Related papers: Estimation of function's supports under arithmetic…
We consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable…
Estimation of the population total of a variable can be improved by calibration on a set of auxiliary variables. It is difficult to establish that such a set of variables is sufficient, that estimation could not be improved by calibration…
Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4)))…
This paper studies a regularized support function estimator for bounds on components of the parameter vector in the case in which the identified set is a polygon. The proposed regularized estimator has three important properties: (i) it has…
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
The classical support uncertainty principle states that the signal and its discrete Fourier transform (DFT) cannot be localized simultaneously in an arbitrary small area in the time and the frequency domain. The product of the number of…
Suppose that a target function is monotonic, namely, weakly increasing, and an available original estimate of this target function is not weakly increasing. Rearrangements, univariate and multivariate, transform the original estimate to a…
Instrumental variable based estimation of a causal effect has emerged as a standard approach to mitigate confounding bias in the social sciences and epidemiology, where conducting randomized experiments can be too costly or impossible.…
We consider a setting where we have a ground set $M$ together with real-valued set functions $f_1, \dots, f_n$, and the goal is to partition $M$ into two sets $S_1,S_2$ such that $|f_i(S_1) - f_i(S_2)|$ is small for every $i$. Many results…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
We consider strictly increasing sequences $\left(a_{n}\right)_{n \geq 1}$ of integers and sequences of fractional parts $\left(\left\{a_{n} \alpha\right\}\right)_{n \geq 1}$ where $\alpha \in \mathbb{R}$. We show that a small additive…
Understanding why a model made a certain prediction is crucial in many data science fields. Interpretable predictions engender appropriate trust and provide insight into how the model may be improved. However, with large modern datasets the…
In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We…
We provide a novel characterization of semiparametric efficiency in a generic supervised learning setting where the outcome mean function -- defined as the conditional expectation of the outcome of interest given the other observed…
We continue to study the relationship between the size of the sum of a set and the common energy of its subsets. We find a rather sharp subexponential dependence between the doubling constant of a set $A$ and the minimal common energy taken…
The problem of variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The aim is to find the best possible upper bound on the norm of the difference of two spectral…
We prove sharp estimates for Fourier transforms of indicator functions of bounded open sets in ${\mathbb R}^n$ with real analytic boundary, as well as nontrivial lattice point discrepancy results. Both will be derived from estimates on…
Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision…
We derive the general analytical expressions for the statistical uncertainties of cumulants up to fourth order including an efficiency correction. The analytical expressions have been tested with a toy Monte Carlo model analysis. An…