Generalized Cross Validation Research Articles

Fourier regression model predicting train-bridge interactions under wind and wave actions

A train-bridge system crossing a sea can be subjected to extreme environmental conditions such as the concomitant actions of wind and waves, which adversely affect the entire system. This study proposes an approach to evaluate the train-bridge interaction under wind and wave actions. The wind and wave parameters are collected using structural health monitoring (SHM), then correlated using copula models. The wind-bridge, wind-train, and wave-bridge interactions are solved using a real-time co-simulation (RTCS) solution. Besides, this paper introduces a surrogate model named the Fourier regression model (FRM) and Generalized cross-validation (GCV) algorithm to substitute further RTCS calculations. The best solution is obtained by searching for the optimal K value using the GCV algorithm. The results indicate that the dynamic indices of the system are more sensitive when the wind-wave coupling action is considered than when only the wind load is applied. Moreover, the bridge responses for 100 years return period are about 5%∼50% greater than that of 50 years and 25 years return periods. The train responses increase by 7%∼16% compared to the 50 years and 25 years return periods.

MODELING OF LOCAL POLYNOMIAL KERNEL NONPARAMETRIC REGRESSION FOR COVID DAILY CASES IN SEMARANG CITY, INDONESIA

Coronavirus disease 2019 (COVID-19) is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) which was recently discovered. Coronavirus disease is now a pandemic that occurs in many countries in the world, one of which is Indonesia. One of the cities in Indonesia that has found many COVID cases is Semarang city, located in Central Java. Data on cases of COVID patients in Semarang City which are measured daily do not form a certain distribution pattern. We can build a model with a flexible statistical approach without any assumptions that must be used, namely the nonparametric regression. The nonparametric regression in this research using Local Polynomial Kernel approach. Determination of the polynomial order and optimal bandwidth in Local Polynomial Kernel Regression modeling use the GCV (Generalized Cross Validation) method. The data used this research are data on the number of COVID patients daily cases in Semarang, Indonesia. Based on the results of the application of the COVID patient daily cases in Semarang City, the optimal bandwidth value is 0.86 and the polynomial order is 4 with the minimum GCV is 3179.568 so that the model estimation results the MSE is 2922.22 and the determination coefficient is 97%. The estimation results show the highest number of Corona in the Semarang City at the beginning of July 2020. After the corona case increased in July, while the corona case in August decreased.

Comparison of simultaneously nonparametric regression based on spline and Fourier series estimator related social aid distribution in Indonesia

Several estimators in the nonparametric regression approach that are often used are the Spline estimator and the Fourier series. Both estimators have high flexibility and can adapt to the local nature of the data effectively. This study applies these two methods to compare the best performance of the formed model. The data used in this study are multi-response data in the form of types of government assistance and multi-predictor data in the form of factors that are thought to affect the distribution of aid receipts in the community. This research is important to optimize the distribution of welfare assistance in Indonesia, especially during the Coronavirus Disease-19 (Covid-19) pandemic. By using the Generalized Cross-Validation (GCV) criteria for the parsimony model, the estimator chosen to predict the distribution of welfare assistance in Indonesia is the Fourier series estimator with cosine and sine bases. The goodness of the nonparametric regression model with the Fourier series estimator can be seen from the minimum GCV value generated with one oscillation parameter, which is 1.483961, with a Mean Square Error (MSE) of 2.1257374, and R 2 of 0.923143. The prediction results are expected to be the government's recommendation for the restoration of community welfare through equitable distribution of aid to support the achievement of the Sustainable Development Goals (SDGs).

Soil radioactivity-depth profiles from regularized inversion of borehole gamma spectrometry data

An in situ borehole gamma logging method using a LaBr3 gamma detector has been developed to characterize a137Cs contaminated site. The activity-depth distribution of 137Cs was derived by inversion of the in situ measurement data using two different least squares methods, (i) Least squares optimization (LSO) and (ii) Tikhonov regularization. The regularization parameter (λ) of the Tikhonov regularization method was estimated using three different methods i.e. the L-curve, Generalized Cross Validation (GCV) and a prior information based method (PIBM). The considered inversion method variants were first validated for a137Cs contaminated pipe, and in most of the cases, the calculated activity of 137Cs was found to be within the acceptable range. The calculated 137Cs activity-depth profiles from in situ measurements were also in good agreement with the ones obtained from soil sample analysis, with an R2 ranging from 0.76 to 0.82. The GCV method for estimating λ appeared to perform better than the two other methods in terms of R2 and root mean squared error (RMSE). The L-curve method resulted in higher RMSE than the other Tikhonov regularization methods. Instability was observed in the activity concentration depth profile obtained from the LSO method. Therefore, we recommend the Tikhonov regularization with GCV for estimating λ for estimating the activity concentration-depth profile. The site studied showed 137Cs activity concentrations above the exemption limit down to depths of 0.50–0.90 m.

Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

<p class='IJASEITAbtract'>Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R²) value and better accuracy for each combination of sample sizes and variance variations.

Tensorial conditional gradient method for solving multidimensional ill-posed problems

We consider solving a class of tensorial ill-conditioned problems. This problem is treated as a convex constrained minimization problem. This kind of ill-conditioned problems appears in several applications as color images and video restoration. A new tensor degradation model to recover color image and video from blur and noise is given. Tikhonov regularization approach is used to reduce the effect of noise in the computed solution. This approach leads to a convex tensor minimization problem, that can be solved basing on the conditional gradient method. We adapted the Generalized Cross Validation method to the tensorial model for appropriate choice of the regularization parameter. Numerical tests for image and video restoration are given to illustrate the effectiveness of the proposed approach compared with the classical method.

The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.

Integral Estimator with Kernel Approach for Estimating Nonparametric Regression Functions

Derivatives are measurements of how a function change as the input value changes, or in general a derivative shows how one quantity changes due to a change in another quantity. The concept of universal or comprehensive function derivatives is widely used in various scientific fields. For example, in economics, people are interested in studying the condition of the derivative of an objective function as the result of an optimization problem. In this study, nonparametric procedures are used to estimate a function where the form of the function does not lead to a particular function model. Suppose we are given a nonparametric regression model where f is an unknown function. The main problem of regression analysis is to determine the form of estimation f. To determine the estimation of f, one approach that can be used is the integral estimator with the Gaussian Kernel approach. Furthermore, as an application, the Labour Force Participation Rate (y) data is used with the predictor variable, namely the Average Length of Schooling (x). By using the GCV (Generalized Cross Validation) method, the optimal bandwidth is obtained at h = 80 with a GCV value of 0.243 with an MSE value of 32.1864.

Selection of Optimal Smoothing Parameters in Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression

In this article, we propose a new method of selecting smoothing parameters in semiparametric regression. This method is used in semiparametric regression estimation where the nonparametric component is partially approximated by multivariable Fourier Series and partly approached by multivariable Kernel. Selection of smoothing parameters using the method with Generalized Cross-Validation (GCV). To see the performance of this method, it is then applied to the data drinking water quality sourced from Regional Drinking Water Company (PDAM) Surabaya by using Fourier Series with trend and Gaussian Kernel. The results showed that this method contributed a good performance in selecting the optimal smoothing parameters.

Mixed estimator of spline truncated, Fourier series, and kernel in biresponse semiparametric regression model

Regression analysis is a method of analysis to determine the relationship between the response and the predictor variables. There are three approaches in regression analysis, namely the parametric, nonparametric, and semiparametric approaches. Biresponse Semiparametric regression model is a regression model that uses a combination approach between parametric and nonparametric components, where two response variables are correlated with each other. For data cases with several predictor variables, different estimation technique approaches can be used for each variable. In this study, the parametric component is assumed to be linear. At the same time, the nonparametric part is approached using a mixture of three estimation techniques, namely, spline truncated, Fourier series, and the kernel. The unknown data pattern is assumed to follow the criteria of each of these estimation techniques. The spline is used when the data pattern tends to change at certain time intervals, the Fourier series is used when the data pattern tends to repeat itself, and the kernel is used when the data does not have a specific way. This study aims to obtain parameter estimates for the mixed semiparametric regression model of spline truncated, Fourier series, and the kernel on the biresponse data using the Weighted Least Square (WLS) method. The formed model depends on the selection of knot points, oscillation parameters, and optimal bandwidth. The best model is based on the smallest Generalized Cross Validation (GCV).

