Journal of Advanced Statistics

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.