Journal of Advanced Statistics

9

Authors: Shuji Ando, Takashi Takeuchi, Kiyotaka Iki, Sadao Tomizawa

For square contingency tables with ordered categories, Tahata et al. (2006) and Tahata et al. (2012) considered measures which represent the degree of departure from the marginal homogeneity (MH) model using the cumulative marginal probabilities. The former measure can judge whether or not the MH model holds, but the latter cannot. Also, the latter measure can distinguish the directionality for two types of maximum marginal inhomogeneities, but the former cannot. The present paper proposes a two-dimensional measure vector with above measures as elements that can simultaneously analyze the degree of departure from MH and the directionality for two types of maximum marginal inhomogeneities. Also, this paper shows the usefulness of the proposed measure vector on comparing visually degrees of departure from MH in several square contingency tables using confidence region.

4

Authors: Owat Sunanta, Reinhard Viertl

Information and its quality are essential for effective decision making, which often takes into account the statistical knowledge of the condition under consideration. Information in form of collected data from continuous quantities is always uncertain, i.e. more or less fuzzy. However, such data can be further described by so-called fuzzy numbers for better understanding. In applied statistics, a more general form of distributions (so-called fuzzy densities) is suitable to model uncertain stochastic information. The combination of fuzziness and stochastic uncertainty calls for a generalization of mathematical models for decision making. As a result, models must be generalized to handle this situation. This is possible and will be explained via decision model and utility.

7

Authors: Qiqing Yu, Qinggang Diao

Yu and Diao [1] studied the estimation problem under the Cox model with linearly time-dependent covariates and with interval-censored (IC) data under the distribution-free set-up. They proposed a modified semi-parametric MLE (MSMLE) and the simulation results suggest that the MSMLE is consistent. In this paper, we establish the consistency of the MSMLE.