Large sample interval estimation for the logarithmic series distribution

It is assumed that a large random sample of fixed size n is drawn from a logarithmic series distribution with parameter $tH and that it is desired to estimate e by means of two-sided confidence interval. Using asymptotic results, charts of confidence intervals are prepared for n = 50, 100, 200, 500 and 1,000, and confidence coefficients 0.90 and 0.95.     

Latino,Asian, and black segregation in U.S. metropolitan areas: Are multiethnic metros different*

This study examines 1990 residential segregation levels and 1980–1990 changes in segregation for Latinos, Asians, and blacks in U.S. metropolitan areas. It also evaluates the effect of emerging multiethnic metropolitan area contexts for these segregation patterns. While black segregation levels are still well above those for Latinos and Asians, there is some trend toward convergence over the decade. More than half of the areas increased their Latino segregation levels over the 1980s, and almost three-fourths increased their Asian segregation levels. In contrast, black segregation levels decreased in 88%ofmetropolitan areas. Multiethnic metropolitan area context is shown to be important for internal segregation dynamics. Black segregation levels are lower, and were more likely to decline in multiethnic metropolitan areas and when other minority groups grew faster than blacks. Latino segregation was also more likely to decline in such areas, and declines in both Latino and Asian segregation were greater when other minority groups were growing. These findings point up the potential for greater mixed-race and mixed-ethnicity coresidence in the neighborhoods of multiethnic metropolitan areas.     

THE CONVERGENCE RATE OF SEQUENTIAL FIXED-WIDTH CONFIDENCE INTERVALS FOR REGULAR FUNCTIONALS

Let X₁X₂,.be i.i.d. random variables and let U_n= (n r)^-1S?^(n,r) h (X_i1,., X_ir,) be a U-statistic with EU_n= v, v unknown. Assume that g(X₁) =E[h(X₁,.,X_r) - v |X₁]has a strictly positive variance s?². Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S²_n be the Jackknife estimator of n Var U_n. Consider the stopping times N(d)= min {n: S²_n: + n^-1≤²a^-2},d > 0, and a confidence interval for v of length 2d,of the form I_n,d= [U_n,-d, Un + d]. We assume that Var U_n is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let I_N(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. lim_{d → 0}P(v ∈ I_N(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ I_N(d),d) converges to α is investigated. We obtain that |P(v ∈ I_N(d),d) - α| = 0 (d^{1/2-(1+k)/2(1+m)}), d → 0, where K = max {0,4 - m}, under the condition that E|h(X₁, X_r)|^m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981).     

Migration differentials by education and occupation: Trends and variations

The effects of education on current migration propensities in the United States are examined for each age group, and an estimate is made of how these age-specific differentials cumulate over a lifetime in determining the number of times that individuals at different educational levels can expect to move over the course of their lives. The independent effects of age, education, and occupation are also examined. Two other sections investigate trends in educational selectivity of migration in the United States and international comparisons of occupational differences in migration.