Uncertain population forecasting

"Errors in population forecasts arise from errors in the jump-off population and errors in the predictions of future vital rates. The propagation of these errors through the linear (Leslie) growth model is studied, and prediction intervals for future population are developed. For U.S. national forecasts, the prediction intervals are compared with the U.S. Census Bureau's high-low intervals." In order to assess the accuracy of the predictions of vital rates, the authors "derive the predictions from a parametric statistical model and estimate the extent of model misspecification and errors in parameter estimates. Subjective, expert opinion, so important in real forecasting, is incorporated with the technique of mixed estimation. A robust regression model is used to assess the effects of model misspecification."     

The relationship between the length of the base period and population forecast errors

"The base period of a population forecast is the time period from which historical data are collected for the purpose of forecasting future population values. The length of the base period is one of the fundamental decisions made in preparing population forecasts, yet very few studies have investigated the effects of this decision on population forecast errors. In this article the relationship between the length of the base period and population forecast errors is analyzed, using three simple forecasting techniques and data from 1900 to 1980 for states in the United States. It is found that increasing the length of the base period up to 10 years improves forecast accuracy, but that further increases generally have little additional effect. The only exception to this finding is long-range forecasts of rapidly growing states, in which a longer base period substantially improves forecast accuracy for two of the forecasting techniques."     

Tests of forecast accuracy and bias for county population projections

"This article deals with the forecast accuracy and bias of population projections for 2,971 counties in the United States. It uses three different projection techniques and data from 1950, 1960, 1970, and 1980 to make two sets of 10-year projections and one set of 20-year projections. These projections are compared with census counts to determine forecast errors. The size, direction, and distribution of forecast errors are analyzed by size of place, rate of growth, and length of projection horizon. A number of consistent patterns are noted, and an extension of the empirical results to the production of confidence intervals for population projections is considered." A comment by Paul M. Beaumont and Andrew M. Isserman is included (pp. 1,004-9) together with a rejoinder by the author (pp. 1,009-12). This is a revised version of a paper presented at the 1986 Annual Meeting of the Population Association of America (see Population Index, Vol. 52, No. 3, Fall 1986, p. 456).     

Total error in PES estimates of population

"We describe a methodology for estimating the accuracy of dual systems estimates (DSE's) of population, census estimates of population, and estimates of undercount in the census. The DSE's are based on the census and a post-enumeration survey (PES). We apply the methodology to the 1988 dress rehearsal census of St. Louis and east-central Missouri and we discuss its applicability to the 1990 [U.S.] census and PES. The methodology is based on decompositions of the total (or net) error into components, such as sampling error, matching error, and other nonsampling errors. Limited information about the accuracy of certain components of error, notably failure of assumptions in the 'capture-recapture' model, but others as well, lead us to offer tentative estimates of the errors of the census, DSE, and undercount estimates for 1988. Improved estimates are anticipated for 1990." Comments are included by Eugene P. Ericksen and Joseph B. Kadane (pp. 855-7) and Kenneth W. Wachter and Terence P. Speed (pp. 858-61), as well as a rejoinder by Mulry and Spencer (pp. 861-3).     

Ratio and product methods of estimation of population mean in the presence of correlated measurement errors

The properties of the estimators of population mean arising from the ratio and product methods of estimation in the context of sample surveys have been analyzed in this paper when the observations on both the study and auxiliary variables are contaminated with measurement errors. The measurement errors in both the variables are also correlated. The properties of the ratio and product estimators along with the sample mean under the influence of measurement errors are derived and studied. The properties of the estimators in finite samples are studied through Monte-Carlo simulation and its findings are reported.     

An evaluation of population projection errors for census tracts

"In this article we evaluate the accuracy and bias of projections of total population and population by age group for census tracts in three counties in Florida. We use [U.S. census] data from 1970 and 1980 and several simple extrapolation techniques to produce projections for 1990; we then compare these projections with 1990 census counts and evaluate the differences. For the total sample, we find mean absolute errors of 17%-20% for the three most accurate techniques for projecting total population and find no indication of overall bias. For individual age groups, mean absolute errors range from 20%-29%." This is a revised version of a paper presented at the 1993 Annual Meeting of the Population Association of America.     

Estimating the population mean in the case of missing data using simple random sampling

In this paper, we suggest three new ratio estimators of the population mean using quartiles of the auxiliary variable when there are missing data from the sample units. The suggested estimators are investigated under the simple random sampling method. We obtain the mean square errors equations for these estimators. The suggested estimators are compared with the sample mean and ratio estimators in the case of missing data. Also, they are compared with estimators in Singh and Horn [Compromised imputation in survey sampling, Metrika 51 (2000), pp. 267–276], Singh and Deo [Imputation by power transformation, Statist. Papers 45 (2003), pp. 555–579], and Kadilar and Cingi [Estimators for the population mean in the case of missing data, Commun. Stat.-Theory Methods, 37 (2008), pp. 2226–2236] and present under which conditions the proposed estimators are more efficient than other estimators. In terms of accuracy and of the coverage of the bootstrap confidence intervals, the suggested estimators performed better than other estimators.     

Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response

Most of the research work in the theory of survey sampling only deals with the sampling errors under the assumptions: (i) there is a complete response and (ii) recorded information from individuals is correct but in practice it is not always true. Non-sampling errors like non-response and measurement errors (MEs) mostly creep into the survey and become more influential for estimators than sampling errors. Considering this practical situation of non-response and MEs jointly, we proposed an optimum class of estimators for population mean under simple random sampling using conventional and non-conventional measures. Bias and mean square error of the proposed estimators are derived up to first degree of approximation. Moreover, a simulation study is conducted to assess the performance of new estimators which proves that proposed estimators are more efficient than the traditional Hansen and Hurwitz estimator and other competing estimators.     

