Advances in Statistics
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© 2014 , Hindawi Publishing Corporation . All rights reserved.

Statistical Test for Bivariate Uniformity
Sun, 19 Oct 2014 09:52:47 +0000
http://www.hindawi.com/journals/as/2014/740831/
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 distancetoboundary 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 distancetoboundary 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
http://www.hindawi.com/journals/as/2014/504325/
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 NguefackTsague and Ingo Bulla
Copyright © 2014 Georges NguefackTsague and Ingo Bulla. All rights reserved.

On Cronbachâ€™s Alpha as the Mean of All Possible Split Alphas
Tue, 30 Sep 2014 12:55:27 +0000
http://www.hindawi.com/journals/as/2014/742863/
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
http://www.hindawi.com/journals/as/2014/432805/
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
http://www.hindawi.com/journals/as/2014/502678/
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 usersupplied 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
http://www.hindawi.com/journals/as/2014/548070/
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 timeseries 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 TwoPhase Sampling
Wed, 03 Sep 2014 07:49:24 +0000
http://www.hindawi.com/journals/as/2014/974604/
This paper suggests some estimators for population mean of the study variable in simple random sampling and twophase 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 twophase 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
http://www.hindawi.com/journals/as/2014/853090/
Kappa coefficients are standard tools for summarizing the information in crossclassifications 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
http://www.hindawi.com/journals/as/2014/830821/
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 TwoDimensional Optimal Controlled Sampling Designs
Sun, 25 May 2014 12:59:33 +0000
http://www.hindawi.com/journals/as/2014/875352/
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 twodimensional 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.