Related papers: Augmented Minimax Linear Estimation
Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary…
We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by…
We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…
When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
When studying treatment effects in multilevel studies, investigators commonly use (semi-)parametric estimators, which make strong parametric assumptions about the outcome, the treatment, and/or the correlation structure between study units…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
Correctly identifying treatment effects in observational studies is very difficult due to the fact that the outcome model or the treatment assignment model must be correctly specified. Taking advantages of semiparametric models in this…
Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions, such as the propensity score and conditional outcome mean for the average treatment effect functional. We consider the problem of how to…
The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process is considered. Estimates are based on observations of the…
A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…
The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
This paper presents a weighted optimization framework that unifies the binary,multi-valued, continuous, as well as mixture of discrete and continuous treatment, under the unconfounded treatment assignment. With a general loss function, the…
This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine…