Background and purpose: In many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. Regression is the most common tool in this situation. If we have some assumptions for such normality for response variable, we could use it. In this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus on longitudinal data.Materials and Methods: Consider nonparametric estimation in a varying coefficient model with repeated measurements (Yij, Xij, tij), for i=1, …, n and j=1, …, ni where Xij=(Xij0,…, Xijk)T and (Yij, Xij,tij) denote the jth outcome, covariate and time design points, respectively, of the ith subject. The model considered here is YijT b(tij)+ei(tij), where b(t)= (b0(t),…bk(t))T, for k³0 are smooth nonparametric functions of interest and ei(t) is a zero-mean stochastic process. The measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject. For evaluating this model, we use data of a cohort of 289 healthy infants born in Shiraz in 2007. The proposed nonparametric regression was fitted to them for obtaining effect rates of mother weight, mother arm circumference and maternal age at delivery time and maternal age at first menarche on boy’s arm circumference.Results: proposed nonparametric regression showed the varied effect of each independent variable over the time but other models achieved constant effect over the time that is in controversy with the inherent property of these natural phenomena.Conclusion: This study shows that this model and the spline nonparametric estimator could be useful in different areas of medical and health studies.

‎The recent advancements in technology have faced an increase in the growth rate of data‎.‎According to the amount of data generated‎, ‎ensuring effective analysis using traditional approaches becomes very complicated‎.‎One of the methods of managing and analyzing big data is classification‎.‎%One of the data mining methods used commonly and effectively to classify big data is the MapReduce‎‎In this paper‎, ‎the feature weighting technique to improve Bayesian classification algorithms for big data is developed based on Correlative Naive Bayes classifier and MapReduce Model‎.‎%Classification models include Naive Bayes classifier‎, ‎correlated Naive Bayes and correlated Naive Bayes with feature weighting‎.‎Correlated Naive Bayes classification is a generalization of the Naive Bayes classification model by considering the dependence between features‎.‎%This paper uses the feature weighting technique and Laplace calibration to improve the correlated Naive Bayes classification‎.‎The performance of all described methods are evaluated by considering accuracy‎, ‎sensitivity and specificity‎, ‎accuracy‎, ‎sensitivity and specificity metrics.

Estimation of a quantile density function from biased data is a frequent problem in industrial life testing experiments and medical studies. The estimation of a quantile density function in the biased nonparametric regression model is inves-tigated. We propose and develop a new wavelet-based methodology for this problem. In particular, an adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we prove that it enjoys powerful mean integrated squared error properties over Besov balls. The performance of proposed estimator is investigated by a numerical study. In this study, we develop two types of wavelet estimators for the quantile density function when data comes from a biased distribution function. Our wavelet hard thresholding estimator which is introduced as a nonlinear estimator, has the feature to be adaptive according to q(x). We show that these estimators attain optimal and nearly optimal rates of convergence over a wide range of Besov function classes.

In the meta-analysis of clinical trials, usually the data of each trail summarized by one or more outcome measure estimates which reported along with their standard errors. In the case that summary data are multi-dimensional, usually, the data analysis will be performed in the form of a number of separated univariate analysis. In such a case the correlation between summary statistics would be ignored. In contrast, a multivariate meta-analysis model, use from these correlations synthesizes the outcomes, jointly to estimate the multiple pooled effects simultaneously. In this paper, we present a nonparametric Bayesian bivariate random effect meta-analysis.

This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean square error (IMSE). The results of simulation studies show a significant improvement achieved by our approach compared to the standard version of confidence intervals algorithm. Finally, real data analysis shows that the accuracy of our method compared to that of previous works for computing the confidence interval.