Federal statistics in a complex environment: the case of the 1980 census

A discussion of the 1980 U.S. census is presented. The authors suggest that the taking of a national census is not just a statistical exercise, but an exercise involving ethics, epistemology, law, and politics. They contend that conducting a national census can be defined as an ill-structured problem in which the various complexities imposed by multidisciplinarity cannot be separated. "The 1980 census is discussed as an ill-structured problem, and a method for treating such problems is presented, within which statistical information is only one component."     

Ethnicity,immigration process and short-term occupational mobility

The relationship between the ethnic characteristics of immigrants to the United States and their occupational mobility in the short term is explored. The data concern the period 1965-1970 and are taken from the 1970 census. The results indicate that race and sociocultural distance have important effects on occupational mobility. The study also shows that if educational status is controlled, the performance of Asian immigrants is more similar to that of blacks or Hispanics than it is to that of whites. (summary in FRE, SPA)     

Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

The paper presents a general method of designing constant-factor approximation algorithms for some discrete optimization problems with assignment-type constraints. The core of the method is a simple deterministic procedure of rounding of linear relaxations (referred to as pipage rounding). With the help of the method we design approximation algorithms with better performance guarantees for some well-known problems including MAXIMUM COVERAGE, MAX CUT with given sizes of parts and some of their generalizations.     

Integrating commercial and residential pickup and delivery networks: A case study

This paper presents a strategic analysis of the network design problem faced by pickup and delivery companies operating in metropolitan areas and serving two or more classes of customers. The focus is on a division that treats commercial and residential customers separately, a situation motivated by their respective geographic densities and the size and frequency of their demand. In constructing driver work areas, it is necessary to take into account expected demand, vehicle capacity, time on the road, and the aspect ratio of the individual territories. This leads to a capacitated clustering problem with side constraints that has been the subject of intense research over the last decade.     

How do marital status,work effort,and wage rates interact?

How marital status interacts with men's earnings is an important analytic and policy issue, especially in the context of debates in the United States over programs that encourage healthy marriage. This paper generates new findings about the earnings-marriage relationship by estimating the linkages among flows into and out of marriage, work effort, and wage rates. The estimates are based on National Longitudinal Survey of Youth panel data, covering 23 years of marital and labor market outcomes, and control for unobserved heterogeneity. We estimate marriage effects on hours worked (our proxy for work effort) and on wage rates for all men and for black and low-skilled men separately. The estimates reveal that entering marriage raises hours worked quickly and substantially but that marriage's effect on wage rates takes place more slowly while men continue in marriage. Together; the stimulus to hours worked and wage rates generates an 18%-19% increase in earnings, with about one-third to one-half of the marriage earnings premium attributable to higher work effort. At the same time, higher wage rates and hours worked encourage men to marry and to stay married. Thus, being married and having high earnings reinforce each other over time.     

Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

Decision Making in `Random in a Broad Sense' Environments

It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.     

Binary probability maps using a hidden conditional autoregressive Gaussian process with an application to Finnish common toad data

The Finnish common toad data of Heikkinen and Hogmander are reanalysed using an alternative fully Bayesian model that does not require a pseudolikelihood approximation and an alternative prior distribution for the true presence or absence status of toads in each 10 km×10 km square. Markov chain Monte Carlo methods are used to obtain posterior probability estimates of the square-specific presences of the common toad and these are presented as a map. The results are different from those of Heikkinen and Hogmander and we offer an explanation in terms of the prior used for square-specific presence of the toads. We suggest that our approach is more faithful to the data and avoids unnecessary confounding of effects. We demonstrate how to extend our model efficiently with square-specific covariates and illustrate this by introducing deterministic spatial changes.     

On the minimum expected quantity for the validity of the chi-squared test in 2 2 2 tables

A 2 2 2 contingency table can often be analysed in an exact fashion by using Fisher's exact test and in an approximate fashion by using the chi-squared test with Yates' continuity correction, and it is traditionally held that the approximation is valid when the minimum expected quantity E is E S 5. Unfortunately, little research has been carried out into this belief, other than that it is necessary to establish a bound E>E*, that the condition E S 5 may not be the most appropriate (Martín Andrés et al., 1992) and that E* is not a constant, but usually increasing with the growth of the sample size (Martín Andrés & Herranz Tejedor, 1997). In this paper, the authors conduct a theoretical experimental study from which they ascertain that E* value (which is very variable and frequently quite a lot greater than 5) is strongly related to the magnitude of the skewness of the underlying hypergeometric distribution, and that bounding the skewness is equivalent to bounding E (which is the best control procedure). The study enables estimating the expression for the above-mentioned E* (which in turn depends on the number of tails in the test, the alpha error used, the total sample size, and the minimum marginal imbalance) to be estimated. Also the authors show that E* increases generally with the sample size and with the marginal imbalance, although it does reach a maximum. Some general and very conservative validity conditions are E S 35.53 (one-tailed test) and E S 7.45 (two-tailed test) for alpha nominal errors in 1% h f h 10%. The traditional condition E S 5 is only valid when the samples are small and one of the marginals is very balanced; alternatively, the condition E S 5.5 is valid for small samples or a very balanced marginal. Finally, it is proved that the chi-squared test is always valid in tables where both marginals are balanced, and that the maximum skewness permitted is related to the maximum value of the bound E*, to its value for tables with at least one balanced marginal and to the minimum value that those marginals must have (in non-balanced tables) for the chi-squared test to be valid.