Related papers: Monotone function estimator and its application
We present effective algorithms for uniform approximation of multivariate functions satisfying some prescribed inner structure. We extend in several directions the analysis of recovery of ridge functions $f(x)=g(\langle a,x\rangle)$ as…
A unit volume zero intelligence (ZI) model is defined and the distribution of its L1 process is recursively described. Further, a generalized ZI (GZI) model allowing non-unit market orders, shifts of quotes and general in-spread events is…
Matching estimators for average treatment effects are widely used in the binary treatment setting, in which missing potential outcomes are imputed as the average of observed outcomes of all matches for each unit. With more than two…
We study the problem of nonparametric estimation of a multivariate function $g:\mathbb {R}^d\to\mathbb{R}$ that can be represented as a composition of two unknown smooth functions $f:\mathbb{R}\to\mathbb{R}$ and $G:\mathbb{R}^d\to…
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,…
This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…
The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…
We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for \textit{any} monotone…
Measuring Mutual Information (MI) between high-dimensional, continuous, random variables from observed samples has wide theoretical and practical applications. Recent work, MINE (Belghazi et al. 2018), focused on estimating tight…
Solutions of a diophantine equation $f(a,b) = g(c,d)$, with $a,b,c,d$ in some finite range, can be efficiently enumerated by sorting the values of $f$ and $g$ in ascending order and searching for collisions. This article considers functions…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
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…
Catoni proposed a robust M-estimator and gave the deviation inequality for one fixed test function. The present paper is devoted to the uniform concentration inequality for a family of test functions. As an application, we consider…
A monotone version of an empirical Bayes estimator for the parameter of the Borel-Tanner distribution is constructed. Some properties of the estimator's regret risk are illustrated through simulations.
This paper examines estimation of skill formation models, a critical component in understanding human capital development and its effects on individual outcomes. Existing estimators are either based on moment conditions and only applicable…
We investigate the monotone representation and measurability of generalized $\psi$-estimators introduced by the authors in 2022. Our first main result, applying the unique existence of a generalized $\psi$-estimator, allows us to construct…
Generalised regression estimation allows one to make use of available auxiliary information in survey sampling. We develop three types of generalised regression estimator when the auxiliary data cannot be matched perfectly to the sample…
In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…
Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating…
This paper introduces a novel approach for learning to rank (LETOR) based on the notion of monotone retargeting. It involves minimizing a divergence between all monotonic increasing transformations of the training scores and a parameterized…