Cramér-Rao lower bounds for estimators based on censored data

The Cramér-Rao lower bounds for the variances of unbiased estimators based on censored data are given. Useful techniques of evaluation are then derived for these lower bounds. Examples are given to illustrate these techniques. Small-sample comparisons are made between the resulting lower bounds, the variances of the best linear unbiased estimators, and the variances of unbiased esti-mators which are based on the maximum likelihood estimators.     

A review of model selection procedures relevant to the weibull distribution

A number of goodness-of-fit and model selection procedures related to the Weibull distribution are reviewed. These procedures include probability plotting, correlation type goodness-of-fit tests, and chi-square goodness-of-fit tests. Also the Kolmogorow-Smirniv, Kuiper, and Cramer-Von Mises test statistics for completely specified hypothesis based on censored data are reviewed, and these test statistics based on complete samples for the unspecified parameters case are considered. Goodness-of-fit tests based on sample spacings, and a goodness-of-fit test for the Weibull process, is also discussed.

Model selection procedures for selecting between a Weibull and gamma model, a Weibull and lognormal model, and for selecting from among all three models are considered. Also tests of exponential versus Weibull and Weibull versus generalized gamma are mentioned.     

Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

Do Cross-National Differences in the Costs of Children Generate Cross-National Differences in Fertility Rates?

Parity-specific probabilities of having a next birth are estimated from national fertility data and are compared with nation-specific costs of having children as measured by time-budget data, by attitude data from the International Social Survey Program, and by panel data on labor earnings and standard of living changes following a birth. We focus on five countries (the United States, the former West Germany, Denmark, Italy, and the United Kingdom), whose fertility rates span the observed fertility range in the contemporary industrialized world and whose social welfare and family policies span the conceptual space of standard welfare-state typologies. Definitive conclusions are difficult because of the multiple dimensions on which child costs can be measured, the possibility that child costs affect both the quantum and the tempo of fertility, the relatively small fertility differences across industrialized nations, and the inherent small-N problem resulting from nation-level comparisons. Empirical analysis, however, supports the assertion that institutionally driven child costs affect the fertility patterns of industrialized nations.     

Fertility and women's employment reconsidered: a macro-level time-series analysis for developed countries, 1960-2000

This paper examines causality and parameter instability in the long-run relationship between fertility and women's employment. This is done by a cross-national comparison of macro-level time-series data from 1960 to 2000 for France, West Germany, Italy, Sweden, the UK, and the USA. By applying vector error correction models (a combination of Granger-causality tests with recent econometric time-series techniques) we find causality in both directions. This finding is consistent with simultaneous movements of both variables brought about by common exogenous factors such as social norms, social institutions, financial incentives, and the availability and acceptability of contraception. We find a negative and significant correlation until about the mid-1970s and an insignificant or weaker negative correlation afterwards. This result is consistent with a recent hypothesis in the demographic literature according to which changes in the institutional context, such as changes in childcare availability and attitudes towards working mothers, might have reduced the incompatibility between child-rearing and the employment of women.     

Probability of correct selection of weibull versus gamma based on livelihood ratio

This paper proposes the use of tne likelihood ratio statistic in choosing between a Neibull or gamma model, values of the probability of correct seeiection are obtained by Monte Carlo simulation. This method provides some basis for decision even when the sample size is small. The technique is applied to four sets of data from the literature.     

Crime and the Decline of Unions

In this paper we investigate the relationship between union membership and crime. Using state level data between 1993 and 2006, we find the elasticity of crime with respect to union membership is roughly −0.5. From our results, we predict the decline in union membership has increased crime by 15 per cent since 1993. Furthermore, we find the elasticity between union jobs and crime is larger in absolute value when using an instrumental variable approach to control for the impact unions have on labor market efficiency.     

Confidence Bounds For The Binomial N Parameter: A Classical Approach

A method is described for finding the distribution of an estimator for the parameter N of the binomial distribution in order to construct confidence bounds for N. Using a partition generating algorithm, tables of lower confidence bounds are provided for a range of values, illustrating the nature of the problems involved in estimating the parameters. Examples are considered and the lower bounds compared with the convenient approximate bounds due to Hoel (1947), suggesting the approximate bounds are appropriate more generally then originally thought.