A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

Deconvolution methods for non-parametric inference in two-level mixed models

Summary.  We develop a general non-parametric approach to the analysis of clustered data via random effects. Assuming only that the link function is known, the regression functions and the distributions of both cluster means and observation errors are treated non-parametrically. Our argument proceeds by viewing the observation error at the cluster mean level as though it were a measurement error in an errors-in-variables problem, and using a deconvolution argument to access the distribution of the cluster mean. A Fourier deconvolution approach could be used if the distribution of the error-in-variables were known. In practice it is unknown, of course, but it can be estimated from repeated measurements, and in this way deconvolution can be achieved in an approximate sense. This argument might be interpreted as implying that large numbers of replicates are necessary for each cluster mean distribution, but that is not so; we avoid this requirement by incorporating statistical smoothing over values of nearby explanatory variables. Empirical rules are developed for the choice of smoothing parameter. Numerical simulations, and an application to real data, demonstrate small sample performance for this package of methodology. We also develop theory establishing statistical consistency.     

ESTIMATING A PARAMETER WHEN IT IS KNOWN THAT THE PARAMETER EXCEEDS A GIVEN VALUE

In some statistical problems a degree of explicit, prior information is available about the value taken by the parameter of interest, θ say, although the information is much less than would be needed to place a prior density on the parameter's distribution. Often the prior information takes the form of a simple bound, ‘θ > θ₁ ’ or ‘θ < θ₁ ’, where θ₁ is determined by physical considerations or mathematical theory, such as positivity of a variance. A conventional approach to accommodating the requirement that θ > θ₁ is to replace an estimator, , of θ by the maximum of and θ₁. However, this technique is generally inadequate. For one thing, it does not respect the strictness of the inequality θ > θ₁ , which can be critical in interpreting results. For another, it produces an estimator that does not respond in a natural way to perturbations of the data. In this paper we suggest an alternative approach, in which bootstrap aggregation, or bagging, is used to overcome these difficulties. Bagging gives estimators that, when subjected to the constraint θ > θ₁ , strictly exceed θ₁ except in extreme settings in which the empirical evidence strongly contradicts the constraint. Bagging also reduces estimator variability in the important case for which is close to θ₁, and more generally produces estimators that respect the constraint in a smooth, realistic fashion.     

Investigating the mechanism of marital mortality reduction: The transition to widowhood and quality of health care

While it is well known that the widowed suffer increased mortality risks, the mechanism of this survival disadvantage is still under investigation. In this article, we examine the quality of health care as a possible link between widowhood and mortality using a unique data set of 475,313 elderly couples who were followed up for up to nine years. We address whether the transition to widowhood affects the quality of care that individuals receive and explore the extent to which these changes mediate the elevated mortality hazard for the widowed. We analyze six established measures of quality of health care in a fixed-effect framework to account for unobserved heterogeneity. Caregiving and acute bereavement during the transition to widowhood appear to distract individuals from taking care of their own health care needs in the short run. However, being widowed does not have long-term detrimental effects on individuals’ ability to sustain contact with the formal medical system. Moreover, the short-run disruption does not mediate the widowhood effect on mortality. Nevertheless, long after spousal death, men suffer from a decline in the quality of informal care, coordination between formal and informal care, and the ability to advocate and communicate in formal medical settings. These findings illustrate women’s centrality in the household production of health and identify important points of intervention in optimizing men’s adjustment to widowhood.     

Mortality attributable to obesity among middle-aged adults in the united states

Obesity is considered a major cause of premature mortality and a potential threat to the longstanding secular decline in mortality in the United States. We measure relative and attributable risks associated with obesity among middle-aged adults using data from the Health and Retirement Study (1992–2004). Although class II/III obesity (BMI _ 35.0 kg/m2) increases mortality by 40% in females and 62% in males compared with normal BMI (BMI = 18.5-24.9), class I obesity (BMI = 30.0-34.9) and being overweight (BMI = 25.0-29.9) are not associated with excess mortality. With respect to attributable mortality, class II/III obesity (BMI _ 35.0) is responsible for approximately 4% of deaths among females and 3% of deaths among males. Obesity is often compared with cigarette smoking as a major source of avoidable mortality. Smoking-attributable mortality is much larger in this cohort: about 36% in females and 50% in males. Results are robust to confounding by preexisting diseases, multiple dimensions of socioeconomic status (SES), smoking, and other correlates. These findings challenge the viewpoint that obesity will stem the long-term secular decline in U.S. mortality.     

Comment: there may be compositional effects,but they do not work that way*

This analysis joins the debate on how declines in marriage have shifted the composition of the unmarried and married populations in the United States, and how compositional shifts have affected nonmarital birth rates. Gray, Stockard, and Stone (2006) presented one model for compositional effects that Ermisch (2009) challenged with alternative statistical tests. I propose an alternative model for compositional shifts based not on theory but on observed marriage and fertility patterns. The results from this alternative model are consistent with Ermisch’s findings yet support Gray et al.’s general case that compositional effects have had an important infiuence on nonmarital birth rates.     

Forced Migration and Mortality in the Very Long Term: Did Perestroika Affect Death Rates Also in Finland?

In this article, we analyze mortality rates of Finns born in areas that were ceded to the Soviet Union after World War II and from which the entire population was evacuated. These internally displaced persons are observed during the period 1971-2004 and compared with people born in the same region but on the adjacent side of the new border. We find that in the 1970s and 1980s, the forced migrants had mortality rates that were on par with those of people in the comparison group. In the late 1980s, the mortality risk of internally displaced men increased by 20% in relation to the expected time trend. This deviation, which manifests particularly in cardiovascular mortality, coincides with perestroika and the demise of the Soviet Union, which were events that resulted in an intense debate in civil society about restitution of the ceded areas. Because state actors were reluctant to engage, the debate declined after some few years, and after the mid-1990s, the death risk again approached the long-term trend. Our findings indicate that when internally displaced persons must adjust to situations for which appropriate coping behaviors are unknown, psychosocial stress might arise several decades after their evacuation.