Estimation of electron fluxes in the Earth's geostationary orbit with Tikhonov regularization during a magnetically quiet period

Electron energy fluxes in the Earth's outer radiation belt are estimated using an inverse theory of the Tikhonov regularization based upon observations in geostationary orbits. Particle Detector (PD) experiment aboard a geostationary satellite GEO-KOMPSAT-2A (GK2A) at a geographic longitude of 128.2°E provided observations of electrons within a 150–2,400 keV energy range with an unprecedented energy resolution of ΔE/E in the range of 5–25%. Instrument response functions, calculated with Monte-Carlo simulations, are deconvoluted with electron observations. Using regularization parameters determined from Generalized Cross Validation (GCV), the Tikhonov method was applied to observations made during a geomagnetically quiet period. This Tikhonov regularization method, now possible for observations in the Earth's radiation belt for the first time, allows direct inference of electron fluxes without resorting to predetermined functional forms. Comparisons of our results with those from conventional methods indicate differences among the results as large as ∼200%.

Consistent Risk Estimation in Moderately High-Dimensional Linear Regression

Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical properties of such estimators have been extensively studied in the low-dimensional settings, where the number of predictors p is much smaller than the number of observations n. However, a unifying methodology accompanied with a rigorous theory is lacking in high-dimensional settings. This paper studies the problem of risk estimation under the moderately high-dimensional asymptotic setting n,p → ∞ and n/p → δ > 1 ( δ is a fixed number), and proves the consistency of three risk estimators that have been successful in numerical studies, i.e., leave-one-out cross validation (LOOCV), approximate leave-one-out (ALO), and approximate message passing (AMP)-based techniques. A corner stone of our analysis is a bound that we obtain on the discrepancy of the `residuals' obtained from AMP and LOOCV. This connection not only enables us to obtain a more refined information on the estimates of AMP, ALO, and LOOCV, but also offers an upper bound on the convergence rate of each estimator.

PEMODELAN KASUS GIZI BURUK PADA BALITA DI PROVINSI BALI TAHUN 2018 MENGGUNAKAN REGRESI SPLINE

Malnutrition associated with an unusual condition of the patient's nutritional status because the body weight index and age are not suitable, where body weight should be positively correlated with age. According to data from the Bali Health Department, malnutrition cases found in 2016 is 3,4% while in 2017 it founded 3,8%. This research uses spIine regression with malnutrition cases of children under 5 years old in Bali Province. To compare basis truncated spIine and B-SpIine, this study using the minimum value of Generalized Cross Validation (GCV) and Mean Square Error (MSE) of each basis. B-SpIine quadratic modeI with four knots is the best model.

Goodness of Fit Test of an Autocorrelated Time Series Cubic Smoothing Spline Model

We investigated the finite properties as well as the goodness of fit test for the cubic smoothing spline selection methods like the Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV) and Mallow CP criterion (MCP) estimators for time-series observation when there is the presence of Autocorrelation in the error term of the model. The Monte-Carlo study considered 1,000 replication with six sample sizes: 30; 60; 120; 240; 480 and 960, four degree of autocorrelations; 0.1; 0.3; 0.5; and 0.9 and three smoothing parameters; lambdaGML= 0.07271685, lambdaGCV= 0.005146929, lambdaMCP= 0.7095105. The cubic smoothing spline selection methods were also applied to a real-life dataset. The Predictive mean square error, R-square, and adjusted R-square criteria for assessing finite properties and goodness of fit among competing models discovered that the performance of the estimators is affected by changes in the sample sizes and autocorrelation levels of the simulated and real-life data set. The study concluded that the Generalized Cross-Validation estimator provides a better fit for Autocorrelated time series observation. It is recommended that the GCV works well at the four autocorrelation levels and provides the best fit for time-series observations at all sample sizes considered. This study can be applied to; non –parametric regression, non –parametric forecasting, spatial, survival and econometric observations.

Pengaruh Indeks Massa Tubuh dan TrigliseridaTerhadap Gula Darah dengan Model Regresi Nonparametrik Spline Biprediktor

The regression approach can be carried out using three approaches namely parametric, nonparametric and semiparametric approaches. Nonparametric regression is a statistical method used to see the relationship between the response variable and the predictor variable when the shape of the data curve is unknown. Diabetes mellitus (DM) or commonly called diabetes is a disease that is found and observed in various parts of the world today. DM is often marked by a significant increase in blood sugar levels. In this study using blood sugar levels as response variables, body mass index and triglycerides as predictor variables. Data were analyzed using truncated linear spline with one, two and three point knots experiments. The best model is obtained based on the minimum generalized cross validation (GCV) value. The results obtained that the best model is linear spline using three point knots.

