This paper deals with RIDGE ESTIMATION of fuzzy nonparametric regression models using triangular fuzzy numbers. This ESTIMATION method is obtained by implementing RIDGE regression learning algorithm in the La- grangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting the optimal value of the smoothing param- eter is fuzzified to fit the presented model. Some simulation experiments are then presented which indicate the performance of the proposed method.

RIDGE estimator has been suggested as an alternative to the maximum likelihood estimator in the presence of collinearity among the elements of unobservable values in functional measurement error models. We derive the influence function of the individual observations on the RIDGE estimate in this context. We also derive different versions of the sample influence functions and we define the Cook's statistic analogues to one given in ordinary linear regression models. Finally, using the influence function we will find the asymptotic distribution of the RIDGE estimator. Among different results, we show that influence of each observation on the RIDGE estimator is linear combination of influence on the maximum likelihood estimator.

Evapotranspiration is one of the most important parameters in the Planning and operation of reservoirs, designing of irrigation systems. The practical importance of accurate estimates of evaporation and the complexity of effect phenomenon, shows the use of new methods of data mining. In this study, the simulation of pan evaporation in Tabriz station using multiple regression models were investigated. Meteorological data, including maximum and minimum air temperature, dew point, maximum and minimum air relative humidity, number of sunshine hours and Daily wind speed during (1992-2012) were used in synoptic Tabriz stations. Various models of multiple linear regression and nonlinear one were derived for Tabriz station. The selected multiple linear regression model were tested by RIDGE Regression method to be considered multi-collinearity among inputs in the model. Variance inflation factor, values for each variable were calculated. The results showed that all Variance inflation factor, s had the value less than 10. In addition, the ratio lmax/lmax for two- variable selected model was 3.34. Therefore, there was no multi-collinearity in the selected multiple linear regression model f (Tmin, n). Durbin-Watson statistic for the selected model was 1.45 that shows the reliability of the selected multiple linear regression model. RMSE and R2 values of the selected models (multiple linear regression and Non- Linear Regression) was calculated as 2.45 and 0.67 and 2.58 and 0.65, respectively. This results demonstrate the ability of regression techniques to estimate Pan evaporation in Tabriz station.

This paper focuses on estimating RIDGE in a type-2 fuzzy non-parametric regression model that utilizes non-fuzzy inputs, type-2 fuzzy output data, and type-2 fuzzy coefficients within a dual Lagrange space. It begins with definitions of type-2 fuzzy sets (T2FSs) and presents a closed parametric form for complete triangular T2FSs. The proposed framework underpins a local linear smoothing method that incorporates a cross-validation procedure for optimizing RIDGE parameters and smoothing values. The research advances statistical modeling with type-2 fuzzy systems, offering innovative techniques for regression analysis in complex data situations. The combination of RIDGE ESTIMATION, local linear smoothing, and cross-validation is highlighted for its potential to yield precise results. Our work is able to model complex and nonlinear relationships between variables, which more effectively deals with uncertainties and ambiguities in the data, prevents overfitting, and ultimately improves the accuracy and reliability of predictions. Numerical simulations are included to validate the theoretical findings and demonstrate the method's effectiveness.

In this article, an attempt has been made to estimate the amount of sound transmission loss in a flat oval channel by applying the approach of statistical energy analysis. Correct ESTIMATION of sound transmission loss in an air conditioning channel is of great importance due to the harmful effects of noise pollution in the environment on human health. Simulation with the statistical energy analysis method is a powerful approach to estimate sound and vibration in problems in which we deal with complex and multi-part systems; is considered. In this method, first, a system is divided into several subsystems, and then by writing a matrix equation that includes the energy exchanges between subsystems and energy loss coefficients; It is investigated from the perspective of vibration and sound ESTIMATION.On average, the model presented in this research is able to estimate the sound transmission loss in different dimensions of the air conditioning channels according to the experimental results in the accuracy range of ± 2.5 dB. Considering that it seems that the results obtained from modeling with this method are in good agreement with the experimental data; The results of this research can be used as an efficient approach to estimate noise in oval shaped channels stretched in different lengths.

