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The study of a linear regression model with an interval-censored covariate, which was motivated by an acquired immunodeficiency syndrome (AIDS) clinical trial, was first proposed by Gómez et al. They developed a likelihood approach, together with a two-step conditional algorithm, to estimate the regression coefficients in the model. However, their method is inapplicable when the interval-censored covariate is continuous. In this article, we propose a novel and fast method to treat the continuous interval-censored covariate. By using logspline density estimation, we impute the interval-censored covariate with a conditional expectation. Then, the ordinary least-squares method is applied to the linear regression model with the imputed covariate. To assess the performance of the proposed method, we compare our imputation with the midpoint imputation and the semiparametric hierarchical method via simulations. Furthermore, an application to the AIDS clinical trial is presented. [ABSTRACT FROM PUBLISHER]

For time series nonparametric regression models with discontinuities, we propose to use polynomial splines to estimate locations and sizes of jumps in the mean function. Under reasonable conditions, test statistics for the existence of jumps are given and their limiting distributions are derived under the null hypothesis that the mean function is smooth. Simulations are provided to check the powers of the tests. A climate data application and an application to the US unemployment rates of men and women are used to illustrate the performance of the proposed method in practice. [ABSTRACT FROM AUTHOR]

For nonparametric time series regression, we propose to apply polynomial splines to squared residuals to develop the variance function estimation. Furthermore, we obtain and use simultaneous confidence bands to detect certain parametric forms for entire variance curves. The proposed method is extremely fast. Asymptotic results are established under the assumption that observations are from a strictly stationary $\alpha$-mixing process. Simulations and a financial data set application are provided to illustrate the performance of the proposed method numerically. [ABSTRACT FROM AUTHOR]