Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

Nonlinear models of disability and age applied to census data

It is usually considered that the proportion of handicapped people grows with age. Namely, the older the man/woman, the more the level of disability he/she suffers. However, empirical evidence shows that this assessment is not always true, or at least, it is not true in the Spanish population. The study tries to assess the impact of age on disability in Spain. Each gender has been treated separately because it can be shown that men and women have their own pattern of behaviour. Three different methods of estimation have been used to check the link between those variables. The results seem to support the idea that the relationship among age and the intensity of disability is not always direct. One of the concluding remarks in this analysis is that the method of estimation has a great incidence in the final results, especially in central ages between 20 and 80 years old.     

Knowledge extraction from a large on-line survey: a case study for a higher education corporate marketing

For a higher education public institution, young in relative terms, featuring local competition with another private and both long-established and reputed one, it is of great importance to become a reference university institution to be better known and felt with identification in the society it belongs to and ultimately to reach a good position within the European Higher Education Area. These considerations have made the university governors setting up the objective of achieving an adequate management of the university institutional brand focused on its logo and on image promotion, leading to the establishment of a university shop as it is considered a highly adequate instrument for such promotion. In this context, an on-line survey is launched on three different kinds of members of the institution, resulting in a large data sample. Different kinds of variables are analysed through appropriate exploratory multivariate techniques (symmetrical methods) and regression-related techniques (non-symmetrical methods). An advocacy for such combination is given as a conclusion. The application of statistical techniques of data and text mining provides us with empirical insights about the institution members’ perceptions and helps us to extract some facts valuable to establish policies that would improve the corporate identity and the success of the corporate shop.     

Counting strings at height j in Dyck paths

Let τ be an arbitrary lattice path, called in this context string, consisting of two kinds of steps (rises and falls) and let j be a non-negative integer.In this paper, the explicit formula for the generating function F_j associated with the Dyck path statistic “number of occurrences of τ at height j” is evaluated.For the expression of F_j some basic characteristics of the string are used, namely its number of rises, height, depth and periodicity, as well as the generating function of the Catalan numbers.     

A frailty model for (interval) censored family survival data,applied to the age at onset of non-physical problems

Family survival data can be used to estimate the degree of genetic and environmental contributions to the age at onset of a disease or of a specific event in life. The data can be modeled with a correlated frailty model in which the frailty variable accounts for the degree of kinship within the family. The heritability (degree of heredity) of the age at a specific event in life (or the onset of a disease) is usually defined as the proportion of variance of the survival age that is associated with genetic effects. If the survival age is (interval) censored, heritability as usually defined cannot be estimated. Instead, it is defined as the proportion of variance of the frailty associated with genetic effects. In this paper we describe a correlated frailty model to estimate the heritability and the degree of environmental effects on the age at which individuals contact a social worker for the first time and to test whether there is a difference between the survival functions of this age for twins and non-twins.     

Slack-variable models versus Scheffé's mixture models

Slack-variable models are compared against Scheffé's polynomial model for mixture experiments. The notion of model equivalence and the use of various diagnostic measures provide effective tools in making such comparisons, particularly when the experimental region is highly constrained. It is demonstrated that the choice of the best fitting model, through variable selection, depends on which mixture component is selected as a slack variable, and on the size of the fitted model. In addition, the equivalence of two well-known representations of a complete mixture model is shown to be valid. Two numerical examples are presented.     

Nonparametric empirical Bayes for the Dirichlet process mixture model

The Dirichlet process prior allows flexible nonparametric mixture modeling. The number of mixture components is not specified in advance and can grow as new data arrive. However, analyses based on the Dirichlet process prior are sensitive to the choice of the parameters, including an infinite-dimensional distributional parameter G ₀. Most previous applications have either fixed G ₀ as a member of a parametric family or treated G ₀ in a Bayesian fashion, using parametric prior specifications. In contrast, we have developed an adaptive nonparametric method for constructing smooth estimates of G ₀. We combine this method with a technique for estimating α, the other Dirichlet process parameter, that is inspired by an existing characterization of its maximum-likelihood estimator. Together, these estimation procedures yield a flexible empirical Bayes treatment of Dirichlet process mixtures. Such a treatment is useful in situations where smooth point estimates of G ₀ are of intrinsic interest, or where the structure of G ₀ cannot be conveniently modeled with the usual parametric prior families. Analysis of simulated and real-world datasets illustrates the robustness of this approach.     

Research on stalking: what do we know and where do we go?

Findings of the article in this two-volume series on stalking are reviewed. Building on the findings of the National Violence Against Women Survey (Tjaden & Thoennes, 1998), this series of studies adds to the literature in defining and measuring stalking behaviors. Repeated stalking victimization is reported by up to 62% of young adults, although frequencies depend on the sample and the precise definition used. Self-definitions of stalking victimization may be quite different from legal definitions. Although the majority of legally defined stalkers (where victim fear is a key component) are men stalking women, studies utilizing other definitions find many more women as stalkers, with no significant gender differences in many studies. In many cases, it does appear that stalking is one part of a larger pattern of relationship physical and psychological abuse. Data on emotional reactions and coping strategies of victims are also reviewed, along with findings on characteristics of stalkers.     

Immigrant incorporation in the garment industry of Los Angeles

This study expands immigrant social network theory and examined employment patterns in the garment industry in Los Angeles, California, among Latino workers employed by Asian immigrant entrepreneurs. The study determined that a large percentage of immigrant employees found their jobs through the immigrant economy. Entrepreneurship increased the supply of local jobs and expanded the economy at destination at no expense to natives. Immigrant entrepreneurs bought firms from nonimmigrant owners or started new ones with an immigrant labor supply. Massey's index is flawed due to its exclusion of the role of entrepreneurs. Migration networks facilitate entrepreneurship, but some ethnic groups have fewer entrepreneurs, such as Mexicans and Central Americans. A 1993 Los Angeles survey identified 3642 garment factories in its county. Mean employment was 27.1 persons. The garment industry was the 4th largest industry in the area in 1996, with 98,700 employees. It represented 6% of all wage and salary employees in the City and 5.5% of the immigrant labor force in the County in 1990. 93% of garment workers in 1990 were immigrants. It is estimated that 51% of garment factory owners were Asians; most employees were Latinos. Census figures on sewing machine operators indicated 47.3% of owners were Whites and 42.45 were Asians. 53.3% of employees were other ethnic groups, 14.5% were Asians, and 32.2% were Whites. It is estimated that 47.2% of total employment was due to the immigration economy. 71.5% of the total employment in the garment industry was in the immigrant sector.