Journal of Advanced Statistics

12

Authors: Egbo M.N, Bartholomew D.C

In this paper, discriminant function analysis was used to classify 68 randomly selected countries to their respective economy status (Weak or Strong) on World Bank website data. The following economic indicators were used as independent variables: Gross Domestic Product (GDP), Ln(Mortality_rate), Ln(Inflation_rate) and Access_to_electricicty. It showed that Ln(Mortality_rate) and Access_to_electricity contributed most to linearly discriminate within the group (economy status) for the two levels (weak or strong) while GDP contributed least with 93.6% sensitivity and 91.2% of cross-validated grouped cases correctly classified.

8

Authors: Arpita Chatterjee

Parametric models have been the dominant paradigm for Bayesian inferential works. This is mainly due to its simplicity and straightforward computations. However, given recent computational advances, Semiparametric Bayesian models have become increasingly popular to fit models under flexible distributional assumption. Dirichlet process mixture models form a particular class of Bayesian semiparametric models by assuming a random mixing distribution, taken to be a realization from a Dirichlet process. In this research, we show that even though hierarchical DP models provide flexibility in model fit, they may not perform uniformly better in other aspects as compared to the parametric models. If the DP model gives a better fit, then it should be used regardless of any effect it might have on the power. However, if it results in a reduction in power, then that is just the price of doing a good statistical analysis.

7

Authors: Kiyotaka Iki, Sadao Tomizawa

For square contingency tables, Iki, Tahata and Tomizawa (2011) considered the measure to represent the degree of departure from the marginal homogeneity model. Using the first-order term in the Taylor series expansion, the estimated measure with the cell probabilities replaced by the corresponding sample proportions is an approximately unbiased estimator when the sample size is large. The present paper proposes the improved approximate unbiased estimator of the measure which is obtained by using the second-order term in the Taylor series expansion. Also, it shows that the improved estimator approaches to the true measure faster than the original estimator as the sample size becomes larger by the simulation studies.

18

Authors: Tai-Chi Wang, Frederick Kin Hing Phoa, Yuan-Lung Lin

Network data have become very popular with the growth of technologies and social applications such as Twitter and Facebook. However, few visualization tools have been created for exploring large-scale networks. We propose a simple and quick procedure to explore a network in this study. The algorithm changes the edge representation based on the complement of a simple graph and the partition method of vertex coloring. Furthermore, the colors provide additional information on top of the partitions. Our proposed method is demonstrated in some famous networks.

6

Authors: Jiajuan Liang

The theory of spherical distributions is employed to develop a generalized F-test for testing the mean of a subfamily of elliptically contoured distributions. The exact null distribution of the generalized F-test is obtained. The power performance of the generalized F-test is illustrated by choosing several distributions in the subfamily of elliptically contoured distributions. The Monte Carlos study shows that the generalized F-test is not sensitive to the increase of sample dimension. The generalized F-test is applicable to the case of any dimension with any sample size. An analysis on a real dataset in financial models illustrates possible applications of the proposed tests.

9

Authors: Miltiadis S. Chalikias

Hedayat and Afsarinejad (1975,1978) introduced the model for repeated measurement designs without interactions which was the basis for the next researchers. We present the optimal designs for the direct and carry over effect of the model for 2,3, and 4 periods. Moreover, universally optimal designs, Φ optimal and balanced designs are also presented based on the conditions of Cheng and Wu (1980) and Chalikias and Kounias (2012)

10

Authors: Mohd Yaziz Bin Mohd Isa, Zulkifflee Bin Mohamed

The purpose of this study is to examine whether there is any genuine long run relationship between Consumer Price Index (CPI) and Non-Performing Loans (NPL). Using the logarithmic values of Consumer Price Index (CPI) inflation and Non-Performing Loans (NPL), different methodologies are employed in the analysis so that the robustness of unit roots and cointegration results is guaranteed. Based on the results, we consistently do not observe any genuine long run relationship between the two variables.

17

Authors: Jingjing Wu, Nana Xing, Shawn Liu

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model. Standard large sample theory guarantees asymptotic efficiency of MLE. On the other hand, MLE does not perform as well as expected for moderate or small sample size. In 2010, a new parameter estimator based on nonextensive entropy ([1]), named Maximum Lq-likelihood Estimator (MLqE), was first introduced and studied by [2]. MLqE is an extension of MLE which introduces a distortion parameter q to make the estimation more adaptive. The purpose of this work is to examine this methodology for gamma distributions that are widely used in engineering, science and business to model continuous but skewed distributions. For specifically standard gamma models, we look at the MLqE’s asymptotics, finite sample performance in terms of efficiency and robustness, and the choice of the distortion parameter q. We investigate these aspects of MLqE and compare it with MLE in parameter estimation and tail probability estimation, through both Monte Carlo simulation and a real data analysis. Our results show that, with appropriately chosen q, MLqE and MLE perform competitively for large sample sizes while MLqE outperforms MLE for small or moderate sample sizes in terms of reducing MSE. In addition, MLqE with q < 1 has much better robustness properties than MLE when outlying observations are present.