Influence measures in blocked designs of experiments with correlated errors

Diagnostics measures for detecting outliers in data from block designs of experiments with correlated errors are considered. Influence is often assessed by deleting suspected outlying observations. Autocorrelation of order one is considered to model correlation in each block. Cook-statistic is developed for detecting the effect of a single outlier, where results are illustrated with an example.     

On Upshifted Reversed Mean Residual Life Order

Recently, the concept of reversed mean residual life order based on the mean of the random variable X _t  = (t ? X | X ≤ t), t > 0, called the reversed residual life, defined for the nonnegative random variable X, has been introduced in the literature. In this paper, a stochastic order based on the shifted version of the reversed mean residual life is proposed, based on the reversed mean residual life function for a random variable X with support (l _X , ∞), where l _X may be negative infinity, and its properties are studied. Closure under the Poisson shock model and properties for spare allocation are also discussed.     

Internal Migration and Rural Inequalities in India

Population Research and Policy Review - The study examines the effects of seasonal and permanent migration on rural inequalities in India. We apply the counterfactual method to estimate income...     

A modification of the partial sequential probability ratio test

For the problem of discriminating between two simple hypoth¬eses concerning a Koopman - Darmois parameter, a modification of the partial sequential probability ratio test is proposed where instead of drawing only one fixed sample, two fixed samples are drawn and then Wald's SPRT is started. The OC and the ASN func¬tions are derived. Numerical comparisons are made with Wald's and Read's procedures for testing the normal mean with known variance. For some parameter values, the test procedure has a lower ASN than that of Read's procedure.     

Testing equality of variances after a preliminary test of significance for correlation coefficient

On the basis of the outcome of a preliminary test of significance for the population correlation coefficient it is decided as to whether the variance ratio or the sample correlation coefficient between u=(x+y)/2 and v=x?y)/2 is to be used as a test statistic for testing the equality of variances. A method for determining the critical points for the preliminary test and the main test has been suggested. The power of the test procedure is compared with those of standard tests.     

Simple bounds on availability in a model with unknown life and repair distributions

We take a fresh look at the classic model of a device supported by a single statistically identical spare and provision for repairs, with system failure resulting whenever the currently operating unit fails before the repair of the previously failed unit is completed to allow it to become a spare. The limiting availability A(F,G) of this system depends on the life distribution F and repair time distribution G through α=∫GdF and the expected downtime. In this paper we derive several computable and sharp bounds on A(F,G) when F,G have suitable life distribution characteristics in the sense of reliability theory but are otherwise unknown except for at most two moments. Among other results, we find a sharp bound which involves the MTBF, MTTR and the second moment of the life-distribution of the device through its coefficient of variation. This leads to a maximin result for DFR repairs and DMRL lives.     

Bias corrected empirical Bayes confidence intervals for the selected mean

Empirical Bayes (EB) methods are very useful for post selection inference. Following Datta et al. (2002 Datta, G. S., M. Ghosh, D. D. Smith, and P. Lahiri. 2002. On an asymptotic theory of conditional and unconditional coverage probabilities of empirical Bayes confidence intervals. Scandinavian Journal of Statistics 29:139–52.[Crossref], [Web of Science ®] , [Google Scholar]), we construct EB confidence intervals for the selected population mean. The EB intervals are adjusted to achieve the target coverage probabilities asymptotically up to the second order. Both unconditional coverage probabilities of EB intervals and corresponding probabilities conditional on ancillary statistics are found.     

Testing for the Proportionality of Hazards in Two Samples Against the Increasing Cumulative Hazard Ratio Alternative

A number of tests of the proportional hazards hypothesis have been proposed in the past. In recent years, researchers have proposed tests geared specially for the alternative hypothesis of "increasing hazard ratio", keeping in mind the case of crossing hazards. This alternative may be too restrictive in many situations. In this paper we develop a test of the proportional hazards model for the weaker "increasing cumulative hazard ratio" alternative. The work is motivated by a data analytic example given by Gill & Schumacher (1987) where their test fails to reject the null hypothesis even though the faster ageing of one group is quite apparent from a plot. The normalized test statistic proposed here has an asymptotically normal distribution under either hypothesis. We also present two graphical methods related to our analytical test.     

Severity and determinants of stunting in children under age 2 years in Odisha (India): a tribal v/s non-tribal analysis

Prevalence of stunting among India’s tribal under-five children has witnessed a 3% annual decline in the last 8 years. Cross-sectional data of 1000 children (287 tribal and 713 non-tribal) aged 0–23 months from Odisha’s Rapid Survey of Children (RSOC, 2014) was analysed to identify the predictors of stunting and severe stunting among tribal children and to suggest policy and programme implications. Results show significant determinants of childhood stunting to be birth order, maternal illiteracy and determinants for severe stunting were maternal age <18 years at marriage and <20 years at birth, and <3 antenatal clinic visits. Severe stunting in tribal children was predicted by basic causes: poverty and maternal age <20 years at first birth and age <18 years at marriage. Findings strongly suggest to accelerate efforts towards reducing childhood stunting in Odisha more specifically among tribal children for whom a special strategy is urgently warranted.     

Predictive Influence of Unavailable Values of Future Explanatory Variables in a Linear Model

We consider an approach to prediction in linear model when values of the future explanatory variables are unavailable, we predict a future response y ^f at a future sample point x ^f when some components of x ^f are unavailable. We consider both the cases where x ^f are dependent and independent but normally distributed. A Taylor expansion is used to derive an approximation to the predictive density, and the influence of missing future explanatory variables (the loss or discrepancy) is assessed using the Kullback–Leibler measure of divergence. This discrepancy is compared in different scenarios including the situation where the missing variables are dropped entirely.