Journal of Data Science

Abstract: Change point problem has been studied extensively since 1950s due to its broad applications in many fields such as finance, biology and so on. As a special case of the multiple change point problem, the epidemic change point problem has received a lot of attention especially in medical studies. In this paper, a nonparametric method based on the empirical likelihood is proposed to detect the epidemic changes of the mean after unknown change points. Under some mild conditions, the asymptotic null distribution of the empirical likelihood ratio test statistic is proved to be the extreme distribution. The consistency of the test is also proved. Simulations indicate that the test behaves comparable to the other available tests while it enjoys less constraint on the data distribution. The method is applied to the Standford heart transplant data and detects the change points successfully.

Abstract: In this paper, we propose a flexible cure rate survival model by as suming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to event follows a generalized gamma distribution. We define the negative binomial-generalized gamma distribution, which can be used to model survival data. The new model in cludes as special cases some of the well-known cure rate models discussed in the literature. We consider a frequentist analysis and nonparametric boot strap for parameter estimation of a negative binomial-generalized gamma regression model with cure rate. Then, we derive the appropriate matri ces for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, we analyze a real data set from the medical area.

A new four-parameter lifetime distribution named as the power Lomax Poisson is introduced and studied. The subject distribution is obtained by combining the power Lomax and Poisson distributions. Structural properties of the power Lomax Poisson model are implemented. Estimation of the model parameters are performed using the maximum likelihood, least squares and weighted least squares techniques. An intensive simulation study is performed for evaluating the performance of different estimators based on their relative biases, standard errors and mean square errors. Eventually, the superiority of the new compounding distribution over some existing distribution is illustrated by means of two real data sets. The results showed the fact that, the suggested model can produce better fits than some well-known distributions.

Abstract: In this article, we present a joint modeling approach that com bines information from multiple diseases. Our model can be used to obtain more reliable estimates in rare diseases by incorporating information from more common diseases for which there exists a shared set of important risk factors. Information is shared through both a latent spatial process and a latent temporal process. We develop a fully Bayesian hierarchical imple mentation of our spatio-temporal model in order to estimate relative risk, adjusted for age and gender, at the county level in Iowa in five-year intervals for the period 1973–2002. Our analysis includes lung, oral, and esophageal cancers which are related to excessive tobacco and alcohol use risk factors. Lung cancer risk estimates tend to be stable due to the large number of occurrences in small regions, i.e. counties. The lower risk cancers (oral and esophageal) have fewer occurrences in small regions and thus have estimates that are highly variable and unreliable. Estimates from individual and joint modeling of these diseases are examined and compared. The joint modeling approach has a profound impact on estimates regarding the low risk oral and esophageal cancers while the higher risk lung cancer is minutely impacted. Clearer spatial and temporal patterns are obtained and the standard errors of the estimates are reduced leading to more reliable estimates.

Abstract: The paper presents a statistical analysis of electricity spot prices in a deregulated market in New South Wales, Australia, in the period 10 May, 1996 – 7 March, 1998. It is unusual that a single set of data, such as this, allows one to consider a relatively systematic sequence of statistical problems, each resulting in clear, although not always obvious, solutions. This is the reason why these data and their analysis can be used as a rel atively good base for training in practical statistical analysis. Existing for merly as a report, the material has been used in lecture courses in several universities in Australia and New Zealand.

In this paper, kumaraswamy reciprocal family of distributions is introduced as a new continues model with some of approximation to other probabilistic models as reciprocal, beta, uniform, power function, exponential, negative exponential, weibull, rayleigh and pareto distribution. Some fundamental distributional properties, force of mortality, mills ratio, bowley skewness, moors kurtosis, reversed hazard function, integrated hazard function, mean residual life, probability weighted moments, bonferroni and lorenz curves, laplace-stieltjes transform of this new distribution with the maximum likelihood method of the parameter estimation are studied. Finally, four real data sets originally presented are used to illustrate the proposed estimators.

Abstract: This article displays an application of the statistical method motivated by Bruno de Finetti’s operational subjective theory of probability. We use exchangeable forecasting distributions based on mixtures of linear combinations of exponential power (EP) distributions to forecast the sequence of daily rates of return from the Dow-Jones index of stock prices over a 20 year period. The operational subjective statistical method for comparing distributions is quite different from that commonly used in data analysis, because it rejects the basic tenets underlying the practice of hypothesis testing. In its place, proper scoring rules for forecast distributions are used to assess the values of various forecasting strategies. Using a logarithmic scoring rule, we find that a mixture linear combination of EP distributions scores markedly better than does a simple mixture over the EP family, which scores much better than does a simple Normal mixture. Surprisingly, a mixture over a linear combination of three Normal distributions also makes a substantial improvement over a simple Normal mixture, although it does not quite match the performance of even the simple EP mixture. All substantive forecasting improvements become most marked after extreme tail phenomena were actually observed in the sequence, in particular after the abrupt drop in market prices in October, 1987. However, the improvements continue to be apparent over the long haul of 1985-2006 which has seen a number of extreme price changes. This result is supported by an analysis of the Negentropies embedded in the forecasting distributions, and a proper scoring analysis of these Negentropies as well.

Abstract: We have extended some previous works by applying the product partition model (PPM) to identify multiple change points in the variance of normal data sequence assuming mean equal to zero. This type of problem is very common in applied economics and finance. We consider the Gibbs sampling scheme proposed in the literature to obtain the posterior estimates or product estimates for the variance and the posterior distributions for the instants when changes take place and also for the number of change points in the sequence. The PPM is used to obtain the posterior behavior of the volatility (measured as the variance) in the series of returns of four important Latin American stock indexes (MERVAL-Argentina, IBOVESPABrazil, IPSA-Chile and IPyC-Mexico). The posterior number of change point as well as the posterior most probable partition for each index series are also obtained.

Abstract: Abstract: Partial least squares (PLS) method has been designed for handling two common problems in the data that are encountered in most of the applied sciences including the neuroimaging data: 1) Collinearity problem among explanatory variables (X) or among dependent variables (Y); 2) Small number of observations with large number of explanatory variables. The idea behind this method is to explain as much as possible covariance between two blocks of X and Y variables by a small number of uncorrelated variables. Apart from the other applied sciences in which PLS are used, in the application of imaging data PLS has been used to identify task dependent changes in activity, changes in the relations between brain and behavior, and to examine functional connectivity of one or more brain regions. The aim of this paper is to give some information about PLS and apply on electroencephalography (EEG) data to identify stimulation dependent changes in EEG activity.