Journal of Data Science

We introduce a four-parameter distribution, called the Zografos-Balakrishnan Burr XII distribution. Our purpose is to provide a Burr XII generalization that may be useful to still more complex situations. The new distribution may be an interesting alternative to describe income distributions and can also be applied in actuarial science, finance, bioscience, telecommunications and modelling lifetime data, for example. It contains as special models some well-known distributions, such as the log-logistic, Weibull, Lomax and Burr XII distributions, among others. Some of its structural properties are investigated. The method of maximum likelihood is used for estimating the model parameters and a simulation study is conducted. We provide two application to real data to demonstrate the usefulness of the proposed distribution. Since the Risti´c-Balakrishnan Burr XII distribution has a similar structure to the studied distribution, we also present some of its properties and expansions.

Abstract: Analysis of spatial panel data is of great importance and inter est in spatial econometrics. Here we consider cigarette demand in a spatial panel of 46 states of the US over a 30-year period. We construct a de mand equation to examine the elasticity of per pack cigarette price and per capita disposable income. The existing spatial panel models account for both spatial autocorrelation and state-wise heterogeneity, but fail to account for temporal autocorrelation. Thus we propose new spatial panel models and adopt a fully Bayesian approach for model parameter inference and predic tion of cigarette demand at future time points using MCMC. We conclude that the spatial panel model that accounts for state-wise heterogeneity, spa tial dependence, and temporal dependence clearly outperforms the existing models. Analysis based on the new model suggests a negative cigarette price elasticity but a positive income elasticity.

Minimum Hellinger distance estimation (MHDE) for parametric model is obtained by minimizing the Hellinger distance between an assumed parametric model and a nonparametric estimation of the model. MHDE receives increasing attention for its efficiency and robustness. Recently, it has been extended from parametric models to semiparametric models. This manuscript considers a two-sample semiparametric location-shifted model where two independent samples are generated from two identical symmetric distributions with different location parameters. We propose to use profiling technique in order to utilize the information from both samples to estimate unknown symmetric function. With the profiled estimation of the function, we propose a minimum profile Hellinger distance estimation (MPHDE) for the two unknown location parameters. This MPHDE is similar to but dif- ferent from the one introduced in Wu and Karunamuni (2015), and thus the results presented in this work is not a trivial application of their method. The difference is due to the two-sample nature of the model and thus we use different approaches to study its asymptotic properties such as consistency and asymptotic normality. The efficiency and robustness properties of the proposed MPHDE are evaluated empirically though simulation studies. A real data from a breast cancer study is analyzed to illustrate the use of the proposed method.

Abstract: Missing data is a common problem in statistical analyses. To make use of information in data with incomplete observation, missing values can be imputed so that standard statistical methods can be used to analyze the data. Variables with missing values are often categorical and the miss ing pattern may not be monotone. Currently, commonly used imputation methods for data with a non-monotone missing pattern do not allow di rect inclusion of categorical variables. Categorical variables are converted to numerical variables before imputation. For many applications, the imputed numerical values for those categorical variables must then be converted back to categorical values. However, this conversion introduces bias which can seriously affect subsequent analyses. In this paper, we propose two direct imputation methods for categorical variables with a non-monotone missing pattern: the direct imputation approach incorporated with the expectation maximization algorithm and the direct imputation approach incorporated with a new algorithm: the imputation-maximization algorithm. Simulation studies show that both methods perform better than the method using vari able conversion. An application to real data is provided to compare the direct imputation method and the method using variable conversion.

Abstract: The association between bivariate binary responses has been studied using Pearson’s correlation coefficient, odds ratio, and tetrachoric correlation coefficient. This paper introduces a copula to model the association. Numerical comparisons between the proposed method and the existing methods are presented. Results show that these methods are comparative. However, the copula method has a clearer interpretation and is easier to extend to bivariate responses with three or more ordinal categories. In addition, a goodness-of-fit test for the selection of a model is performed. Applications of the method on two real data sets are also presented.

Abstract: Family background factor can be a very important part of a person’s life. One of the main interests of this paper is to investigate whether the family background factors alter performance on mathematical achievement of the stronger students the same way that weaker students are affected. Using large sample of 2000, 2001 and 2002 mathematics participation in Alberta, Canada, such questions have been investigated by means of quantile regression approach. The findings suggest that there may be differential family-background-factor effects at different points in the conditional distribution of mathematical achievements.

Abstract: When comparing two independent groups, the shift function compares all of the quantiles in a manner that controls the probability of at least one Type I error, assuming random sampling only. Moreover, it provides a much more detailed sense of how groups compare, versus using a single measure of location, and the associated plot of the data can yield valuable insights. This note examines the small-sample properties of an ex tension of the shift function where the goal is to compare the distributions of two specified linear sums of the random variables under study, with an emphasis on a two-by-two design. A very simple method controls the proba bility of a Type I error. Moreover, very little power is lost versus comparing means when sampling is from normal distributions with equal variances.

This paper examines the performance of different kind of GARCH models with Gaussian, Student-t and generalized error distribution for Colombo Stock Exchange (CSE), in Sri Lanka. Analyzing the daily closing price index of CSE from January 02, 2007 to March 10, 2013. It was found that the Asymmetric GARCH models give better result than symmetric GARCH model. According to distributional assumption these models under Student-t as well as generalized error provided better fit than normal distributional assumption. The Non-Parametric Specification test suggest that the GARCH, EGARCH, TARCH and APARCH models with Student-t distributional assumption are the most successful model for CSE.

Abstract: We propose a simple method for evaluating agreement between methods of measurement when the measured variable is continuous and the data consists of matched repeated observations made with the same method under different conditions. The conditions may represent different time points, raters, laboratories, treatments, etc. Our approach allows the values of the measured variable and the magnitude of disagreement to vary across the conditions. The coefficient of individual agreement (CIA), which is based on the comparison of the between and within-methods mean squared deviation (MSD) is used to quantify the magnitude of agreement between measurement methods. The new approach is illustrated via two examples from studies designed to compare (a) methods of evaluating carotid stenosis and (b) methods of measuring percent body fat.