Journal of Data Science

Abstract: Considering the importance of science and mathematics achieve ments of young students, one of the most well known observed phenomenon is that the performance of U.S. students in mathematics and sciences is undesirable. In order to deal with the problem of declining mathematics and science scores of American high school students, many strategies have been implemented for several decades. In this paper, we give an in-depth longitudinal study of American youth using a double-kernel approach of non parametric quantile regression. Two of the advantages of this approach are: (1) it guarantees that a Nadaraya-Watson estimator of the conditional func tion is a distribution function while, in some cases, this kind of estimator being neither monotone nor taking values only between 0 and 1; (2) it guar antees that quantile curves which are based on Nadaraya-Watson estimator not absurdly cross each other. Previous work has focused only on mean re gression and parametric quantile regression. We obtained many interesting results in this study.

Abstract: We compare two linear dimension-reduction methods for statisti cal discrimination in terms of average probabilities of misclassification in re duced dimensions. Using Monte Carlo simulation we compare the dimension reduction methods over several different parameter configurations of multi variate normal populations and find that the two methods yield very different results. We also apply the two dimension-reduction methods examined here to data from a study on football helmet design and neck injuries.

Abstract: Longitudinal studies represent one of the principal research strategies employed in medical and social research. These studies are the most appropriate for studying individual change over time. The prematurely withdrawal of some subjects from the study (dropout) is termed nonrandom when the probability of missingness depends on the missing value. Nonrandom dropout is common phenomenon associated with longitudinal data and it complicates statistical inference. Linear mixed effects model is used to fit longitudinal data in the presence of nonrandom dropout. The stochastic EM algorithm is developed to obtain the model parameter estimates. Also, parameter estimates of the dropout model have been obtained. Standard errors of estimates have been calculated using the developed Monte Carlo method. All these methods are applied to two data sets.

The choice of an appropriate bivariate parametrical probability distribution for pairs of lifetime data in presence of censored observations usually is not a simple task in many applications. Each existing bivariate lifetime probability distribution proposed in the literature has different dependence structure. Commonly existing classical or Bayesian discrimination methods could be used to discriminate the best among different proposed distributions, but these techniques could not be appropriate to say that we have good fit of some particular model to the data set. In this paper, we explore a recent dependence measure for bivariate data introduced in the literature to propose a graphical and simple criterion to choose an appropriate bivariate lifetime distribution for data in presence of censored data.

Abstract: The power law process (PLP) (i.e., the nonhomogeneous Poisson process with power intensity law) is perhaps the most widely used model for analyzing failure data from reliability growth studies. Statistical inferences and prediction analyses for the PLP with left-truncated data with classical methods were extensively studied by Yu et al. (2008) recently. However, the topics discussed in Yu et al. (2008) only included maximum likelihood estimates and confidence intervals for parameters of interest, hypothesis testing and goodness-of-fit test. In addition, the prediction limits of future failure times for failure-truncated case were also discussed. In this paper, with Bayesian method we consider seven totally different prediciton issues besides point estimates and prediction limits for xn+k. Specifically, we develop estimation and prediction methods for the PLP in the presence of left-truncated data by using the Bayesian method. Bayesian point and credible interval estimates for the parameters of interest are derived. We show how five single-sample and three two-sample issues are addressed by the proposed Bayesian method. Two real examples from an engine development program and a repairable system are used to illustrate the proposed methodologies.

We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, R𝑒́nyi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also propose bivariate generalizations. We constructed a simple type Copula and intro-duced a useful stochastic property. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors via a simulation study.

In this paper, we consider functional varying coefficient model in present of a time invariant covariate for sparse longitudinal data contaminated with some measurement errors. We propose a regularization method to estimate the slope function based on a reproducing kernel Hilbert space approach. As we will see, our procedure is easy to implement. Our simulation results show that the procedure performs well, especially when either sampling frequency or sample size increases. Applications of our method are illustrated in an analysis of a longitudinal CD4+ count dataset from an HIV study.