Stochastic restricted Liu predictors in linear mixed models

In this article, we propose the stochastic restricted Liu predictors by augmenting the stochastic restrictions to the linear mixed models. The Liu biasing parameter is selected via generalized cross validation (GCV) criterion. Comparisons between the stochastic restricted Liu estimators and several other estimators, namely the BLUE, the mixed and Liu estimators are made through the mean square error matrix criterion. Finally, a numerical example and a simulation study are done to show the performance of the estimators.

Forecast of Hemorrhagic Fever With Renal Syndrome and Meteorological Factors of Three Cities in Liaoning Province, China, 2005–2019

Background: Hemorrhagic fever with renal syndrome (HFRS) is an endemic in China, accounting for 90% of HFRS cases worldwide and growing. Therefore, it is urgent to monitor and predict HFRS cases to make control measures more effective. In this study, we applied generalized additive models (GAMs) in Liaoning Province, an area with many HFRS cases. Our aim was to determine whether GAMs could be used to accurately predict HFRS cases and to explore the association between meteorological factors and the incidence of HFRS.Methods: HFRS data from Liaoning were collected from January 2005 to May 2019 and used to construct GAMs. Generalized cross-validation (GCV) and adjusted R-square (R2) values were used to evaluate the constructed models. The interclass correlation coefficient (ICC) was used as an index to assess the quality of the proposed models.Results: HFRS cases of the previous month and meteorological factors with different lag times were used to construct GAMs for three cities in Liaoning. The three models predicted the number of HFRS cases in the following month. The ICCs of the three models were 0.822, 0.832, and 0.831. Temperature and the number of cases in the previous month had a positive association with HFRS.Conclusion: GAMs applied to HFRS case data are an important tool for HFRS control in China. This study shows that meteorological factors have an effect on the occurrence of HFRS. A mathematical model based on surveillance data could also be used in forecasting. Our study will inform local CDCs and assist them in carrying out more effective measures for HFRS control and prevention through simple modeling and forecasting.

Improved Generalized Cross-Validation and Unbiased Predictive Risk Estimator Methods Using the RGSVD: Application to Inversion of Potential Field Data

The inversion of potential field data has widely utilized the generalized cross-validation (GCV) and the unbiased predictive risk estimator (UPRE) methods to determine the regularization parameter. However, these two methods are time-consuming and it is difficult for them to determine the optimal linear search range including the optimal regularization. To solve these problems, this article improves the GCV and UPRE methods using the RGSVD (randomized generalized singular value decomposition) algorithm. The improved methods first use the randomized algorithm to compute an approximate generalized singular value decomposition (GSVD) with less computational time. Then, the optimal linear search range is determined based on the generalized singular values. Finally, the GCV and the UPRE functions are efficiently computed on the basis of the results from the RGSVD algorithm. In this way, the GCV and UPRE methods using the RGSVD algorithm are able to determine the optimal regularization parameter fast and effectively. One comparative test shows the effectiveness and efficiency of the GCV and the UPRE methods using the RGSVD algorithm.

Least Squares Model Averaging Based on Generalized Cross Validation

Least Squares Model Averaging Based on Generalized Cross Validation

Analisis Faktor-Faktor Yang Berpengaruh Terhadap Pencemaran Air Sungai Mahakam Menggunakan Pemodelan Geographically Weighted Logistic Regression Pada Data Dissolved Oxygen

Geographically Weighted Logistic Regression (GWLR) model is a local model of the logistic regression model applied to spatial data. Parameter estimation is performed at each observation location using spatial weighting. The spatial weighting is calculated by using an adaptive tricube function and bandwidth optimum was obtained based on Generalized Cross Validation (GCV) criteria. The purpose of this study was to obtain a GWLR model on the water pollution indicator Dissolve Oxygen (DO) in Mahakam River in East Kalimantan Province and to find factors affecting the probability of the Mahakam River water was not polluted based on DO indicator. The research data is secondary obtained from Environmental Department of East Kalimantan. The parameter estimation method was Maximum Likelihood Estimation (MLE). The research result showed that the closed form of ML estimator could not be found analytically and it can be approximed by using Newton-Raphson iterative methods. Based on the result of partial hypothesis test, the factors influencing the probability of the Mahakam River water was not polluted is different for every observation location. They were phosphate consentration, total dissolved solid and nitrite consentration. The factor influencing globally was total dissolved solid.