scholarly journals A Bayesian Semiparametric Regression Model for Joint Analysis of Microbiome Data

2018 ◽  
Vol 9 ◽  
Author(s):  
Juhee Lee ◽  
Marilou Sison-Mangus
Keyword(s):  
Regression Model ◽  
Semiparametric Regression ◽  
Joint Analysis ◽  
Semiparametric Regression Model ◽  
Bayesian Semiparametric ◽  
Bayesian Semiparametric Regression ◽  
Microbiome Data

The Zero-Inflated Negative Binomial Semiparametric Regression Model: Application to Number of Failing Grades Data

2021 ◽  
Author(s):  
Elton G. Aráujo ◽  
Julio C. S. Vasconcelos ◽  
Denize P. dos Santos ◽  
Edwin M. M. Ortega ◽  
Dalton de Souza ◽  
...  
Keyword(s):  
Regression Model ◽  
Negative Binomial ◽  
Semiparametric Regression ◽  
Model Application ◽  
Semiparametric Regression Model

scholarly journals Estimation of Heteroskedasticity Semiparametric Regression Curve Using Fourier Series Approach

2020 ◽  
Vol 2 (1) ◽  
pp. 14-20
Author(s):  
Rahmawati Pane ◽  
Sutarman
Keyword(s):  
Fourier Series ◽  
Regression Model ◽  
Variable Parameter ◽  
Predictor Variable ◽  
Semiparametric Regression ◽  
Least Square ◽  
Parameter Vector ◽  
Regression Curve ◽  
Semiparametric Regression Model ◽  
Main Components

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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