Asymptotic properties of wavelet estimators in a semiparametric regression model with censored data

2012 ◽  
Vol 17 (4) ◽  
pp. 290-296
Author(s):  
Hongchang Hu ◽  
Yuan Feng
Keyword(s):  
Regression Model ◽  
Censored Data ◽  
Asymptotic Properties ◽  
Semiparametric Regression ◽  
Semiparametric Regression Model ◽  
Wavelet Estimators

scholarly journals A flexible semiparametric regression model for bimodal, asymmetric and censored data

2017 ◽  
Vol 45 (7) ◽  
pp. 1303-1324 ◽  
Author(s):  
Thiago G. Ramires ◽  
Edwin M. M. Ortega ◽  
Niel Hens ◽  
Gauss M. Cordeiro ◽  
Gilberto A. Paula
Keyword(s):  
Regression Model ◽  
Censored Data ◽  
Semiparametric Regression ◽  
Semiparametric Regression Model

scholarly journals Asymptotic properties of wavelet estimators in heteroscedastic semiparametric model based on negatively associated innovations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xueping Hu ◽  
Jinbiao Zhong ◽  
Jiashun Ren ◽  
Bing Shi ◽  
Keming Yu
Keyword(s):  
Strong Consistency ◽  
Closed Interval ◽  
Asymptotic Properties ◽  
Semiparametric Regression ◽  
Slope Parameter ◽  
Random Errors ◽  
Semiparametric Regression Model ◽  
Negatively Associated ◽  
Na Random Variables ◽  
Wavelet Estimators

AbstractConsider the heteroscedastic semiparametric regression model $y_{i}=x_{i}\beta+g(t_{i})+\varepsilon_{i}$yi=xiβ+g(ti)+εi, $i=1, 2, \ldots, n$i=1,2,…,n, where β is an unknown slope parameter, $\varepsilon_{i}=\sigma_{i}e_{i}$εi=σiei, $\sigma^{2}_{i}=f(u_{i})$σi2=f(ui), $(x_{i},t_{i},u_{i})$(xi,ti,ui) are nonrandom design points, $y_{i}$yi are the response variables, f and g are unknown functions defined on the closed interval $[0,1]$[0,1], random errors $\{e_{i} \}${ei} are negatively associated (NA) random variables with zero means. Whereas kernel estimators of β, g, and f have attracted a lot of attention in the literature, in this paper, we investigate their wavelet estimators and derive the strong consistency of these estimators under NA error assumption. At the same time, we also obtain the Berry–Esséen type bounds of the wavelet estimators of β and g.

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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