I Nyoman Budiantara

Spline Nonparametric Regression Analysis of Stress-Strain Curve of Confined Concrete

Note from the Editor: The ability to forecast maximum water depth during maximum discharge of a design flood is very important in designing flood protection scheme along the river reach. This paper explains the use of ISIS Flow, a one-dimensional hydrodinamic computer modelling for river flood forecasting. The computer simulations produced detailed information from each node including the maximum water depth during maximum discharge, thus it can be expected that an economical flood protection structure can be produced.Variable Message Sign (VMS) is especially recommended for congested flow conditions. The aim of this study is to investigate how drivers in a large city in a developing country with many specific geometric and traffic conditions and also specific driver behaviour, use VMS in aid of choosing route for their inter-city trips. Furthermore, to explore the impact of the use of the information on increasing traffic performance measures. A case study was carried out in Bandung, Indonesia. Microscopic traffic simulations were used in this study to evaluate traffic performance measures. The results of the evaluation found that VMS has insignificant impact on drivers’ route choice behaviour. The results indicated that drivers in Bandung rely much on their experience of traffic conditions commonly occur in the city and demonstrated that VMS has no significant impact to increase traffic performance, but has better impact on the roads with higher number of alternative roads.Due to enormous uncertainties in confinement models associated with the maximum compressive strength and ductility of concrete confined by rectilinear ties, the implementation of spline nonparametric regression analysis is proposed herein as an alternative approach. The statistical evaluation is carried out based on 128 large-scale column specimens of either normalor high-strength concrete tested under uniaxial compression. The main advantage of this kind of analysis is that it can be applied when the trend of relation between predictor and response variables are not obvious. The error in the analysis can, therefore, be minimized so that it does not depend on the assumption of a particular shape of the curve. This provides higher flexibility in the application. The results of the statistical analysis indicates that the stress-strain curves of confined concrete obtained from the spline nonparametric regression analysis proves to be in good agreement with the experimental curves available in literatures.

Unbiased risk and cross-validation method for selecting optimal knots in multivariable nonparametric regression spline truncated (case study: Unemployment rate in Central Java, Indonesia, 2015)

Nonparametric regression gives better flexibility because the form of the regression curve estimation adjusts to the data. One nonparametric regression method is spline truncation. The number of knots and their locations affect the form of this regression curve estimation. The optimal knot is needed in order to obtain the best model. There are methods to select optimal knots, such as unbiased risk (UBR) and cross-validation (CV). This paper discusses UBR and CV, then, using both simulated data and the unemployment rate data of Central Java Province, Indonesia, in 2015, compares UBR and CV for selecting the optimal knots. The criteria for selecting the best model were based on Mean Squared Error and R-square. The simulation was performed on a spline truncated function with error generated from normal distribution for varied sample sizes and error variance. The results of the simulation study showed that CV estimates the knots more accurately than UBR. From the application to unemployment rate data, the optimal knot by using CV was a combination of 2-3-2-1-3 knot with MSE of 0.3946 and R-square of 93.047%. Meanwhile, by using UBR, the optimal knot was a three knot with MSE of 0.6865 and R-square of 90.59%. In conclusion, from the results of simulation data and application to unemployment rate data, the CV method generated a better model than the UBR method.Nonparametric regression gives better flexibility because the form of the regression curve estimation adjusts to the data. One nonparametric regression method is spline truncation. The number of knots and their locations affect the form of this regression curve estimation. The optimal knot is needed in order to obtain the best model. There are methods to select optimal knots, such as unbiased risk (UBR) and cross-validation (CV). This paper discusses UBR and CV, then, using both simulated data and the unemployment rate data of Central Java Province, Indonesia, in 2015, compares UBR and CV for selecting the optimal knots. The criteria for selecting the best model were based on Mean Squared Error and R-square. The simulation was performed on a spline truncated function with error generated from normal distribution for varied sample sizes and error variance. The results of the simulation study showed that CV estimates the knots more accurately than UBR. From the application to unemployment rate data, the opt...

Multiresponse semiparametric regression for modelling the effect of regional socio-economic variables on the use of information technology

Multiresponse semiparametric regression is simultaneous equation regression model and fusion of parametric and nonparametric model. The regression model comprise several models and each model has two components, parametric and nonparametric. The used model has linear function as parametric and polynomial truncated spline as nonparametric component. The model can handle both linearity and nonlinearity relationship between response and the sets of predictor variables. The aim of this paper is to demonstrate the application of the regression model for modeling of effect of regional socio-economic on use of information technology. More specific, the response variables are percentage of households has access to internet and percentage of households has personal computer. Then, predictor variables are percentage of literacy people, percentage of electrification and percentage of economic growth. Based on identification of the relationship between response and predictor variable, economic growth is treated as no...

Bootstrap inference longitudinal semiparametric regression model

Semiparametric regression contains two components, i.e. parametric and nonparametric component. Semiparametric regression model is represented by yti=μ(x˜′ti,zti)+eti where μ(x˜′ti,zti)=x˜′tiβ˜+g(zti) and yti is response variable. It is assumed to have a linear relationship with the predictor variables x˜′ti=(x1i1,x2i2,…,xTir). Random error eti, i = 1, …, n, t = 1, …, T is normally distributed with zero mean and variance σ2 and g(zti) is a nonparametric component. The results of this study showed that the PLS approach on longitudinal semiparametric regression models obtain estimators β˜^t=[X′H(λ)X]−1X′H(λ)y˜ and g˜^λ(z)=M(λ)y˜. The result also show that bootstrap was valid on longitudinal semiparametric regression model with g^λ(b)(z) as nonparametric component estimator.

Mixture model of spline truncated and kernel in multivariable nonparametric regression

Given the data (x1i, x2i,…, xpi,t1i,t2i,…,tqi, yi) with predictors (xsi, tki) and response variables yi are assumed to follow unknown function such that their dependence can be approximated by a nonparametric regression model y˜=μ˜(x,t)+e˜=∑i=1pf˜s(x)+∑k=1qg˜k(t)+e˜. The component f˜s(x) is approximated by additive spline regression with p-(number of predictors whereas g˜(t) is approximated by kernel regression with q-number of predictors. The error e˜ is assumed normally distributed with mean zero and constant variance. The objective of this article is to provide the estimators of f˜^s(x) and g˜^k(t) as well as the mixture model µ˜^(x,t) by means of Maximum Likelihood Estimation (MLE) method.

Simulation study for model performance of multiresponse semiparametric regression

The objective of this paper is to evaluate the performance of multiresponse semiparametric regression model based on both of the function types and sample sizes. In general, multiresponse semiparametric regression model consists of parametric and nonparametric functions. This paper focuses on both linear and quadratic functions for parametric components and spline function for nonparametric component. Moreover, this model could also be seen as a spline semiparametric seemingly unrelated regression model. Simulation study is conducted by evaluating three combinations of parametric and nonparametric components, i.e. linear-trigonometric, quadratic-exponential, and multiple linear-polynomial functions respectively. Two criterias are used for assessing the model performance, i.e. R-square and Mean Square Error (MSE). The results show that both of the function types and sample sizes have significantly influenced to the model performance. In addition, this multiresponse semiparametric regression model yields th...