Statistical analysis of the number of self-overlapping leftmost repeats in an homogeneous stationary Markov chain on finite states

ABSTRACT

This article addresses the problem of repeats detection used in the comparison of significant repeats in sequences. The case of self-overlapping leftmost repeats for large sequences generated by an homogeneous stationary Markov chain has not been treated in the literature. In this work, we are interested by the approximation of the number of self-overlapping leftmost long enough repeats distribution in an homogeneous stationary Markov chain. Using the Chen–Stein method, we show that the number of self-overlapping leftmost long enough repeats distribution is approximated by the Poisson distribution. Moreover, we show that this approximation can be extended to the case where the sequences are generated by a m-order Markov chain.     

Microsimulation as a tool for evaluating redistribution policies

During the last 20 years, microsimulation models have been increasingly applied in qualitative and quantitative analysis of public policies. This paper discusses microsimulation techniques and their theoretical background as a tool for the analysis of public policies. It next analyses basic principles for using microsimulation models and interpreting their results, with emphasis on tax incidence, redistribution and poverty analysis. It then discusses social welfare analysis permitted by microsimulation techniques and points to the limits of present approaches and some directions for future developments.     

On a new goodness‐of‐fit process for families of copulas

A goodness‐of‐fit procedure is proposed for parametric families of copulas. The new test statistics are functionals of an empirical process based on the theoretical and sample versions of Spearman's dependence function. Conditions under which this empirical process converges weakly are seen to hold for many families including the Gaussian, Frank, and generalized Farlie–Gumbel–Morgenstern systems of distributions, as well as the models with singular components described by Durante [Durante ( 2007 ) Comptes Rendus Mathématique. Académie des Sciences. Paris, 344, 195–198]. Thanks to a parametric bootstrap method that allows to compute valid P‐values, it is shown empirically that tests based on Cramér–von Mises distances keep their size under the null hypothesis. Simulations attesting the power of the newly proposed tests, comparisons with competing procedures and complete analyses of real hydrological and financial data sets are presented. The Canadian Journal of Statistics 37: 80‐101; 2009 © 2009 Statistical Society of Canada     

Prenatal Health,Educational Attainment,and Intergenerational Inequality: The Northern Finland Birth Cohort 1966 Study

In this article, we study the effects of prenatal health on educational attainment and on the reproduction of family background inequalities in education. Using Finnish birth cohort data, we analyze several maternal and fetal health variables, many of which have not been featured in the literature on long-term socioeconomic effects of health despite the effects of these variables on birth and short-term health outcomes. We find strong negative effects of mother’s prenatal smoking on educational attainment, which are stronger if the mother smoked heavily but are not significant if she quit during the first trimester. Anemia during pregnancy is also associated with lower levels of attained education. Other indicators of prenatal health (pre-pregnancy obesity, mother’s antenatal depressed mood, hypertension and preeclampsia, early prenatal care visits, premature birth, and small size for gestational age) do not predict educational attainment. Our measures explain little of the educational inequalities by parents’ class or education. However, smoking explains 12%—and all health variables together, 19%—of the lower educational attainment of children born to unmarried mothers. Our findings point to the usefulness of proximate health measures in addition to general ones. They also point to the potentially important role played by early health in intergenerational processes.     

Qualitative Heuristics For Balancing the Pros and Cons

Balancing the pros and cons of two options is undoubtedly a very appealing decision procedure, but one that has received scarce scientific attention so far, either formally or empirically. We describe a formal framework for pros and cons decisions, where the arguments under consideration can be of varying importance, but whose importance cannot be precisely quantified. We then define eight heuristics for balancing these pros and cons, and compare the predictions of these to the choices made by 62 human participants on a selection of 33 situations. The Levelwise Tallying heuristic clearly emerges as a winner in this competition. Further refinements of this heuristic are considered in the discussion, as well as its relation to Take the Best and Cumulative Prospect Theory.     

Turkey: a pilot study of elder mistreatment in a convenience sample

Attitudes towards elder abuse were explored through a survey on International Perspectives on Family Violence and Abuse in a Turkish convenience sample of 25 females and 14 males, ranging in age from 22 to 58. Participants gave examples of behaviors considered in their culture to be extremely abusive, moderately abusive, and mildly abusive from an adult child toward his or her older parent. Responses were coded into four major categories of abuse, each of which had several subcategories: psychological aggression (including the subcategories of verbal aggression, emotional abuse, disrespect, disobedience, power assertion, blame, and imprisonment), neglect (including physical neglect, psychological neglect, abandonment, and putting the older individual into a nursing home), physical aggression (including beating and hitting), and mistreatment related to goods and services (including economic demands, economic withholding, and labor). The most common examples of extreme abuse were neglect, particulary physical neglect, followed by physical abuse. At the moderate and mild levels, various forms of psychological aggression were most commonly mentioned. The only significant gender difference was that men listed more instances of verbal aggression as examples of extreme abuse than women. A positive correlation was found between age and the number of abandonment examples at the extreme level. Results were interpreted from a cultural perspective.     

Scatter Plot and Additional Variables

We often want to complete the interpretation of the usual graphs (x, y) with additional quantitative variables. The Prefmap method (vectorial model) proposes a representation of these additional variables but this representation has some drawbacks when the variables x and y are correlated. To solve this problem, we propose to substitute the coefficients of the linear regression by the coefficient of the PLS regression in the Prefmap method. The graph obtained is made operational thanks to contour lines of quality of representation and it becomes richer than the Prefmap one.     

Joint Modeling of Event Time and Nonignorable Missing Longitudinal Data

Survival studies usually collect on each participant, both duration until some terminal event and repeated measures of a time-dependent covariate. Such a covariate is referred to as an internal time-dependent covariate. Usually, some subjects drop out of the study before occurence of the terminal event of interest. One may then wish to evaluate the relationship between time to dropout and the internal covariate. The Cox model is a standard framework for that purpose. Here, we address this problem in situations where the value of the covariate at dropout is unobserved. We suggest a joint model which combines a first-order Markov model for the longitudinaly measured covariate with a time-dependent Cox model for the dropout process. We consider maximum likelihood estimation in this model and show how estimation can be carried out via the EM-algorithm. We state that the suggested joint model may have applications in the context of longitudinal data with nonignorable dropout. Indeed, it can be viewed as generalizing Diggle and Kenward's model (1994) to situations where dropout may occur at any point in time and may be censored. Hence we apply both models and compare their results on a data set concerning longitudinal measurements among patients in a cancer clinical trial.