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Extremile regression, as a least squares analog of quantile regression, is potentially useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric…

We propose a new class of semiparametric regression models of mean residual life for censored outcome data. The models, which enable us to estimate the expected remaining survival time and generalize commonly used mean residual life models,…

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…

Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0,1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error.…

We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group related variables are available. This problem involves clustering to infer the missing group variable…

Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit…

We propose an approach to better inform treatment decisions at an individual level by adapting recent advances in average treatment effect estimation to conditional average treatment effect estimation. Our work is based on doubly robust…

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…

One important problem in microbiome analysis is to identify the bacterial taxa that are associated with a response, where the microbiome data are summarized as the composition of the bacterial taxa at different taxonomic levels. This paper…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

The statistical machine learning community has demonstrated considerable resourcefulness over the years in developing highly expressive tools for estimation, prediction, and inference. The bedrock assumptions underlying these developments…

We explore a statistical distribution that can simultaneously model the probability of zero outcome for non-users of health care utilization and continuous costs for users. We compare this distribution to other com- monly used models on…

Regression methods dominate the practice of biostatistical analysis, but biostatistical training emphasises the details of regression models and methods ahead of the purposes for which such modelling might be useful. More broadly,…

We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…

We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…

In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…

Combining information from multiple samples is often needed in biomedical and economic studies, but the differences between these samples must be appropriately taken into account in the analysis of the combined data. We study estimation for…

Treatment effects in regression discontinuity designs (RDDs) are often estimated using local regression methods. \cite{Hahn:01} demonstrated that the identification of the average treatment effect at the cutoff in RDDs relies on the…

Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…

Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic…