Nonparametric additive model is one of the common models for modeling the relationship between variables. In this paper, we consider the high-dimensional nonparametric additive model in which the number of explanatory variables can exceed the number of observations, but the number of important explanatory variables relative to the number of observations is small. When the number of explanatory variables in the model is large, model interpretation becomes more difficult and computational costs increase. Therefore, identifying the explanatory variables that have a significant impact on the response or non-zero additive components in this model is crucial. To this end, we first approximate the additive components using B-spline bases. By employing this approximation, the problem of variable selection is transformed into selecting groups of non-zero coefficients. Then, we use grouped penalty functions for selecting non-zero coefficients. This is usually done by minimizing the sum of squared errors subject to a constraint. Minimizing this target function requires the use of optimization methods. In this paper, we utilize a group descent algorithm to solve the aforementioned minimization problem. Finally, the performance of this algorithm is examined under three different penalty functions through simulation studies and analysis of a real dataset.

Assessing the vulnerability of groundwater is an effective tool to identify vulnerable areas and conservation activities in order to maintain water quality in these areas. DRASTIC method has been used for vulnerability assessment more than other methods in scale area. The weakness of this method is estimating the weights of the model parameter. The aim of this research is to optimize the weights of DRASTIC model by using statistical nonparametric method. In this regard, the appropriate inputs of DARSTIC model were collected from Dezful area, and then vulnerability of the groundwater of this area was determined based on the primary weights of the model parameters. The final weights of the parameters were optimized using nonparametric test and the concentration of the nitrates in Dezful area. Results show better performance of optimized DRASTIC model than original DRASTIC model.

Nonlinear regression models have widespread applications across diverse scientific disciplines‎. ‎Achieving precise fitting of the optimal nonlinear model is essential‎, ‎taking into account the biases inherent in Bayesian optimal design‎. ‎This study introduces a Bayesian optimal design utilizing the Dirichlet process as a prior‎. ‎The Dirichlet process is a fundamental tool in exploring Nonparametric Bayesian inference‎, ‎providing multiple well-suited representations‎. ‎The research paper presents a novel one-parameter model‎, ‎termed the ``unit-exponential distribution"‎, ‎specifically designed for the unit interval‎. ‎Additionally‎, ‎a representation is employed to approximate the D-optimality criterion‎, ‎considering the Dirichlet process as a functional tool‎. ‎Through this approach‎, ‎the aim is to identify a nonparametric Bayesian optimal design.

In this paper, a nonparametric logit modelling was introduced to estimate the probability of participation of Iranian female labour using household income- expended in 2008. The logistic function for women’s participation was regressed based on the maximum likelihood estimator that the geographical location (urban/rural), husband’s income, education, female age, non-labour income, number of children above and under six years were implemented for input variables. The accuracies of the logit models based on the parametric and nonparametric modeling approaches were evaluated using White statistic, confidence index, and root mean square error. Finally, the marginal effects of input variables on women’s probability of participation were estimated based the results of calibrated unknown coefficients of parametric and nonparametric models. The results demonstrated that nonparametric logit model is more accurate than parametric logit model. Education and number of child under six years have effective positive and negative effects compared to another input variables, respectively.

Introduction: Diabetes is a chronic disease, non-epidemic disease that costs a lot of money in each year. One of the diagnostic criteria for diabetes is Glycosylated Hemoglobin (HBA1C), which in this study the effective factors on it examined by additive regression model. Materials and Methods: In this cross-sectional study, 130 patients with diabetes type-2 were selected based on simple random sampling in Ilam city (Iran). Several variables were examined such as gender, age, weight, height, systolic and diastolic blood pressure, hypertension, smoking, family history of diabetes, daily walking for at least 30 minutes, waist and hip circumferences, HbA1c, fasting blood sugar (FBS), RBC mean corpuscular volume (MCV) and BMI. The data were collected based on Canadian diabetes checklist questionnaire. Results: In simple linear regression, waist and hip circumferences and in multiple regression, hip circumference and BMI had a significant effect on HBA1C (P<0. 05). Importantly, in simple additive regression waist, hip circumferences and fasting blood Sugar as well as in multiple additive regression waist, hip circumferences, fasting blood sugar and BMI had significant effects on HbA1C (P<0. 05). Conclusion: Additive regression model with 0. 878 adjusted R-squared and AIC equal to 603. 464 was better model for examining the influential factors on HbA1C compared with the multiple regression model with adjusted R-squared and AIC equal to 0. 386 and 844. 730, respectively.

Introduction: Parkinson disease is a neurodegenerative disease that disrupts functional brain networks. Many neurodegenerative disorders are associated with changes in brain communication patterns. Resting-state functional connectivity studies can distinguish the topological structure of Parkinson patients from healthy individuals by analyzing patterns between different regions of the brain. Accordingly, the present study aimed to determine the brain topological features and functional connectivity in patients with Parkinson disease, using a Bayesian approach. Methods: The data of this study were downloaded from the open neuro site. These data include resting-state functional magnetic resonance imaging (rs-fMRI) of 11 healthy individuals and 11 Parkinson patients with mean ages of 64. 36 and 63. 73, respectively. An advanced nonparametric Bayesian model was used to evaluate topological characteristics, including clustering of brain regions and correlation coefficient of the clusters. The significance of functional relationships based on each edge between the two groups was examined through false discovery rate (FDR) and network-based statistics (NBS) methods. Results: Brain connectivity results showed a major difference in terms of the number of regions in each cluster and the correlation coefficient between the patient and healthy groups. The largest clusters in the patient and control groups were 26 and 53 regions, respectively, with clustering correlation values of 0. 36 and 0. 26. Although there are 15 common areas across the two clusters, the intensity of the functional relationship between these areas was different in the two groups. Moreover, using NBS and FDR methods, no significant difference was observed for each edge between the patient and healthy groups (P>0. 05). Conclusion: The results of this study show a different topological configuration of the brain network between the patient and healthy groups, indicating changes in the functional relationship between a set of areas of the brain.

Sharp bounds for medians of L-statistics in the nonparametric statistical model with all continuous and strictly increasing distribution functions are given. As a corollary we conclude that L-statistics are very poor nonparametric quantile estimators.