the 1980 and 1970 censuses. A final section presents the results of the first statistical assessment of the uncertainty in the demographic coverage estimates for 1990.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476375

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476376

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476377

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476378

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

In July 1991 the Census Bureau recommended to its parent agency, the Department of Commerce, that the 1990 census be adjusted for undercount. The Secretary of Commerce decided not to adjust, however. Those decisions relied at least partly on the Census Bureau's analyses of the accuracy of the census and of the proposed undercount adjustments based on the Post-Enumeration Survey (PES). Error distributions for the nation, states, and smaller geographic units were estimated with extensions of methods applied to test censuses. To summarize and assess the relative importance of errors in different units, the Census Bureau used aggregate loss functions. This article describes the total error analysis and loss function analysis of the Census Bureau. In its decision not to adjust the census, the Department of Commerce cited different criteria than aggregate loss functions. Those criteria are identified and discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476379

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The 1990 census and Post-Enumeration Survey produced census and dual system estimates (DSE) of population by domain, together with an estimated sampling covariance matrix of the DSE. Estimates of the bias of the DSE were derived from various PES evaluation programs. Of the three sources, the unadjusted census is the least variable but is believed to be the most biased, the DSE is less biased but more variable, and the bias estimates may be regarded as unbiased but are the most variable. This article addresses methods for combining the census, the DSE, and bias estimates obtained from the evaluation programs to produce accurate estimates of population shares, as measured by weighted squared- or absolute-error loss functions applied to estimated population shares of domains. Several procedures are reviewed that choose between the census and the DSE using the bias evaluation data or that average the two with weights that are constant across domains. A multivariate hierarchical Bayes model is proposed for the joint distribution of the undercount rates and the biases of the DSE in the various domains. The specification of the model is sufficiently flexible to incorporate prior information on factors likely to be associated with undercount and bias. When combined with data on undercount and bias estimates, the model yields posterior distributions for the true population shares of each domain. The performance of the estimators was compared through an extensive series of simulations. The hierarchical Bayes procedures are shown to outperform the other estimators over a wide range of conditions and to be robust against misspecification of the models. The various composite estimators, applied to preliminary data from the 1990 Census and evaluation programs, yield similar results that are closer to the DSE than to the census. Analysis of a revised data set yields qualitatively similar estimates but shows that the revised post-stratification improves on the original one.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476380

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Population estimates from the 1990 Post-Enumeration Survey (PES), used to measure decennial census undercount, were obtained from dual system estimates (DSE's) that assumed independence within strata defined by age-race-sex-geography and other variables. We make this independence assumption for females, but develop methods to avoid the independence assumption for males within strata by using national level sex ratios from demographic analysis (DA). This is done by using DSE results for females and the DA sex ratios to determine national level control totals for male population by age-race groups. These control totals are then used to determine some function of the individual strata 2 × 2 table probabilities for males that is assumed constant across strata within age-race groups. One such candidate function is the cross-product ratio, but other functions can be used that lead to different DSEs. We consider several such alternative DSE's, and use DA results for 1990 to apply them to data from the 1990 U.S. census and PES.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476381

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor