Data Augmentation Based Quantile Regression Estimation for Censored Partially Linear Additive Model

Li, Lu; Hao, Ruiting; Yang, Xiaorong

doi:10.1007/s10614-023-10473-5

Cited by 1 publication

(1 citation statement)

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“…To improve on this, Powel investigated quantile regression estimation for the Tobit model in 1986 [9], but its asymptotic covariance matrix is affected by the error density function, which affects estimation reliability [10]. When applied to high-dimensional longitudinal data, the complexity of truncated-tailed data, random effects, and random errors further exacerbates the difficulty of parameter estimation [11]. Therefore, the development of novel and efficient sampling algorithms to optimize parameter estimation and variable selection for Tobit quantile regression models is important in terms of improving model accuracy and providing reliable statistical tools for related fields.…”

Section: Introductionmentioning

confidence: 99%

Research on Quantile Regression Method for Longitudinal Interval-Censored Data Based on Bayesian Double Penalty

Zhao,

Shu,

et al. 2024

Mathematics

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The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response variable is restricted by the bilateral limit, a double-penalty Bayesian Tobit quantile regression model was constructed to carry out parameter estimation and variable selection in the interval-censored mixed-effects model, and at the same time, the fixed-effects and random effects coefficients are compressed in Tobit’s mixed-effects model, so as to reduce the estimation error of the model at the same time as the variable selection of the model is carried out. The posterior distribution of each unknown parameter was derived using the conditional Laplace prior and the mixed truncated normal distribution of interval-censored data, and then the Gibbs sampling algorithm for unknown parameter estimation was constructed. Through Monte Carlo simulation, it was found that the new method is more advantageous than the classical method in terms of variable selection and parameter estimation accuracy in various situations, such as different model sparsity, different data censoring ratios and different random error distributions, and the model is able to realize automatic variable selection. Finally, the new method is used to analyze the correlation between the crime rate and various economic indicators in China.

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Section: Introductionmentioning

confidence: 99%