On the Estimation of the Density of a Directional Data Stream

Many directional data such as wind directions can be collected extremely easily so that experiments typically yield a huge number of data points that are sequentially collected. To deal with such big data, the traditional nonparametric techniques rapidly require a lot of time to be computed and therefore become useless in practice if real time or online forecasts are expected. In this paper, we propose a recursive kernel density estimator for directional data which (i) can be updated extremely easily when a new set of observations is available and (ii) keeps asymptotically the nice features of the traditional kernel density estimator. Our methodology is based on Robbins–Monro stochastic approximations ideas. We show that our estimator outperforms the traditional techniques in terms of computational time while being extremely competitive in terms of efficiency with respect to its competitors in the sequential context considered here. We obtain expressions for its asymptotic bias and variance together with an almost sure convergence rate and an asymptotic normality result. Our technique is illustrated on a wind dataset collected in Spain. A Monte‐Carlo study confirms the nice properties of our recursive estimator with respect to its non‐recursive counterpart.     

Language Policy in Practice: Re‐bordering the Nation

We present findings from an anthropological field study on the role of language and language policy in migration from Poland to Norway, and the larger implications for emerging language and immigration policy in Europe. Initial fieldwork in Norway found that Polish workers without knowledge of the Norwegian language struggled to secure employment in the formal economy. The 2008 financial crisis intensified competition in the labour market and underscored fluency in Norwegian as a means of discriminating among workers. Comparative case studies of language schools revealed that these organizations are active participants in channeling Polish migrants' movements into a segmented labour market, often in ways that involve cooperation between private companies and the State. We frame the Norwegian case within the larger context of Europe and the trend there toward favoring integration over multiculturalism. The emergence of restrictive language policies in Europe may be interpreted as a legally and culturally acceptable means for discouraging access to rights associated with permanent residency or citizenship by work migrants from CEE countries, while at the same time permitting them access to the labour market for temporary work. The long‐term consequences of such policies for European society are uncertain.     

Consistency of the recursive nonparametric regression estimation for dependent functional data

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.     

Liminality and learning: international placements as a rite of passage

This article reports findings from a collaborative study of UK student learning in Malaysia. We analyze the concept of liminality as a means of understanding the transitional process between states and statuses that social work students experience in practice learning. Here, in specific reference to immersion in new cultural contexts represented by international placements, the development and learning of students are explored in relation to the overlapping domains of familiar and unfamiliar ‘cultures’ and disciplinary practice. These findings carry implications in terms of the increasing popularity of international placements and the potential imposition of hegemonies of values and knowledge.     

Strong consistency result of a non parametric conditional mode estimator under random censorship for functional regressors

Abstract

Let (T, C, X) be a vector of random variables (rvs) where T, C, and X are the interest variable, a right censoring rv, and a covariate, respectively. In this paper, we study the kernel conditional mode estimation when the covariate takes values in an infinite dimensional space and is α-mixing. Under some regularity conditions, the almost complete convergence of the estimate with rates is established.     

Relationship between sources of counseling self-efficacy and counseling self-efficacy among Malaysian school counselors

School counselors’ role in the formation and transformation of the Malaysian education system is indispensable. This study employs the Social Cognitive Theory to examine the relationship between the sources of counseling self-efficacy and the Malaysian school counselors’ counseling self-efficacy. The Sources of Counseling Self-Efficacy questionnaire and the Counseling Self-Estimate Inventory were used on 541 school counselors nationwide, as the respondents. The result reveals mastery experience has the strongest relationship with counseling self-efficacy. Recommendations on how to strengthen self-efficacy are proposed.     

Ageism in the Lesbian Community

Ageist messages are everywhere. Lesbians of all ages must raise their awareness of the harm done by ageism and actively combat it.     

PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE

This paper investigates the roles of partial correlation and conditional correlation as measures of the conditional independence of two random variables. It first establishes a sufficient condition for the coincidence of the partial correlation with the conditional correlation. The condition is satisfied not only for multivariate normal but also for elliptical, multivariate hypergeometric, multivariate negative hypergeometric, multinomial and Dirichlet distributions. Such families of distributions are characterized by a semigroup property as a parametric family of distributions. A necessary and sufficient condition for the coincidence of the partial covariance with the conditional covariance is also derived. However, a known family of multivariate distributions which satisfies this condition cannot be found, except for the multivariate normal. The paper also shows that conditional independence has no close ties with zero partial correlation except in the case of the multivariate normal distribution; it has rather close ties to the zero conditional correlation. It shows that the equivalence between zero conditional covariance and conditional independence for normal variables is retained by any monotone transformation of each variable. The results suggest that care must be taken when using such correlations as measures of conditional independence unless the joint distribution is known to be normal. Otherwise a new concept of conditional independence may need to be introduced in place of conditional independence through zero conditional correlation or other statistics.