Related papers: Unbiased Estimation Equation under $f$-Separable B…
Unbiased estimation for parameters of maximal distribution is a very fundamental problem in the statistical theory of sublinear expectation. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper…
We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…
Despite the empirical success of meta reinforcement learning (meta-RL), there are still a number poorly-understood discrepancies between theory and practice. Critically, biased gradient estimates are almost always implemented in practice,…
The shortcomings of maximum likelihood estimation in the context of model-based reinforcement learning have been highlighted by an increasing number of papers. When the model class is misspecified or has a limited representational capacity,…
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…
Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…
In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to…
This paper considers reparameterization invariant Bayesian point estimates and credible regions of model parameters for scientific inference and communication. The effect of intrinsic loss function choice in Bayesian intrinsic estimates and…
Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In addition, the intractable element of the infinite…
We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing…
Model calibration is essential for ensuring that the predictions of deep neural networks accurately reflect true probabilities in real-world classification tasks. However, deep networks often produce over-confident or under-confident…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
Point estimation is a fundamental statistical task. Given the wide selection of available point estimators, it is unclear, however, what, if any, would be universally-agreed theoretical reasons to generally prefer one such estimator over…
We study the excess risk evaluation of classical penalized empirical risk minimization (ERM) with Bregman losses. We show that by leveraging the idea of wild refitting, one can efficiently upper bound the excess risk through the so-called…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…