Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Approximability and exact resolution of the multidimensional binary vector assignment problem

In this paper we consider the multidimensional binary vector assignment problem. An input of this problem is defined by m disjoint multisets \(V^1, V^2, \ldots , V^m\), each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each multiset \(V^i\). To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. We denote this problem by Open image in new window , and the restriction of this problem where every vector has at most c zeros by Open image in new window . Open image in new window was only known to be Open image in new window -hard, even for Open image in new window . We show that, assuming the unique games conjecture, it is Open image in new window -hard to Open image in new window -approximate Open image in new window for any fixed Open image in new window and Open image in new window . This result is tight as any solution is a Open image in new window -approximation. We also prove without assuming UGC that Open image in new window is Open image in new window -hard even for Open image in new window . Finally, we show that Open image in new window is polynomial-time solvable for fixed Open image in new window (which cannot be extended to Open image in new window ).     

A multistate approach for estimating the incidence of human immunodeficiency virus by using data from a prevalent cohort study

Summary.  Cohort studies of individuals infected with the human immunodeficiency virus (HIV) provide useful information on the past pattern of HIV diagnoses, progression of the disease and use of antiretroviral therapy. We propose a new method for using individual data from an open prevalent cohort study to estimate the incidence of HIV, by jointly modelling the HIV diagnosis, the inclusion in the cohort and the progression of the disease in a Markov model framework. The estimation procedure involves the construction of a likelihood function which takes into account the probability of observing the total number of subjects who are enrolled in the cohort and the probabilities of passage through the stages of disease for each observed subject conditionally on being included in the cohort. The estimator of the HIV infection rate is defined as the function which maximizes a penalized likelihood, and the solution of this maximization problem is approximated on a basis of cubic M -splines. The method is illustrated by using cohort data from a hospital-based surveillance system of HIV infection in Aquitaine, a region of south-western France. A simulation study is performed to study the ability of the model to reconstruct the incidence of HIV from prevalent cohort data.     

Calibration of FISK, an Invasiveness Screening Tool for Nonnative Freshwater Fishes

Adapted from the weed risk assessment (WRA) of Pheloung, Williams, and Halloy, the fish invasiveness scoring kit (FISK) was proposed as a screening tool for freshwater fishes. This article describes improvements to FISK, in particular the incorporation of confidence (certainty/uncertainty) ranking of the assessors' responses, and reports on the calibration of the score system, specifically: determination of most appropriate score thresholds for classifying nonnative species into low-, medium-, and high-risk categories, assessment of the patterns of assessors' confidences in their responses in the FISK assessments. Using receiver operating characteristic (ROC) curves, FISK was demonstrated to distinguish accurately (and with statistical confidence) between potentially invasive and noninvasive species of nonnative fishes, with the statistically appropriate threshold score for high-risk species scores being ≥19. Within the group of species classed as high risk using this new threshold, a "higher risk" category could be visually identified, at present consisting of two species (topmouth gudgeon Pseudorasbora parva and gibel carp Carassius gibelio ). FISK represents a useful and viable tool to aid decision- and policymakers in assessing and classifying freshwater fishes according to their potential invasiveness.     

On residual approximation in solution extension problems

The solution extension variant of a problem consists in, being given an instance and a partial solution, finding the best solution comprising the given partial solution. Many problems have been studied with a similar approach. For instance the Pre-Coloring Extension problem, the clustered variant of the Travelling Salesman problem, or the General Routing Problem are in a way typical examples of solution extension variant problems. Motivated by practical applications of such variants, this work aims to explore different aspects around extension on classical optimization problems. We define residue-approximations as algorithms whose performance ratio on the non-prescribed part can be bounded, and corresponding complexity classes. Using residue-approximation, we classify problems according to their residue-approximability, exhibit distinct behaviors and give several examples and first interesting results.