Uniformly strong consistency and Berry-Esseen bound of frequency polygons for α-mixing samples

In this article, the frequency polygon investigated by Scott is studied as a nonparametric estimator for α-mixing samples. By some known exponent and moment inequalities, we obtain the uniformly strong consistency and Berry-Esseen bound of the estimator. The present results relax the relevant conditions used by Carbon et al. Furthermore, the convergence rate of the uniformly asymptotic normality is derived, which is O(n^{? 1/11}) under the given conditions.     

Bayes shrinkage estimator for consistency assessment of treatment effects in multi-regional clinical trials

The primary objective of a multi-regional clinical trial is to investigate the overall efficacy of the drug across regions and evaluate the possibility of applying the overall trial result to some specific region. A challenge arises when there is not enough regional sample size. We focus on the problem of evaluating applicability of a drug to a specific region of interest under the criterion of preserving a certain proportion of the overall treatment effect in the region. We propose a variant of James-Stein shrinkage estimator in the empirical Bayes context for the region-specific treatment effect. The estimator has the features of accommodating the between-region variation and finiteness correction of bias. We also propose a truncated version of the proposed shrinkage estimator to further protect risk in the presence of extreme value of regional treatment effect. Based on the proposed estimator, we provide the consistency assessment criterion and sample size calculation for the region of interest. Simulations are conducted to demonstrate the performance of the proposed estimators in comparison with some existing methods. A hypothetical example is presented to illustrate the application of the proposed method.     

Infill asymptotics for adaptive kernel estimators of spatial intensity

We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.     

Quantifying the Establishment Likelihood of Invasive Alien Species Introductions Through Ports with Application to Honeybees in Australia

The cost of an uncontrolled incursion of invasive alien species (IAS) arising from undetected entry through ports can be substantial, and knowledge of port‐specific risks is needed to help allocate limited surveillance resources. Quantifying the establishment likelihood of such an incursion requires quantifying the ability of a species to enter, establish, and spread. Estimation of the approach rate of IAS into ports provides a measure of likelihood of entry. Data on the approach rate of IAS are typically sparse, and the combinations of risk factors relating to country of origin and port of arrival diverse. This presents challenges to making formal statistical inference on establishment likelihood. Here we demonstrate how these challenges can be overcome with judicious use of mixed‐effects models when estimating the incursion likelihood into Australia of the European (Apis mellifera) and Asian (A. cerana) honeybees, along with the invasive parasites of biosecurity concern they host (e.g., Varroa destructor). Our results demonstrate how skewed the establishment likelihood is, with one‐tenth of the ports accounting for 80% or more of the likelihood for both species. These results have been utilized by biosecurity agencies in the allocation of resources to the surveillance of maritime ports.     

COMMENTARY (12 YEARS ON) ON ‘THE CONTRIBUTION OF OBSERVATION TRAINING TO PROFESSIONAL DEVELOPMENT IN SOCIAL WORK’ BY JUDITH TROWELL AND GILLIAN MILES

This article aims to stimulate discussion about relationships between the lives of professionals and of service users. The idea is that when parallels are explored and developed, power dynamics between professionals and social workers are reduced, the quality of interaction and work with service users can be improved, and professionals can also be helped in overcoming difficulties in their own lives. I start with an outline of my own personal background and highlight my development throughout, including my emerging identity as a Buddhist. I discuss a case study involving ‘Sally’ and her family and our work together while I was a social work assistant in a Children and Family's team. I try to show the interconnections between the different difficulties that we faced and how that informed my work. I look at some of the benefits, pitfalls and boundaries of working from the point of view that service user and professional are both working to overcome their problems. I also interweave interactions I had at the time with Carlos, a drug user friend in a crisis and the impact he had on me. Because I include my own situation I have called this article a ‘case experience’.

Throughout I refer to Buddhist and psychoanalytic thinking and particularly to agreement between the two around ideas that inner‐resistance is the main barrier to personal evolution. I argue that faith is the key to unlocking resistance, and that faith should be understood as the development of a belief within people that they are able to progress rather than be destroyed in the face of inevitable problems.     

Model Checks in Inverse Regression Models with Convolution‐Type Operators

Abstract. We consider the problem of testing parametric assumptions in an inverse regression model with a convolution‐type operator. An L ₂ ‐type goodness‐of‐fit test is proposed which compares the distance between a parametric and a non‐parametric estimate of the regression function. Asymptotic normality of the corresponding test statistic is shown under the null hypothesis and under a general non‐parametric alternative with different rates of convergence in both cases. The feasibility of the proposed test is demonstrated by means of a small simulation study. In particular, the power of the test against certain types of alternative is investigated. Finally, an empirical example is provided, in which the proposed methods are applied to the determination of the shape of the luminosity profile of the elliptical galaxy NGC 5017.     

An upper bound for the distribution function of a positive definite quadratic form

In this paper the researchers are presenting an upper bound for the distribution function of quadratic forms in normal vector with mean zero and positive definite covariance matrix. They also will show that the new upper bound is more precise than the one introduced by Okamoto [4] and the one introduced by Siddiqui [5]. Theoretical Error bounds for both, the new and Okamoto upper bounds are derived in this paper. For larger number of terms in any given positive definite quadratic form, a rough and easier upper bound is suggested.     

The Common Assessment Framework form 9 years on: a creative process

Legislation within England states that local authorities should provide services for all those families in need. However, research has identified that regardless of the introduction of strategies to identify need and enhance family support, ongoing barriers to services adhere. Taking a social constructionist approach, this study explored professionals' experiences of the use of the Common Assessment Framework form. Data were collected in four different local authorities in two phases. Forty‐one professionals from a variety of agencies took part in semi‐structured interviews. Data were analyzed thematically. Findings demonstrate that the professionals experienced difficulties in working through the Common Assessment Framework process, for example, in completing the form and engaging families. This situation led to the more experienced and knowledgeable professionals utilising creative ways to successfully navigate the ‘referral process’. Such creative working practices included the terminology used to complete the form and how the process was ‘sold’ to parents, so that they could be in a better position to engage parents and complete the Common Assessment Framework form. Because of this, more experienced professionals seem to be able to accelerate the referral process in order to access much needed support services for children and young people.     

Smooth tail-index estimation

The two parametric distribution functions appearing in the extreme-value theory – the generalized extreme-value distribution and the generalized Pareto distribution – have log-concave densities if the extreme-value index γ∈[?1, 0]. Replacing the order statistics in tail-index estimators by their corresponding quantiles from the distribution function that is based on the estimated log-concave density ? f _n leads to novel smooth quantile and tail-index estimators. These new estimators aim at estimating the tail index especially in small samples. Acting as a smoother of the empirical distribution function, the log-concave distribution function estimator reduces estimation variability to a much greater extent than it introduces bias. As a consequence, Monte Carlo simulations demonstrate that the smoothed version of the estimators are well superior to their non-smoothed counterparts, in terms of mean-squared error.     

Rank invariant tests with left truncated and interval censored data

Peto and Peto (1972) have studied rank invariant tests to compare two survival curves for right censored data. We apply their tests, including the logrank test and the generalized Wilcoxon test, to left truncated and interval censored data. The significance levels of the tests are approximated by Monte Carlo permutation tests. Simulation studies are conducted to show their size and power under different distributional differences. In particular, the logrank test works well under the Cox proportional hazards alternatives, as for the usual right censored data. The methods are illustrated by the analysis of the Massachusetts Health Care Panel Study dataset.