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In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared…
Instrumental variables (IVs) provide a powerful strategy for identifying causal effects in the presence of unobservable confounders. Within the nonparametric setting (NPIV), recent methods have been based on nonlinear generalizations of…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
Physical activity (PA) is an important risk factor for many health outcomes. Wearable-devices such as accelerometers are increasingly used in biomedical studies to understand the associations between PA and health outcomes. Statistical…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
Despite increasing popularity in empirical studies, the integration of machine learning generated variables into regression models for statistical inference suffers from the measurement error problem, which can bias estimation and threaten…
Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. Instruments are variables which only affect the outcome…
To effect behavior change a successful algorithm must make high-quality decisions in real-time. For example, a mobile health (mHealth) application designed to increase physical activity must make contextually relevant suggestions to…
The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…
We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box.…
We propose a penalized least-squares method to fit the linear regression model with fitted values that are invariant to invertible linear transformations of the design matrix. This invariance is important, for example, when practitioners…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
The method of instrumental variables (IV) provides a framework to study causal effects in both randomized experiments with noncompliance and in observational studies where natural circumstances produce as-if random nudges to accept…
In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. Recently, many flexible machine learning methods have been developed for instrumental variable estimation. However, these methods have at least one…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional…