Semiparametric inference for the recurrent event process by means of a single-index model

In this paper, we introduce new parametric and semiparametric regression techniques for a recurrent event process subject to random right censoring. We develop models for the cumula- tive mean function and provide asymptotically normal estimators. Our semiparametric model which relies on a single-index assumption can be seen as a dimension reduction technique that, contrary to a fully nonparametric approach, is not stroke by the curse of dimensional- ity when the number of covariates is high. We discuss data-driven techniques to choose the parameters involved in the estimation procedures and provide a simulation study to support our theoretical results

Nonparametric Statistical Inference with an Emphasis on Information-Theoretic Methods

This book addresses contemporary statistical inference issues when no or minimal assumptions on the nature of studied phenomenon are imposed. Information theory methods play an important role in such scenarios. The approaches discussed include various high-dimensional regression problems, time series and dependence analyses

Estimation of Nonlinear Models with Mismeasured Regressors Using Marginal Information

We consider the estimation of nonlinear models with mismeasured explanatory variables, when information on the marginal distribution of the true values of these variables is available. We derive a semi-parametric MLE that is shown to be $\sqrt{n}$ consistent and asymptotically normally distributed. In a simulation experiment we find that the finite sample distribution of the estimator is close to the asymptotic approximation. The semi-parametric MLE is applied to a duration model for AFDC welfare spells with misreported welfare benefits. The marginal distribution of the correctly measured welfare benefits is obtained from an administrative source.

Nonlinear regression with censored data

Suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + sigma(X)epsilon, where m(.) = E(Y vertical bar.) belongs to some parametric class (m(theta)(.):theta is an element of Theta) of regression functions, sigma(2)(.) = var(Y vertical bar.) is unknown, and e is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new estimation procedure for the true, unknown parameter vector theta(0) is proposed that extends the classical least squares procedure for nonlinear regression to the case where the response is subject to censoring. The consistency and asymptotic normality of the proposed estimator are established. The estimator is compared through simulations with an estimator proposed by Stute in 1999, and both methods are also applied to a fatigue life dataset of strain-controlled materials.Peer reviewe

A Provable Smoothing Approach for High Dimensional Generalized Regression with Applications in Genomics

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting the response $Y$ to a single index $X^T\beta^*$ of explanatory variables $X\in\mathbb{R}^d$. The generalized regression model is flexible and covers many widely used statistical models. It fits the data generating mechanisms well in many real problems, which makes it useful in a variety of applications where regression models are regularly employed. In low dimensions, rank-based M-estimators are recommended to deal with the generalized regression model, giving root-$n$ consistent estimators of $\beta^*$. Applications of these estimators to high dimensional data, however, are questionable. This article studies, both theoretically and practically, a simple yet powerful smoothing approach to handle the high dimensional generalized regression model. Theoretically, a family of smoothing functions is provided, and the amount of smoothing necessary for efficient inference is carefully calculated. Practically, our study is motivated by an important and challenging scientific problem: decoding gene regulation by predicting transcription factors that bind to cis-regulatory elements. Applying our proposed method to this problem shows substantial improvement over the state-of-the-art alternative in real data.Comment: 53 page

Causal Inference Methods For Joint Censored Cost And Effectiveness Outcomes

Informed healthcare policy decisions must be driven by consideration of an intervention\u27s effectiveness as well as its cost. Cost-effectiveness analyses provide a framework for decision making that balances these joint outcomes in some optimal way. However, because these studies often use data from observational sources, results may be biased due to unmeasured or time-varying confounding, informative cost censoring, and skewed or zero-inflated data. The goals of this dissertation are two-fold; we aim to (1) elucidate the conditions under which causal conclusions can be drawn from cost-effectiveness data, and (2) develop novel statistical methods for identifying cost-effective treatments while accounting for confounding and other data irregularities. We discuss three such developments: regression methodology for a novel probabilistic measure of cost-effectiveness, interpretable Q-learning based methods for identifying cost-effective treatment strategies, and a flexible and efficient influence function based estimator of average treatment cost that is robust to unmeasured confounding given a valid instrumental variable. We evaluate the operating characteristics of our proposed methods under several realistic data scenarios through simulation studies. We also illustrate usage by identifying cost-effective adjuvant treatments for early-stage endometrial cancer patients as well as assessing differences in costs between surgical and non-surgical interventions for gallstones and hemorrhaging using observational data