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.

Background: The prevalence of type 2 diabetes mellitus (T2DM) is increasing in Iran. This study determined the prevalence of undiagnosed type 2 diabetes mellitus in apparently normal individuals in Hamadan, west of Iran. Study design: A cross-sectional study. Methods: A sample of 106 apparently normal volunteers aged 18 yr and more were enrolled, and T2DM was diagnosed using hemoglobin A1c (HbA1c) levels from 2015-2016. The nonparametric bootstrap method was used to eliminate the undesirable effect of small sample size on the estimation of standard error of multiple logistic regression coefficients and confidence interval for the prevalence of undiagnosed T2DM. Results: Overall, 23 (21. 69%) were male. The mean (± sd) age of the participants was 43. 76 ± 14. 01 year. In 78. 3% of individuals, HbA1c level was within normal range (<5. 7), 13. 21% was in the range of 5. 7-6. 4 (undiagnosed pre-T2DM), and 8. 49% was ≥ 6. 5 (undiagnosed T2DM). Multiple logistic regression gave the characteristic distribution of volunteers such as sedentary hour (P=0. 001), family history of diabetes (P=0. 001), smoking (P=0. 002), and age (P=0. 012) had the odds on the significant effect on undiagnosed T2DM. Conclusions: The prevalence of undiagnosed T2DM among apparently normal individuals in Hamadan was relatively high. Addition to age, factors such as sedentary, exposure to smoking and having a history of diabetes in family can be a prognosis for undiagnosed T2DM in apparently normal individuals.

The purpose of this paper is to express and calculate the variance confidence interval with the Chachi method of data conversion and without converting the initial data with the bootstrap method. Because the data conversion depends on the amount of variance in the denominator of the conversion expression, it fluctuates and as a result, estimating the confidence intervals and testing the hypothesis is challenged. The results of both methods are compared and their advantages and disadvantages are examined. For this purpose, they first deal with concepts such as the fuzzy random variable and the distance between fuzzy data based on the concept of α,-shak as well as α,-cut. The hypothesis testing process is then performed for the variance of a sample fuzzy data. The bootstrap method was used to test the hypothesis and the mentioned confidence intervals were compared with the confidence intervals obtained by α,-bresh method.

Neural networks are among those mathematical models which are used to model non-linear time series with high accuracy. The advantage with these linear times series as opposed to topical ones is that they don’t require restrictive assumptions. The accuracy of neural network based estimators as nonparametric models is of high importance. In that light, we can use bootstrapping to calculate the accuracy of estimators in the time series’ complex nonlinear structures. Though introduced in recent years these methods yield more accurate results in the bias calculation of estimators compared to the other ones. This paper introduces neural network bootstrap, bootstrap autoregressive, moving block bootstrap method and residual bootstrap methods in time. Then these four algorithms are compared with each other in a simulation study. Finally an example related to Iran’s kerosene price monthly data is worked out.

Kernel estimation of the cumulative distribution function (CDF), when the support of the data is bounded, suffers from bias at the boundaries. To solve this problem, we introduce a new estimator for the CDF with support (0,1) based on the beta kernel function. By studying the asymptotic properties of the proposed estimator, we show that it is consistent and free from boundary bias. We conducted an extensive simulation to illustrate the performance of the proposed estimator. The results demonstrate the superiority of the proposed estimator over other commonly used estimators. As an application, we use the estimated CDF for nonparametric simulation. Using a numerical study, we show that the performance of the kernel probability density function (PDF) estimation in which a large sample simulated from the estimated CDF is employed can be noticeably improved. We also use the proposed estimator to estimate the CDF of the household health cost in Iran in 2019.

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 reviews Bayesian Nonparametric methods and discusses how parametric predictive densities can be constructed using nonparametric ideas.