Journal of Data Science

Abstract: Identification of representative regimes of wave height and direction under different wind conditions is complicated by issues that relate to the specification of the joint distribution of variables that are defined on linear and circular supports and the occurrence of missing values. We take a latent-class approach and jointly model wave and wind data by a finite mixture of conditionally independent Gamma and von Mises distributions. Maximum-likelihood estimates of parameters are obtained by exploiting a suitable EM algorithm that allows for missing data. The proposed model is validated on hourly marine data obtained from a buoy and two tide gauges in the Adriatic Sea.

Abstract: Kang (2006) used the log-likelihood function with Lagrangian multipliers for estimation of cell probabilities in two-way incomplete contingency tables. The constraints on cell probabilities can be incorporated through Lagrangian multipliers for the likelihood function. The method can be readily extended to multidimensional tables. Variances of the MLEs are derived from the matrix of second derivatives of the log likelihood with respect to cell probabilities and the Lagrange multiplier. Wald and likelihood ratio tests of independence are derived using the estimates and estimated variances. Simulation results, when data are missing at random, reveal that maximum likelihood estimation (MLE) produces more efficient estimates of population proportions than either multiple imputation (MI) based on data augmentation or complete case (CC) analysis. Neither MLE nor MI, however, leads to an improvement over CC analysis with respect to power of tests for independence in 2×2 tables. Thus, the partially classified marginal information increases precision about proportions, but is not helpful for judging independence.

Abstract: In maximum likelihood exploratory factor analysis, the estimates of unique variances can often turn out to be zero or negative, which makes no sense from a statistical point of view. In order to overcome this difficulty, we employ a Bayesian approach by specifying a prior distribution for the variances of unique factors. The factor analysis model is estimated by EM algorithm, for which we provide the expectation and maximization steps within a general framework of EM algorithms. Crucial issues in Bayesian factor analysis model are the choice of adjusted parameters including the number of factors and also the hyper-parameters for the prior distribution. The choice of these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating a Bayesian factor analysis model. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure. We observe that our modeling procedure prevents the occurrence of improper solutions and also chooses the appropriate number of factors objectively.

Abstract: We consider the Autoregressive Conditional Marked Duration (ACMD) model and apply it to 16 stocks traded in Hong Kong Stock Ex change (SEHK). By examining the orderings of appropriate sets of model parameters, market microstructure phenomena can be explained. To sub stantiate these conclusions, likelihood ratio test is used for testing the sig nificance of the parameter orderings of the ACMD model. While some of our results resolve a few controversial market microstructure hypotheses and echo some of the existing empirical evidence, we discover some interesting market microstructure phenomena that may be characteristic to SEHK.

Abstract: Mixture of Weibull distributions has wide application in modeling of heterogeneous data sets. The parameter estimation is one of the most important problems related to mixture of Weibull distributions. In this pa per, we propose a L-moment estimation method for mixture of two Weibull distributions. The proposed method is compared with maximum likelihood estimation (MLE) method according to the bias, the mean absolute error, the mean total error and completion time of the algorithm (time) by sim ulation study. Also, applications to real data sets are given to show the flexibility and potentiality of the proposed estimation method. The com parison shows that, the proposed method is better than MLE method.