A new estimation method for continuous threshold expectile model

<p>The continuous threshold expectile regression model could capture the effect of a covariate on the response variable with two different straight lines, while intersecting an unknown threshold needed be estimated. This article proposes a new estimation method via a linearization technique to estimate the regression coefficients and the threshold simultaneously. Statistical inferences of the proposed estimators are easily derived from the existing theory. Moreover, the estimation procedure is readily implemented by the current software. Simulation studies and an application on GDP per capita and quality of electricity supply data illustrate the proposed method.</p

Weighted expectile regression neural networks for right censored data

As a favorable alternative to the censored quantile regression, censored expectile regression has been popular in survival analysis due to its flexibility in modeling the heterogeneous effect of covariates. The existing weighted expectile regression (WER) method assumes that the censoring variable and covariates are independent, and that the covariates effects has a global linear structure. However, these two assumptions are too restrictive to capture the complex and nonlinear pattern of the underlying covariates effects. In this article, we developed a novel weighted expectile regression neural networks (WERNN) method by incorporating the deep neural network structure into the censored expectile regression framework. To handle the random censoring, we employ the inverse probability of censoring weighting (IPCW) technique in the expectile loss function. The proposed WERNN method is flexible enough to fit nonlinear patterns and therefore achieves more accurate prediction performance than the existing WER method for right censored data. Our findings are supported by extensive Monte Carlo simulation studies and a real data application.</p