We propose a piecewise linear conditional survival function estimator based on the complete solution surface we develop for the censored kernel quantile regression (CKQR). The proposed CSF estimator is a flexible nonparametric method which does not require any specific model assumption such as linearity of the survival time and proportional hazards. We carry out asymptotic analysis to theoretically justify the estimator and numerical experiments to demonstrate its competitive finite-sample performance under various scenarios.

Dynamic treatment regimes operationalize clinical decision making by providing a sequence of rules, one at each decision time point, where each decision rule takes patient history as input and outputs a recommended treatment. Interactive Q-learning is a method that can be used to estimate optimal dynamic treatment regimes from data that arises from sequentially randomized clinical trials. In contrast to the traditional Q-learning algorithm, our proposed method involves modeling only smooth functionals of the data, which facilitates the use of standard techniques for model building and results in higher-quality estimates of optimal regimes.

We propose a multiscale model for Gaussian noised images in a Bayesian framework for both 2-dimensional (2D) and 3-dimensional(3D) images, using the Chinese restaurant process to generate ties among neighboring values of images. The proposed estimators enjoy desirable asymptotic properties of identifying precise structures in the images; the denoising procedure is completely data-driven and computationally, efficient benefiting from the conditional conjugacy. A simulation study shows the proposed approach outperforms the commonly used wedgelet, platelet methods both visually and numerically.