On an adaptive transformation–retransformation estimate of multivariate location

An affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied. The work is primarily motivated by earlier work on different versions of the multivariate median and their properties. We explore an issue related to efficiency and equivariance that was originally raised by Bickel and subsequently investigated by Brown and Hettmansperger. Our estimate has better asymptotic performance than the vector of co-ordinatewise medians when the variables are substantially correlated. The finite sample performance of the estimate is investigated by using Monte Carlo simulations. Some examples are presented to demonstrate the effect of the adaptive transformation–retransformation strategy in the construction of multivariate location estimates for real data.     

On multivariate quantile regression

To detect the dependence on the covariates in the lower and upper tails of the response distribution, regression quantiles are very useful tools in linear model problems with univariate response. We consider here a notion of regression quantiles for problems with multivariate responses. The approach is based on minimizing a loss function equivalent to that in the case of univariate response. To construct an affine equivariant notion of multivariate regression quantiles, we have considered a transformation retransformation procedure based on ‘data-driven coordinate systems’. We indicate some algorithm to compute the proposed estimates and establish asymptotic normality for them. We also, suggest an adaptive procedure to select the optimal data-driven coordinate system. We discuss the performance of our estimates with the help of a finite sample simulation study and to illustrate our methodology, we analyzed an interesting data-set on blood pressures of a group of women and another one on the dependence of sales performances on creative test scores.     

Resampling method to estimate intra-cluster correlation for clustered binary data

ABSTRACT

Various methods have been proposed to estimate intra-cluster correlation coefficients (ICCs) for correlated binary data, and many are very sensitive to the type of design and underlying distributional assumptions. We proposed a new method to estimate ICC and its 95% confidence intervals based on resampling principles and U-statistics, where we resampled with replacement pairs of individuals from within and between clusters. We concluded from our simulation study that the resampling-based estimates approximate the population ICC more precisely than the analysis of variance and method of moments techniques for different event rates, varying number of clusters, and cluster sizes.     

A Superstructure of Process Capability Indices for Circular Specification Region

Circular specification regions can be seen in processes like hitting a target (in ballistics), drilling a hole (in manufacturing industries) and so on. However, only a few process capability indices are available in the literature to address the problem. Most of these indices, in turn, make some assumptions like equality of variance and independence of the two axes of the circular tolerance region. Since, in most of the cases, these assumptions are not practically viable, in the present article, we have proposed a few of the process capability indices which do not need the above assumptions to be valid. Also, we propose a superstructure which unifies all the proposed indices. Some properties of these indices have been studied including the threshold value and the relationship of the proportion of non-conformance with the member indices of the superstructure. These strengthen the practical utility of the superstructure. Distributional properties like expectations and variances of the member indices of the superstructure are also studied to have a better insight about the indices. A real life example has been discussed to carry out a comparative study of the performance of the existing as well as the newly developed indices.     

A new generalization of the gamma distribution with application to negatively skewed survival data

We propose a three-parameter distribution referred to as the reflected- shifted-truncated gamma (RSTG) distribution to model negatively skewed data. Various properties of the proposed distribution are derived. The estimation of the model parameters is approached by maximum likelihood methods and the observed information matrix is derived. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Using information theoretic criteria, we compare the RSTG distribution to the exponential, generalized F, generalized gamma, Gompertz, log-logistic, lognormal, Rayleigh, and Weibull distributions in three negatively skewed real datasets.     

RESERVE PRICE VERSUS ENTRY FEE IN STANDARD AUCTIONS

Analysis of standard auction rules when bidders are risk averse is usually carried out under the assumption that the seller is able to set an optimal reserve. The role of entry fees has been generally overlooked in that analysis. We consider bidders with constant absolute risk aversion and show that reserve price is an essential tool in the second price auction while entry fee is essential in the first price auction. Furthermore, setting a reserve price and entry fee combination optimally may change some of the rankings of the standard auctions that hold under optimal reserves. (JEL D44)     

Joint modelling of longitudinal response and time-to-event data using conditional distributions: a Bayesian perspective

Over the last 20 or more years a lot of clinical applications and methodological development in the area of joint models of longitudinal and time-to-event outcomes have come up. In these studies, patients are followed until an event, such as death, occurs. In most of the work, using subject-specific random-effects as frailty, the dependency of these two processes has been established. In this article, we propose a new joint model that consists of a linear mixed-effects model for longitudinal data and an accelerated failure time model for the time-to-event data. These two sub-models are linked via a latent random process. This model will capture the dependency of the time-to-event on the longitudinal measurements more directly. Using standard priors, a Bayesian method has been developed for estimation. All computations are implemented using OpenBUGS. Our proposed method is evaluated by a simulation study, which compares the conditional model with a joint model with local independence by way of calibration. Data on Duchenne muscular dystrophy (DMD) syndrome and a set of data in AIDS patients have been analysed.     

Kinship institutions and sex ratios in India

This article explores the relationship between kinship institutions and sex ratios in India at the turn of the twentieth century. Because kinship rules vary by caste, language, religion, and region, we construct sex ratios by these categories at the district level by using data from the 1901 Census of India for Punjab (North), Bengal (East), and Madras (South). We find that the male-to-female sex ratio varied positively with caste rank, fell as one moved from the North to the East and then to the South, was higher for Hindus than for Muslims, and was higher for northern Indo-Aryan speakers than for the southern Dravidian-speaking people. We argue that these systematic patterns in the data are consistent with variations in the institution of family, kinship, and inheritance.     

Hispanic heterogeneity and environmental injustice: intra-ethnic patterns of exposure to cancer risks from traffic-related air pollution in Miami

To explore intra-ethnic diversity in patterns of environmental health injustice in Miami (Florida), we related modeled estimates of cancer risks from on-road pollutants from the 2005 National-scale Air Toxics Assessment with 2005–2009 American Community Survey tract-level sociodemographic data. Neighborhoods with lower incomes and higher proportions of Hispanics were at risk. When disaggregating “Hispanic” based on country of origin, we found that Cuban and Colombian neighborhoods faced significantly increased cancer risk from vehicular air pollution while Mexican neighborhoods faced significantly decreased risk. These divergent patterns of environmental injustice based on Hispanic country-of-origin groupings have been shaped by the differing migration and settlement patterns of Hispanic subgroups in Miami. Our findings highlight the growing need to consider racial/ethnic heterogeneity in future EJ analysis and policy.