Exponential inequalities for the Robbins–Monro’s algorithm under mixing condition

Abstract

In this work, we establish exponential inequalities for the Robbins–Monro’s algorithm with ψ-mixing variables, and we give a result on the almost complete convergence rate.     

The distribution of the first j digits of beta related random variables

This paper gives the discrete distribution of the first j significant digits of two random variables: (1) a beta variable with integer parameter n and the other parameter m > 0, and (2) the reciprocal of (1). As a special case for n=1, we obtain the distribution of the first j significant digits of the pwoers of uniformly distributed random variables. These generalize the results of Kennard and Reith (1981) and Friedberg (1984), who considered only uniformly distributed random variables.     

House Demolition and Mental Health: Victims and Witnesses

This research examines the immediate effects of losing one's home and witnessing the demolition of others' houses on the mental health of Palestinian adults and children. The loss group consisted of 47 adults whose homes were demolished, the witness group of 24 adults who witnessed the house demolition, and the control group of 33 adults. The groups were compared for their anxiety, depression, and paranoiac symptoms. In addition, 38 children in the loss group, 36 children in the witness group, and 50 children in the control group were compared for their psychological symptoms. The results showed that adults who were exposed to house demolition showed a higher level of anxiety, depression, and paranoiac symptoms than the witness and control groups. The children in the loss group showed a higher level of psychological symptoms than the children in the witness and control groups. The witness group differed from the control group in having more depression among women and more psychological symptoms among children. Women suffered more from anxiety, depression, and paranoiac symptoms than men in the loss and witness groups but not in the control group.     

Green supply‐chain management: A state‐of‐the‐art literature review

There is a growing need for integrating environmentally sound choices into supply‐chain management research and practice. Perusal of the literature shows that a broad frame of reference for green supply‐chain management (GrSCM) is not adequately developed. Regulatory bodies that formulate regulations to meet societal and ecological concerns to facilitate growth of business and economy also suffer from its absence. A succinct classification to help academicians, researchers and practitioners in understanding integrated GrSCM from a wider perspective is needed. Further, sufficient literature is available to warrant such classification. This paper takes an integrated and fresh look into the area of GrSCM. The literature on GrSCM is covered exhaustively from its conceptualization, primarily taking a ‘reverse logistics angle’. Using the rich body of available literature, including earlier reviews that had relatively limited perspectives, the literature on GrSCM is classified on the basis of the problem context in supply chain's major influential areas. It is also classified on the basis of methodology and approach adopted. Various mathematical tools/techniques used in literature vis‐à‐vis the contexts of GrSCM are mapped. A timeline indicating relevant papers is also provided as a ready reference. Finally, the findings and interpretations are summarized, and the main research issues and opportunities are highlighted.     

On wavelet analysis of the nth order fractional Brownian motion

In this paper, we investigate the use of wavelet techniques in the study of the nth order fractional Brownian motion (n-fBm). First, we exploit the continuous wavelet transform??s capabilities in derivative calculation to construct a two-step estimator of the scaling exponent of the n-fBm process. We show, via simulation, that the proposed method improves the estimation performance of the n-fBm signals contaminated by large-scale noise. Second, we analyze the statistical properties of the n-fBm process in the time-scale plan. We demonstrate that, for a convenient choice of the wavelet basis, the discrete wavelet detail coefficients of the n-fBm process are stationary at each resolution level whereas their variance exhibits a power-law behavior. Using the latter property, we discuss a weighted least squares regression based-estimator for this class of stochastic process. Experiments carried out on simulated and real-world datasets prove the relevance of the proposed method.     

Environmental sampling with a concomitant variable: A comparison between ranked set sampling and stratified simple random sampling

In many environmental sampling situations, the variable of interest is either not easily observable or is too expensive to observe. Under such circumstances, the need arises to observe another variable, related to the variable of interest, so as to estimate the population parameters of interest. We study the performance of two different sampling procedures, i.e. ranked set sampling and stratified simple random sampling, when both stratification and ranking are accomplished on the basis of such a concomitant variable. The relative precision of the two methods is obtained and expressed as a function of population variance, between-stratum and between-rank variation, and the correlation coefficient between the variable of interest and the concomitant variable. The relative precision is computed for several important families of distributions that occur frequently in environmental and ecological work. Under equal allocation of sampling units, stratified simple random sampling is found to perform better than ranked set sampling, when the costs incurred to obtain sample measurements are ignored. When optimum allocation is considered for both methods, ranked set sampling performs better than stratified simple random sampling, when the concomitant variable is not highly correlated with the variable of interest. Furthermore, when the costs of sampling and the costs of measurement are incorporated into the assessment of the relative precision, the ranked set sampling is seen to be more efficient than stratified simple random sampling, particularly when the cost of stratification is high compared with that of ranking. This is generally the case in practice.     

Identifying Gaps in Health Research among Refugees Resettled in Canada

While the global number of resettled refugees rises annually, the summaries of research on refugee health needs in countries of asylum remain sparse. We conducted a systematic review of published research on refugee health in Canada in order to: (i) identify studies addressing health outcomes among refugees recently resettled in Canada; (ii) identify general trends in health research conducted in Canada among refugee populations; (iii) identify significant gaps in current knowledge of health‐related issues among refugees recently resettled in Canada; (iv) evaluate the quality and consistency of available information; (v) develop a summary of available research results; and (vi) identify priorities for future research. A search of several major citation indices resulted in the analysis of 196 research reports after reviewing more than 5,000 articles. This review is timely, systematic and inclusive; furthermore, potential biases in methodology are clearly assessed. The results indicate an immediate need to address specific gaps in health knowledge for refugee populations and lead us to draw five primary conclusions. First, mental health outcomes dominate the research landscape. Second, cross‐sectional studies are most commonly the study design of choice. Third, studies examining some aspect of health among refugees from Asia dominate the literature. Fourth, there is a notable lack of information on cardiovascular diseases and its antecedents. Fifth, indications show that screenings for pre‐existing conditions are biased towards communicable diseases. These findings have implications for health monitoring, evaluation and policy affecting the health of refugees resettled in Canada and elsewhere.