The interpretation of maximum-likelihood estimation

Maximum-likelihood estimation is interpreted as a procedure for generating approximate pivotal quantities, that is, functions u(X;θ) of the data X and parameter θ that have distributions not involving θ. Further, these pivotals should be efficient in the sense of reproducing approximately the likelihood function of θ based on X, and they should be approximately linear in θ. To this end the effect of replacing θ by a parameter ϕ = ϕ(θ) is examined. The relationship of maximum-likelihood estimation interpreted in this way to conditional inference is discussed. Examples illustrating this use of maximum-likelihood estimation on small samples are given.     

Sequential procedures based on M-estimators with discontinuous score functions

Bounded-width sequential confidence intervals and sequential tests for regression parameter based on M-estimators are extended to the case where the score-functions generating the M-estimators have jump-discontinuities. In the context of the asymptotic normality of the stopping variable, for the confidence interval problem, it is observed that the jump-discontinuities induce a slower rate of convergence. The proofs of the main theorems rest on the weak convergence of some related processes and this is also studied.     

Why females live longer than males: control of longevity by sex hormones

Females live longer than males in many species, including humans. We have traced a possible explanation for this phenomenon to the beneficial action of estrogens, which bind to estrogen receptors and increase the expression of longevity-associated genes, including those encoding the antioxidant enzymes superoxide dismutase and glutathione peroxidase. As a result, mitochondria from females produce fewer reactive oxygen species than those from males. Administering estrogens has serious drawbacks, however--they are feminizing (and thus cannot be administered to males) and may increase the incidence of serious diseases such as uterine cancer in postmenopausal women. Phytoestrogens, which are present in soy or wine, may have some of the favorable effects of estrogens without their undesirable effects. Study of gender differences in longevity may help us to understand the basic processes of aging and to devise practical strategies to increase the longevity of both females and males.     

Rurality Index for Small Areas in Spain

An operational definition for “rural area” is pivotal if proposals, policies and decisions aimed at optimising the distribution of resources, closing the gap on inequity between areas and raising standards of living for the least advantaged populations are to be put in place. The concept of rurality, however, is often based on alternative and conflicting definitions, requiring clarification of the underlying theoretical model. Traditionally a geographical area has been classified as rural by taking into account either the number of inhabitants or population density. Two kinds of problem are raised with this approach, however, namely: it is inherently difficult to describe such a complex concept as rurality with a single variable; and reducing the concept down to a rural/urban dichotomy by setting a non-universal cut-off point does not usually provide an accurate account of reality. Within the context of the rural–urban continuum, this paper has devised a rurality index for Spanish municipalities based on the 1991 Population, Housing and Household Survey. The index was built on a principal components factor analysis, giving rise to a single factor that is correlated to the aging of the population, economic dependency, farming, livestock or fishing-related employment, habitability of housing and population density. A score to each municipality was allocated. This index can be regularly updated thus enabling the progress of the concept of rurality to be monitored in our setting over time and then compared with other countries using the same methods.     

The 3 F 2 with Complex Parameters as Generating Function of Discrete Distribution

A new discrete family of probability distributions that are generated by the ₃ F ₂ function with complex parameters is presented. Some of the properties of this new family are studied as well as methods of estimation for its parameters. It affords considerable flexibility of shape which turns the distribution into an appropriate candidate for modeling data that cannot be adequately fitted by classical families with fewer parameters. Finally, three examples in the fields of Agriculture and Education are included in order to show the versatility and utility of this distribution.     

Presmoothed Estimation with Left-Truncated and Right-Censored Data

We propose a new method to estimate the cumulative hazard function and the corresponding distribution function of survival times under randomly left-truncated and right-censored observations (LTRC). The new estimators are based on presmoothing ideas, the estimation of the conditional expectation m of the censoring indicator. An almost sure representation for both estimators is established, from which a strong consistency rate and asymptotic normality are derived. It is shown that the presmoothed modification leads to a gain in terms of asymptotic mean squared error. This efficiency with respect to the classical estimators is also shown in a simulation study. Finally, an application to a real data set is provided.     

Identifying Preferences for Conditional Cooperation Using Individual Beliefs

The relationship between contributions and elicited beliefs in a repeated two-person public good experiment is modeled with the help of a parsimounious random-utility function that allows for conditionally cooperative, opportunistic, and altruistic patterns of behavior. Under standard assumptions, a latent-class mixed logit specification with three sub-populations is shown to capture well heterogeneity in individual contribution levels over time, while also accomodating for different degrees of heteroscedasticity. The estimation results are consistent with the conjecture that the majority of players in public goods games are strongly conditional cooperators, with smaller fractions of the population leaning to opportunistic or altruistic behavior.     

Marshall–Olkin gamma–Weibull distribution with applications

Abstract

A Marshall–Olkin variant of the Provost type gamma–Weibull probability distribution is being introduced in this paper. Some of its statistical functions and numerical characteristics among others characteristics function, moment generalizing function, central moments of real order are derived in the computational series expansion form and various illustrative special cases are discussed. This density function is utilized to model two real data sets. The new distribution provides a better fit than related distributions as measured by the Anderson–Darling and Cramér–von Mises statistics. The proposed distribution could find applications for instance in the physical and biological sciences, hydrology, medicine, meteorology, engineering, etc.