On Some Applications of Poisson Point Processes

Poisson point processes play important role in various domains of Probability Theory and Mathematical Statistics. In this article, we investigate only two applications of Poisson point processes: a generated white noise problem and parameters estimation problem. This work continues the investigations started in paper Egorov and Kondybaev (2009 Egorov , V. A. , Kondybaev , N. S. ( 2009 ). On the estimation of a signal covered by background om Poisson noise . Methods and programs of data processing 4 : 75 – 81 . [Google Scholar]).     

Least Squares Consistent Estimates for Arbitrary Regression Functions Over an Abstract Space

In this article, we propose a new approach to sieve estimation for a general regression function when the dimension of the finite dimensional subspaces is a random quantity depending on the values of the observations.

The technique is introduced with the help of a simulation study on a functional linear model under extremely mild assumptions.

A sketch of the proof concerning the main statements is then given in the more general case when the regression function is not necessarily linear.     

A Small Area Predictor under Area-Level Linear Mixed Models with Restrictions

A calibrated small area predictor based on an area-level linear mixed model with restrictions is proposed. It is showed that such restricted predictor, which guarantees the concordance between the small area estimates and a known estimate at the aggregate level, is the best linear unbiased predictor. The mean squared prediction error of the calibrated predictor is discussed. Further, a restricted predictor under a particular time-series and cross-sectional model is presented. Within a simulation study based on real data collected from a longitudinal survey conducted by a national statistical office, the proposed estimator is compared with other competitive restricted and non-restricted predictors.     

Bayesian analysis of skew-normal independent linear mixed models with heterogeneity in the random-effects population

We present a new class of models to fit longitudinal data, obtained with a suitable modification of the classical linear mixed-effects model. For each sample unit, the joint distribution of the random effect and the random error is a finite mixture of scale mixtures of multivariate skew-normal distributions. This extension allows us to model the data in a more flexible way, taking into account skewness, multimodality and discrepant observations at the same time. The scale mixtures of skew-normal form an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-Student-t, skew-slash and the skew-contaminated normal distributions as special cases, being a flexible alternative to the use of the corresponding symmetric distributions in this type of models. A simple efficient MCMC Gibbs-type algorithm for posterior Bayesian inference is employed. In order to illustrate the usefulness of the proposed methodology, two artificial and two real data sets are analyzed.     

Efficient estimation for incomplete multivariate data

We review the Fisher scoring and EM algorithms for incomplete multivariate data from an estimating function point of view, and examine the corresponding quasi-score functions under second-moment assumptions. A bias-corrected REML-type estimator for the covariance matrix is derived, and the Fisher, Godambe and empirical sandwich information matrices are compared. We make a numerical investigation of the two algorithms, and compare with a hybrid algorithm, where Fisher scoring is used for the mean vector and the EM algorithm for the covariance matrix.     

Convolution power kernels for density estimation

We propose a new type of non-parametric density estimators fitted to random variables with lower or upper-bounded support. To illustrate the method, we focus on nonnegative random variables. The estimators are constructed using kernels which are densities of empirical means of m i.i.d. nonnegative random variables with expectation 1. The exponent m   plays the role of the bandwidth. We study the pointwise mean square error and propose a pointwise adaptive estimator. The risk of the adaptive estimator satisfies an almost oracle inequality. A noteworthy result is that the adaptive rate is in correspondence with the smoothness properties of the unknown density as a function on (0,+∞)$(0,+\infty )$. The adaptive estimators are illustrated on simulated data. We compare our approach with the classical kernel estimators.     

Openings,absences and omissions: Aspects of the treatment of ‘race’, culture and ethnicity in British cultural studies

Abstract

British cultural studies has, in an innovative and exciting way over the last three or four decades, opened up spaces for the serious analysis of many aspects of culture, including those inextricably related to questions of ‘race’, ethnicity and subordinated groups in urban environments in Britain. However, there have been a number of weaknesses and omissions with regard to Britain's black, Caribbean-descended population. Some of these are possibly the result of earlier, unresolved theoretical and methodological disputes within the field of cultural studies; others stem, perhaps, from an over-reliance on approaches arising out of youth subcultural analytical frameworks. Consequently, less than the required attention has been paid to the active cultures of achievement developed by the adult, black working-class population of Caribbean descent in Britain from the 1950s to the 1990s.     

Estimating Age: College Males Versus Convicted Male Child Sex Offenders

Two samples, male college students and convicted male child sex offenders, are compared on their abilities to accurately estimate the age group of a series of photographs of a sole female ranging in age from 11 to 29. Both samples tend to overestimate the age group of the subject photos, and no significant difference was found between college students and convicted child sex offenders in their ability to estimate the age of females. Both groups are compared demographically, and only limited differences were found. The implications are discussed in regard to theory and prevention of child sexual abuse.     

Self Esteem,Academic Achievement,and Moral Development Among Adolescent Girls

Abstract

Girls who play sports are known to display more self-confidence and tend to have a higher moral development. Using data on high school girls, we explore the effectiveness of competitive team sports on their self-confidence, use of drugs and alcohol, spirituality/religiosity, and academic achievement. Good performance in sports enables them to have some control over their behavior and their future. We suggest that school administrators might want to encourage their female students to be active in sports, and parents might want to encourage their daughters to be active in sports, as it helps in achievement orientation and moral development.     

The Academic Achievement Gap Between Blacks and Whites

ABSTRACT

This paper considers the academic achievement gap between African American and White students at the elementary and high school levels. It attempts to determine if race or lower socioeconomic status impact results of standardized test results at high performing and low performing schools. It presents research involving regression analysis of data for the state of Illinois. Results indicate race is not a negative factor at high performing or low performing schools for both elementary or high school years, given the samples. Also, low socioeconomic status is not a negative factor at high performing or low performing schools for both the elementary and high school years. High performing schools had low to moderate quantities of the identified variables, while low performing schools had high levels of the identified variables. Societal biases toward Blacks-rich or poor-are challenged in this paper.