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As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…
The interpretation of coefficients from multivariate linear regression relies on the assumption that the conditional expectation function is linear in the variables. However, in many cases the underlying data generating process is…
In this paper, we propose an empirical likelihood-based weighted estimator of regression parameter in quantile regression model with nonignorable missing covariates. The proposed estimator is computationally simple and achieves…
This paper develops a semi-parametric procedure for estimation of unconditional quantile partial effects using quantile regression coefficients. The estimator is based on an identification result showing that, for continuous covariates,…
Scientific experiments study interventions that show evidence of an effect size that is meaningfully large, negligibly small, or inconclusively broad. Previously, we proposed contra-analysis as a decision-making process to help determine…
Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…
This paper aims to provide a tutorial for upper level undergraduate and graduate students in statistics, biostatistics and epidemiology on deriving influence functions for non-parametric and semi-parametric models. The author will build on…
In many machine learning problems, understanding variable importance is a central concern. Two common approaches are Permute-and-Predict (PaP), which randomly permutes a feature in a validation set, and Leave-One-Covariate-Out (LOCO), which…
Control variables are included in regression analyses to estimate the causal effect of a treatment on an outcome. In this paper, we argue that the estimated effect sizes of controls are unlikely to have a causal interpretation themselves,…
Composite indicators aggregate a set of variables using weights which are understood to reflect the variables' importance in the index. In this paper we propose to measure the importance of a given variable within existing composite…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
We present Collaborative Trees, a novel tree model designed for regression prediction, along with its bagging version, which aims to analyze complex statistical associations between features and uncover potential patterns inherent in the…
When a strict subset of covariates are given, we propose conditional quantile treatment effect to capture the heterogeneity of treatment effects via the quantile sheet that is the function of the given covariates and quantile. We focus on…
Practitioners use feature importance to rank and eliminate weak predictors during model development in an effort to simplify models and improve generality. Unfortunately, they also routinely conflate such feature importance measures with…
Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of…
Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…
The goal of regression analysis is to predict the value of a numeric outcome variable y given a vector of joint values of other (predictor) variables x. Usually a particular x-vector does not specify a repeatable value for y, but rather a…
Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed…
Significant treatment effects are often emphasized when interpreting and summarizing empirical findings in studies that estimate multiple, possibly many, treatment effects. Under this kind of selective reporting, conventional treatment…
The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's $d$. A recently proposed generalized estimator allows conditioning on further independent variables…