Novel Computational Methods for Censored Data and Regression

This dissertation can be divided into three topics. In the first topic, we derived a recursive algorithm for the constrained Kaplan-Meier estimator, which promotes the computation speed up to fifty times compared to the current method that uses EM algorithm. We also showed how this leads to the vast improvement of empirical likelihood analysis with right censored data. After a brief review of regularized regressions, we investigated the computational problems in the parametric/non-parametric hybrid accelerated failure time models and its regularization in a high dimensional setting. We also illustrated that, when the number of pieces increases, the discussed models are close to a nonparametric one. In the last topic, we discussed a semi-parametric approach of hypothesis testing problem in the binary choice model. The major tools used are Buckley-James like algorithm and empirical likelihood. The essential idea, which is similar to the first topic, is iteratively computing linear constrained empirical likelihood using optimization algorithms including EM, and iterative convex minorant algorithm

Implementation of complex interactions in a Cox regression framework

The standard Cox proportional hazards model has been extended by functionally describable interaction terms. The first of which are related to neural networks by adopting the idea of transforming sums of weighted covariables by means of a logistic function. A class of reasonable weight combinations within the logistic transformation is described. Apart from the standard covariable product interaction, a product of logistically transformed covariables has also been included in the analysis of performance of the new terms. An algorithm combining likelihood ratio tests and AIC criterion has been defined for model choice. The critical values of the likelihood ratio test statistics had to be corrected in order to guarantee a maximum type I error of 5% for each interaction term. The new class of interaction terms allows interpretation of functional relationships between covariables with more flexibility and can easily be implemented in standard software packages

Robust and Scalable Distributed Recursive Least Squares

We consider a problem of robust estimation over a network in an errors-in-variables context. Each agent measures noisy samples of a local pair of signals related by a linear regression defined by a common unknown parameter, and the agents must cooperate to find the unknown parameter in presence of uncertainty affecting both the regressor and the regressand variables.We propose a recursive least squares estimation method providing global exponential convergence to the unknown parameter in absence of uncertainty, and robust stability of the estimate, formalized in terms of input-to-state stability, in presence of uncertainty affecting all the variables. The result relies on a cooperative excitation assumption that is proved to be strictly weaker than persistency of excitation of each local data set. The proposed estimator is validated on an adaptive road pricing application

A model-based multithreshold method for subgroup identification

Thresholding variable plays a crucial role in subgroup identification for personalizedmedicine. Most existing partitioning methods split the sample basedon one predictor variable. In this paper, we consider setting the splitting rulefrom a combination of multivariate predictors, such as the latent factors, principlecomponents, and weighted sum of predictors. Such a subgrouping methodmay lead to more meaningful partitioning of the population than using a singlevariable. In addition, our method is based on a change point regression modeland thus yields straight forward model-based prediction results. After choosinga particular thresholding variable form, we apply a two-stage multiple changepoint detection method to determine the subgroups and estimate the regressionparameters. We show that our approach can produce two or more subgroupsfrom the multiple change points and identify the true grouping with high probability.In addition, our estimation results enjoy oracle properties. We design asimulation study to compare performances of our proposed and existing methodsand apply them to analyze data sets from a Scleroderma trial and a breastcancer study