Independent attributes control chart for Markov-dependent processes

Statistical process monitoring (SPM) is a very efficient tool to maintain and to improve the quality of a product. In many industrial processes, end product has two or more attribute-type quality characteristics. Some of them are independent, but the observations are Markovian dependent. It is essential to develop a control chart for such situations. In this article, we develop an Independent Attributes Control Chart for Markov Dependent Processes based on error probabilities criterion under the assumption of one-step Markov dependency. Implementation of the chart is similar to that of Shewhart-type chart. Performance of the chart has been studied using probability of detecting shift criterion. A procedure to identify the attribute(s) responsible for out-of-control status of the process is given.     

A new stratified three-stage unrelated randomized response model for estimating a rare sensitive attribute based on the Poisson distribution

This article suggests an efficient method of estimating a rare sensitive attribute which is assumed following Poisson distribution by using three-stage unrelated randomized response model instead of the Land et al. model (2011 Land, M., S. Singh, and S. A. Sedory. 2011. Estimation of a rare sensitive attribute using poisson distribution. Statistics 46 (3):351–60. doi:10.1080/02331888.2010.524300.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) when the population consists of some different sized clusters and clusters selected by probability proportional to size(:pps) sampling. A rare sensitive parameter is estimated by using pps sampling and equal probability two-stage sampling when the parameter of a rare unrelated attribute is assumed to be known and unknown.

We extend this method to the case of stratified population by applying stratified pps sampling and stratified equal probability two-stage sampling. An empirical study is carried out to show the efficiency of the two proposed methods when the parameter of a rare unrelated attribute is assumed to be known and unknown.     

Minimally informative distributions with given rank correlation for use in uncertainty analysis

Minimum information bivariate distributions with uniform marginals and a specified rank correlation are studied in this paper. These distributions play an important role in a particular way of modeling dependent random variables which has been used in the computer code UNICORN for carrying out uncertainty analyses. It is shown that these minimum information distributions have a particular form which makes simulation of conditional distributions very simple. Approximations to the continuous distributions are discussed and explicit formulae are determined. Finally a relation is discussed to DAD theorems, and a numerical algorithm is given (which has geometric rate of covergence) for determining the minimum information distributions.     

Construction of balanced incomplete block designs with partial cycles of blocks

When considering systems statisfying balanced incomplete block design structure, one is interested only in distinct configurations in the sense of isomorphism. We have determined additional non-isomorphic solutions to designs with previously established solutions through consideration of automorphism groups. This effort utilizes a classic technique of direct construction, namely, symmetrically repeated differences, modified slightly when constucting designs with partial cycles of blocks. To determine te base blocks, we utilize the computer to expedite some formidable enumeration     

Flood Catastrophe Model for Designing Optimal Flood Insurance Program: Estimating Location‐Specific Premiums in the Netherlands

As flood risks grow worldwide, a well‐designed insurance program engaging various stakeholders becomes a vital instrument in flood risk management. The main challenge concerns the applicability of standard approaches for calculating insurance premiums of rare catastrophic losses. This article focuses on the design of a flood‐loss‐sharing program involving private insurance based on location‐specific exposures. The analysis is guided by a developed integrated catastrophe risk management (ICRM) model consisting of a GIS‐based flood model and a stochastic optimization procedure with respect to location‐specific risk exposures. To achieve the stability and robustness of the program towards floods with various recurrences, the ICRM uses stochastic optimization procedure, which relies on quantile‐related risk functions of a systemic insolvency involving overpayments and underpayments of the stakeholders. Two alternative ways of calculating insurance premiums are compared: the robust derived with the ICRM and the traditional average annual loss approach. The applicability of the proposed model is illustrated in a case study of a Rotterdam area outside the main flood protection system in the Netherlands. Our numerical experiments demonstrate essential advantages of the robust premiums, namely, that they: (1) guarantee the program's solvency under all relevant flood scenarios rather than one average event; (2) establish a tradeoff between the security of the program and the welfare of locations; and (3) decrease the need for other risk transfer and risk reduction measures.     

Confidence distributions applied to propagating uncertainty to inference based on estimating the local false discovery rate: A fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases

Empirical Bayes estimates of the local false discovery rate can reflect uncertainty about the estimated prior by supplementing their Bayesian posterior probabilities with confidence levels as posterior probabilities. This use of coherent fiducial inference with hierarchical models generates set estimators that propagate uncertainty to varying degrees. Some of the set estimates approach estimates from plug-in empirical Bayes methods for high numbers of comparisons and can come close to the usual confidence sets given a sufficiently low number of comparisons.     

Monte carlo estimates of the distributions of the random polygons of the voronoi tessellation with respect to a poisson process

A large-scale study, in which two million random Voronoi polygons (with respect to a homogeneous Poisson point process) were generated and mensurated, is described. The polygon characteristics recorded are number of sides (or vertices), perimeter, area and interior angles. A feature is the efficient “quantile” method of replicating Poisson-type random structures, which it is hoped may find useful application elsewhere.     

A modified LGB method for detecting significant effects based on a half-normal probability plot

In analyzing data from unreplicated factorial designs, the half-normal probability plot is commonly used to screen for the ‘vital few’ effects. Recently, many formal methods have been proposed to overcome the subjectivity of this plot. Lawson (1998) (hereafter denoted as LGB) suggested a hybrid method based on the half-normal probability plot, which is a blend of Lenth (1989) and Loh (1992) method. The method consists of fitting a simple least squares line to the inliers, which are determined by the Lenth method. The effects exceeding the prediction limits based on the fitted line are candidates for the vital few effects. To improve the accuracy of partitioning the effects into inliers and outliers, we propose a modified LGB method (hereafter denoted as the Mod_LGB method), in which more outliers can be classified by using both the Carling’s modification of the box plot (Carling, 2000) and Lenth method. If no outlier exists or there is a wide range in the inliers as determined by the Lenth method, more outliers can be found by the Carling method. A simulation study is conducted in unreplicated $2^4$ designs with the number of active effects ranging from 1 to 6 to compare the efficiency of the Lenth method, original LGB methods, and the proposed modified version of the LGB method.     

Estimating ordered quantiles of two exponential populations with a common minimum guarantee time

The problem of estimating ordered quantiles of two exponential populations is considered, assuming equality of location parameters (minimum guarantee times), using the quadratic loss function. Under order restrictions, we propose new estimators which are the isotonized version of the MLEs, call it, restricted MLE. A sufficient condition for improving equivariant estimators is derived under order restrictions on the quantiles. Consequently, estimators improving upon the old estimators have been derived. A detailed numerical study has been done to evaluate the performance of proposed estimators using the Monte-Carlo simulation method and recommendations have been made for the use of the estimators.     

Treatment Evaluation in the Presence of Sample Selection

Sample selection and attrition are inherent in a range of treatment evaluation problems such as the estimation of the returns to schooling or training. Conventional estimators tackling selection bias typically rely on restrictive functional form assumptions that are unlikely to hold in reality. This paper shows identification of average and quantile treatment effects in the presence of the double selection problem into (i) a selective subpopulation (e.g., working—selection on unobservables) and (ii) a binary treatment (e.g., training—selection on observables) based on weighting observations by the inverse of a nested propensity score that characterizes either selection probability. Weighting estimators based on parametric propensity score models are applied to female labor market data to estimate the returns to education.