On estimating the mean of the selected population with unknown variance

This paper compares four estimators of the mean of the selected population from two normal populations with unknown means and common but unknown variance. The selection procedure is that the population yielding the largest sample mean is selected. The four estimators considered are invariant under both location and scale transformations. The bias and mean square errors of the four estimators are computed and compared. The conclusions are close to those reported by Dahiya ‘1974’, even for small sample sizes     

The accuracy of population projections

A review of past population projection errors is presented as a means for constructing confidence intervals for future projections. The author first defines a statistic to measure projection errors independent of the size of population and the length of the projection period. A sample of U.S. and U.N. projections is used to show that the distributions of components of the error statistic are relatively stable. This information is then used to construct confidence intervals for the U.S. population up to the year 2000.     

A review and evaluation of the housing unit method of population estimation

"The housing unit (HU) method is used by public and private agencies throughout the United States to make local population estimates. This article describes many of the different types of data and techniques that can be used in applying the HU method, and it discusses the strengths and weaknesses of each. Empirical evidence from four different states is provided, comparing the accuracy of HU population estimates with the accuracy of other commonly used estimation techniques. Several conclusions are drawn regarding the usefulness of the HU method for local population estimation."     

Statistical Properties of Model-Based Signal Extraction Diagnostic Tests

The problem of choosing the loss function in the Bayesian problem of many hypotheses testing is considered. It is shown that linear and quadratic loss functions are the most-used ones. For any kind of loss function, the risk function in the Bayesian problem of many hypotheses testing contains the errors of two kinds. The Bayesian decision rule minimizes the total effect of these errors. The share of each of them in the optimal value of risk function is unknown. When solving many important problems, the results caused by different errors significantly differ from each other. Therefore, it is necessary to guarantee the limitation on the most undesirable kind of these errors and to minimize the errors of the second kind. For solving these problems, this article are states and solves conditional Bayesian tasks of testing many hypotheses. The results of sensitivity analysis of the classical and conditional Bayesian problems are given and their advantages and drawbacks are considered.     

Discussion

A number of studies have investigated the numerical reliability of the GAUSS Mathematical and Statistical System by Aptech Inc. Those studies identified several critical accuracy errors for different computational methods. We conducted comprehensive tests of this widely used package on estimation, statistical distributions, and random number generation and found that GAUSS 8.0 still has serious problems, especially with statistical distributions and random number generation.     

Exact and Approximate Distributions of the Maximum Likelihood Estimate in a Simple Factor Analysis Model

We study a factor analysis model with two normally distributed observations and one factor. In the case when the errors have equal variance, the maximum likelihood estimate of the factor loading is given in closed form. Exact and approximate distributions of the maximum likelihood estimate are considered. The exact distribution function is given in a complex form that involves the incomplete Beta function. Approximations to the distribution function are given for the cases of large sample sizes and small error variances. The accuracy of the approximations is discussed     

The design of experiments for correlated error structures: Layout and robustness

Observations with correlated error structures are sometimes unavoidable. Appropriate designs and analyses are reviewed for such situations. Serious problems can occur if conventional designs and analyses are used when correlated errors and layout are ignored or when the error structure is not known. Robust designs are discussed which guard against these problems.     

Testing purchasing power parity: some evidence of the effects of transaction costs

Empirical tests of purchasing power parity often recognize the problems created by simultaneous equations, but seldom recognize the effects of measurement error or transaction costs. Presumably because most researchers believe that they are unimportant. We present evidence that shows that measurement error and transaction costs and create serious econometric problems for testing purchasing power parity. One effect of these problems is that conventional tests of purchasing power parity can accept PPP when predictive errors are relatively large and reject it when predictive errors are relatively small. Another effect is to bias test of cointegration toward accepting the null of no cointegration between exchange rates and relative price indexes. We also construct a simple model of the determination of exchange rates that shows how transaction costs lead to regression switiching.     

Estimation of population mean in two-occasion successive sampling

In the present article, we have proposed some classes of estimators based on transformed auxiliary variable. The biases and mean squared errors (MSEs) of the proposed estimators have been obtained. The proposed estimators have been compared with simple mean estimator when there is no matching and the optimum estimator, which is a combination of the means of the matched and unmatched portion of the sample at the second occasion. Optimum replacement policy and the efficiency of the proposed estimators have been discussed. Theoretical results are well supported with an empirical study.     

Computational and statistical efficiency of semiparametric gls estimators

In this note, we report a dramatic improvement in the computational efficiency of semiparametric generalized least squares(SGLS) estimation. Computation of SGLS estimates no longer presents serious problems with data sets of moderate size. We also correct a numerical error in the standard errors of the SGLS estimates reported in our recent paper in this journal (Horowitz and Neumann, 1987). The corrected standard errors of SGLS are comparable to those we reported for quantile estimates.     

Computational and statistical efficiency of semiparametric gls estimators

In this note, we report a dramatic improvement in the computational efficiency of semiparametric generalized least squares(SGLS) estimation. Computation of SGLS estimates no longer presents serious problems with data sets of moderate size. We also correct a numerical error in the standard errors of the SGLS estimates reported in our recent paper in this journal (Horowitz and Neumann, 1987). The corrected standard errors of SGLS are comparable to those we reported for quantile estimates.