LEAST SQUARE-SPLINE ESTIMATOR IN MULTI-RESPONSE SEMIPARAMETRIC REGRESSION MODEL FOR ESTIMATING MEDIAN GROWTH CHARTS OF CHILDREN IN EAST JAVA, INDONESIA

A heteroskedastic semiparametric regression model consists of two main components, i.e. parametric component and nonparametric component. The model assumes that any data (x̰ i′ , t i , y i ) follows y i = x̰ i′ β̰+ f(t i ) + σ i ε i , where i = 1,2, … , n , x̰ i′ = (1, x i1 , x i2 , … , x ir ) and t i is the predictor variable. Parameter vector β̰ = (β 1 , β 2 , … , β r ) ′ ∈ ℜ r is unknown and f(t i ) is also unknown and is assumed to be in interval of C[0,π] . Random error ε i is independent on zero mean and varianceσ 2 . Estimation of the heteroskedastic semiparametric regression model was conducted to evaluate the parametric and nonparametric components. The nonparametric component f(t i ) regression was approximated by Fourier series F(t) = bt + 12 α 0 + ∑ α k 𝑐 𝑜𝑠 kt Kk=1 . The estimation was obtained by means of Weighted Penalized Least Square (WPLS): min f∈C(0,π) {n −1 (y̰− Xβ̰−f̰) ′ W −1 (y̰− Xβ̰− f̰) + λ ∫ 2π [f ′′ (t)] 2 dt π0 } . The WPLS solution provided nonparametric component f̰̂ λ (t) = M(λ)y̰ ∗ for a matrix M(λ) and parametric component β̰̂ = [X ′ T(λ)X] −1 X ′ T(λ)y̰

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LOCAL LINEAR ESTIMATOR IN BI-RESPONSE SEMIPARAMETRIC REGRESSION MODEL FOR ESTIMATING MEDIAN GROWTH CHARTS OF CHILDREN

Far East Journal of Mathematical Sciences (FJMS) ◽

10.17654/ms099081233 ◽

2016 ◽

Vol 99 (8) ◽

pp. 1233-1244 ◽

Cited By ~ 8

Author(s):

N. Chamidah ◽

M. Rifada

Keyword(s):

Regression Model ◽

Semiparametric Regression ◽

Linear Estimator ◽

Growth Charts ◽

Semiparametric Regression Model ◽

Local Linear ◽

Local Linear Estimator

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

IOP Conference Series Earth and Environmental Science ◽

10.1088/1755-1315/880/1/012046 ◽

2021 ◽

Vol 880 (1) ◽

pp. 012046

Author(s):

Hartina Husain ◽

I N Budiantara ◽

Ismaini Zain

Keyword(s):

Regression Analysis ◽

Fourier Series ◽

Regression Model ◽

Semiparametric Regression ◽

Least Square ◽

Predictor Variables ◽

Parameter Estimates ◽

Semiparametric Regression Model ◽

Estimation Techniques ◽

Truncated Fourier Series

Abstract 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).

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ESTIMASI SELANG KEPERCAYAAN NILAI UJIAN NASIONAL BERBASIS KOMPETENSI BERDASARKAN MODEL REGRESI SEMIPARAMETRIK MULTIRESPON TRUNCATED SPLINE

MEDIA STATISTIKA ◽

10.14710/medstat.13.1.92-103 ◽

2020 ◽

Vol 13 (1) ◽

pp. 92-103

Author(s):

Lilik Hidayati ◽

Nur Chamidah ◽

I Nyoman Budiantara

Keyword(s):

Confidence Interval ◽

Regression Model ◽

Parental Education ◽

Interval Estimation ◽

Semiparametric Regression ◽

Report Card ◽

Least Square ◽

Model Parameters ◽

Semiparametric Regression Model ◽

Confidence Interval Estimation

Confidence interval estimation is important in statistical inference for the parameters of the regression model, but the theory of confidence interval estimation for multi-response semiparametric regression model parameters based on the truncated spline estimator has not been examined. In this study, we estimate the confidence interval of the multi-response semiparametric regression model based on the truncated spline estimator by using pivotal quantity method with the central limit theorem approach. This confidence interval theory is applied to data of competency-based national exam (UNBK) scores in West Nusa Tenggara Province where its UNBK in the lowest position among other provinces in Indonesia. The method used for estimating parameters is weighted least square. The best model is determined based on the Generalized Cross Validation (GCV) minimum value. Based on the estimated 95% confidence interval of parameters of the multi-response truncated spline semiparametric regression model, the results showed that the insignificant factors affecting the UNBK scores were gender and parental education duration while the report card of scores and USBK scores had a positive effect on the UNBK scores but only the UNBK scores of mathematics that report card of scores factor has a negative effect on it.

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