The hydraulic conductivity of soil is an important physical characteristic, which is used for water modeling and the modeling of solutes and pollutants transport. The direct measurement of soil hydraulic conductivity is a time-consuming and costly process, and due to experimental errors and soil heterogeneity, the results are sometimes unrealistic. Besides, it could be estimated by easily measurable soil properties. The purpose of this study is to develop genetic programming and linear regression models to estimate the saturated hydraulic conductivity of soil using readily available soil properties. With this purpose, 160 soil samples with different properties were gathered from various areas of East Azerbaijan province of Iran. Then some physical and chemical characteristics of soil such as the proportions of sand, silt and clay in the soil, and organic matter, bulk density, pH and EC values were measured. Then the data was divided into two different data sets, namely training (75% of data) and testing (25% of data) datasets. GeneXproTools 4. 0 and Statistica softwares were used to calibrate Genetic programming and regression models, respectively. Six pedotranfer functions (PTFs) with a combination of different mathematical operators were designed by the genetic programming. Finally, one of the PTFs which was more accurate than the others was selected. Also, the RIDGE regression was utilized to develop regression PTFs. The accuracy and reliability of PTFs were determined by R2, RMSE, and MAE criteria. The research results showed that the genetic programming PTF (GP-PTF) is more accurate and reliable in comparison with the regression-PTF. In a way that the R2, RMSE (Cm h-1) and MAE (Cm h-1) of GP-PTF were 0. 91, 1. 82 and 1. 23 for the training dataset, respectively, and for the test dataset, the values were 0. 92, 2. 27 and 1. 59, respectively; whereas the values of the above mentioned criteria of regression-PTF for the training dataset were 0. 70, 3. 48 and 2. 07, respectively, and for the test dataset were 0. 76, 3. 11 and 1. 88, respectively.

This study aimed to estimate the genetic parameters of body weight traits in Markhoz goats, using B-spline random regression models. The data used in this study included 19549 records collected during 29 years (1992-2021) in Markhoz goat Breeding Research Station, located in Sanandaj, Iran. The model used to analyze data included fixed effects (year of birth, sex, type of birth and age of dam) and random effects including direct additive genetic, maternal additive genetic, permanent environmental and maternal permanent environmental assuming homogeneous and heterogeneous residual variance during the time. Akaike (BIC) and Bayesian (BIC) information criteria were used to compare the models and bspq.4.4.4.4 was selected as the best model. The direct heritability values for birth, 3-month, 6-month, 9-month and 12-month weights were estimated to be 0.14, 0.16, 0.08, 0.28 and 0.26, respectively. Genetic correlation between body weights at birth and 3-month, birth and 6-month, birth and 9-month, birth and 12-month, 3-month and 6-month, 3-month and 9-month, 3-month and 12-month, 6-months and 9-month and 9-month and 12-month were 0.22, 0.38, 0.21, 0.56, -0.26, 0.30, 0.62, 0.86 and 0.77, respectively. The highest phenotypic correlation was between the weight of 9-month and 12-month (0.82) and the lowest correlation was between birth weight and 3-month and 6-month (0.12). The results showed that the 9-month weight is a good criterion for selection in Markhoz goats.

This paper considers an extension of the linear mixed model, called semiparametric mixed effects model, for longitudinal data, when multicollinearity is present. To overcome this problem, a new mixed RIDGE estimator is proposed while the nonparametric function in the semiparametric model is approximated by the kernel method. The proposed approache integrates RIDGE method into the semiparametric mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. The asymptotic normality of the exhibited estimator is established. To improve efficiency, the ESTIMATION of the covariance function is accomplished using an iterative algorithm. Performance of the proposed estimator is compared through a simulation study and analysis of CD4 data.