Advances in Statistics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function Thu, 29 Jan 2015 12:54:37 +0000 Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function. Kamaljit Kaur, Sangeeta Arora, and Kalpana K. Mahajan Copyright © 2015 Kamaljit Kaur et al. All rights reserved. Relative Entropies and Jensen Divergences in the Classical Limit Tue, 27 Jan 2015 11:48:46 +0000 Metrics and distances in probability spaces have shown to be useful tools for physical purposes. Here we use this idea, with emphasis on Jensen Divergences and relative entropies, to investigate features of the road towards the classical limit. A well-known semiclassical model is used and recourse is made to numerical techniques, via the well-known Bandt and Pompe methodology, to extract probability distributions from the pertinent time-series associated with dynamical data. A. M. Kowalski and A. Plastino Copyright © 2015 A. M. Kowalski and A. Plastino. All rights reserved. Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments Mon, 01 Dec 2014 09:20:53 +0000 Generalized Estimating Equation (GEE) is a marginal model popularly applied for longitudinal/clustered data analysis in clinical trials or biomedical studies. We provide a systematic review on GEE including basic concepts as well as several recent developments due to practical challenges in real applications. The topics including the selection of “working” correlation structure, sample size and power calculation, and the issue of informative cluster size are covered because these aspects play important roles in GEE utilization and its statistical inference. A brief summary and discussion of potential research interests regarding GEE are provided in the end. Ming Wang Copyright © 2014 Ming Wang. All rights reserved. On Marginal Dependencies of the 2 × 2 Kappa Wed, 19 Nov 2014 13:10:32 +0000 Cohen’s kappa is a standard tool for the analysis of agreement in a 2 × 2 reliability study. Researchers are frequently only interested in the kappa-value of a sample. Various authors have observed that if two pairs of raters have the same amount of observed agreement, the pair whose marginal distributions are more similar to each other may have a lower kappa-value than the pair with more divergent marginal distributions. Here we present exact formulations of some of these properties. The results provide a better understanding of the 2 × 2 kappa for situations where it is used as a sample statistic. Matthijs J. Warrens Copyright © 2014 Matthijs J. Warrens. All rights reserved. Designing Bayesian Sampling Plans with Adaptive Progressive Hybrid Censored Samples Sun, 16 Nov 2014 07:51:08 +0000 This paper studies the acceptance sampling for exponential distributions with type-I and type-II adaptive progressive hybrid censored samples. Algorithms are proposed for deriving Bayesian sampling plans. We compare the performance of the proposed sampling plans with the sampling plans of Lin and Huang (2012). The numerical results indicate that the proposed sampling plans outperform the sampling plans of Lin and Huang (2012). TaChen Liang Copyright © 2014 TaChen Liang. All rights reserved. Statistical Analysis of a Weibull Extension with Bathtub-Shaped Failure Rate Function Mon, 27 Oct 2014 07:02:44 +0000 We consider the parameter inference for a two-parameter life distribution with bathtub-shaped or increasing failure rate function. We present the point and interval estimations for the parameter of interest based on type-II censored samples. Through intensive Monte-Carlo simulations, we assess the performance of the proposed estimation methods by a comparison of precision. Example applications are demonstrated for the efficiency of the methods. Ronghua Wang, Naijun Sha, Beiqing Gu, and Xiaoling Xu Copyright © 2014 Ronghua Wang et al. All rights reserved. Statistical Test for Bivariate Uniformity Sun, 19 Oct 2014 09:52:47 +0000 The purpose of the multidimension uniformity test is to check whether the underlying probability distribution of a multidimensional population differs from the multidimensional uniform distribution. The multidimensional uniformity test has applications in various fields such as biology, astronomy, and computer science. Such a test, however, has received less attention in the literature compared with the univariate case. A new test statistic for checking multidimensional uniformity is proposed in this paper. Some important properties of the proposed test statistic are discussed. As a special case, the bivariate statistic test is discussed in detail in this paper. The Monte Carlo simulation is used to compare the power of the newly proposed test with the distance-to-boundary test, which is a recently published statistical test for multidimensional uniformity. It has been shown that the test proposed in this paper is more powerful than the distance-to-boundary test in some cases. Zhenmin Chen and Tieyong Hu Copyright © 2014 Zhenmin Chen and Tieyong Hu. All rights reserved. A Focused Bayesian Information Criterion Tue, 14 Oct 2014 13:03:03 +0000 Myriads of model selection criteria (Bayesian and frequentist) have been proposed in the literature aiming at selecting a single model regardless of its intended use. An honorable exception in the frequentist perspective is the “focused information criterion” (FIC) aiming at selecting a model based on the parameter of interest (focus). This paper takes the same view in the Bayesian context; that is, a model may be good for one estimand but bad for another. The proposed method exploits the Bayesian model averaging (BMA) machinery to obtain a new criterion, the focused Bayesian model averaging (FoBMA), for which the best model is the one whose estimate is closest to the BMA estimate. In particular, for two models, this criterion reduces to the classical Bayesian model selection scheme of choosing the model with the highest posterior probability. The new method is applied in linear regression, logistic regression, and survival analysis. This criterion is specially important in epidemiological studies in which the objective is often to determine a risk factor (focus) for a disease, adjusting for potential confounding factors. Georges Nguefack-Tsague and Ingo Bulla Copyright © 2014 Georges Nguefack-Tsague and Ingo Bulla. All rights reserved. On Cronbach’s Alpha as the Mean of All Possible -Split Alphas Tue, 30 Sep 2014 12:55:27 +0000 Coefficient alpha is the most commonly used internal consistency reliability coefficient. Alpha is the mean of all possible -split alphas if the items are divided into parts of equal size. This result gives proper interpretations of alpha: interpretations that also hold if (some of) its assumptions are not valid. Here we consider the cases where the items cannot be split into parts of equal size. It is shown that if a -split is made such that the items are divided as evenly as possible, the difference between alpha and the mean of all possible -split alphas can be made arbitrarily small by increasing the number of items. Matthijs J. Warrens Copyright © 2014 Matthijs J. Warrens. All rights reserved. Exact Inference for the Dispersion Matrix Sun, 14 Sep 2014 10:10:51 +0000 We develop a new and novel exact permutation test for prespecified correlation structures such as compound symmetry or spherical structures under standard assumptions. The key feature of the work contained in this note is the distribution free aspect of our procedures that frees us from the standard and sometimes unrealistic multivariate normality constraint commonly needed for other methods. Alan D. Hutson, Gregory E. Wilding, Jihnhee Yu, and Albert Vexler Copyright © 2014 Alan D. Hutson et al. All rights reserved. Entering the Era of Data Science: Targeted Learning and the Integration of Statistics and Computational Data Analysis Wed, 10 Sep 2014 07:20:28 +0000 This outlook paper reviews the research of van der Laan’s group on Targeted Learning, a subfield of statistics that is concerned with the construction of data adaptive estimators of user-supplied target parameters of the probability distribution of the data and corresponding confidence intervals, aiming at only relying on realistic statistical assumptions. Targeted Learning fully utilizes the state of the art in machine learning tools, while still preserving the important identity of statistics as a field that is concerned with both accurate estimation of the true target parameter value and assessment of uncertainty in order to make sound statistical conclusions. We also provide a philosophical historical perspective on Targeted Learning, also relating it to the new developments in Big Data. We conclude with some remarks explaining the immediate relevance of Targeted Learning to the current Big Data movement. Mark J. van der Laan and Richard J. C. M. Starmans Copyright © 2014 Mark J. van der Laan and Richard J. C. M. Starmans. All rights reserved. Horizon Detection in Seismic Data: An Application of Linked Feature Detection from Multiple Time Series Tue, 09 Sep 2014 00:00:00 +0000 Seismic studies are a key stage in the search for large scale underground features such as water reserves, gas pockets, or oil fields. Sound waves, generated on the earth’s surface, travel through the ground before being partially reflected at interfaces between regions with high contrast in acoustic properties such as between liquid and solid. After returning to the surface, the reflected signals are recorded by acoustic sensors. Importantly, reflections from different depths return at different times, and hence the data contain depth information as well as position. A strong reflecting interface, called a horizon, indicates a stratigraphic boundary between two different regions, and it is the location of these horizons which is of key importance. This paper proposes a simple approach for the automatic identification of horizons, which avoids computationally complex and time consuming 3D reconstruction. The new approach combines nonparametric smoothing and classification techniques which are applied directly to the seismic data, with novel graphical representations of the intermediate steps introduced. For each sensor position, potential horizon locations are identified along the corresponding time-series traces. These candidate locations are then examined across all traces and when consistent patterns occur the points are linked together to form coherent horizons. Robert G. Aykroyd and Fathi M. O. Hamed Copyright © 2014 Robert G. Aykroyd and Fathi M. O. Hamed. All rights reserved. Efficient Estimators Using Auxiliary Variable under Second Order Approximation in Simple Random Sampling and Two-Phase Sampling Wed, 03 Sep 2014 07:49:24 +0000 This paper suggests some estimators for population mean of the study variable in simple random sampling and two-phase sampling using information on an auxiliary variable under second order approximation. Bahl and Tuteja (1991) and Singh et al. (2008) proposed some efficient estimators and studied the properties of the estimators to the first order of approximation. In this paper, we have tried to find out the second order biases and mean square errors of these estimators using information on auxiliary variable based on simple random sampling and two-phase sampling. Finally, an empirical study is carried out to judge the merits of the estimators over others under first and second order of approximation. Rajesh Singh and Prayas Sharma Copyright © 2014 Rajesh Singh and Prayas Sharma. All rights reserved. On Agreement Tables with Constant Kappa Values Sun, 24 Aug 2014 08:23:00 +0000 Kappa coefficients are standard tools for summarizing the information in cross-classifications of two categorical variables with identical categories, here called agreement tables. When two categories are combined the kappa value usually either increases or decreases. There is a class of agreement tables for which the value of Cohen’s kappa remains constant when two categories are combined. It is shown that for this class of tables all special cases of symmetric kappa coincide and that the value of symmetric kappa is not affected by any partitioning of the categories. Matthijs J. Warrens Copyright © 2014 Matthijs J. Warrens. All rights reserved. The Fence Methods Thu, 24 Jul 2014 12:13:29 +0000 This paper provides an overview of a recently developed class of strategies for model selection, known as the fence methods. It also offers directions of future research as well as challenging problems. Jiming Jiang Copyright © 2014 Jiming Jiang. All rights reserved. A Simplified Approach for Two-Dimensional Optimal Controlled Sampling Designs Sun, 25 May 2014 12:59:33 +0000 Controlled sampling is a unique method of sample selection that minimizes the probability of selecting nondesirable combinations of units. Extending the concept of linear programming with an effective distance measure, we propose a simple method for two-dimensional optimal controlled selection that ensures zero probability to nondesired samples. Alternative estimators for population total and its variance have also been suggested. Some numerical examples have been considered to demonstrate the utility of the proposed procedure in comparison to the existing procedures. Neeraj Tiwari and Akhil Chilwal Copyright © 2014 Neeraj Tiwari and Akhil Chilwal. All rights reserved.