English
Related papers

Related papers: Isotonic regression for functionals of elicitation…

200 papers

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…

Machine Learning · Statistics 2013-01-16 Hachem Kadri , Philippe Preux , Emmanuel Duflos , Stéphane Canu

In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…

Statistics Theory · Mathematics 2018-10-09 Xi Chen , Qihang Lin , Bodhisattva Sen

The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive…

Econometrics · Economics 2024-01-24 Yoichi Arai , Taisuke Otsu , Mengshan Xu

We consider the problem of nonparametric regression when the covariate is $d$-dimensional, where $d \geq 1$. In this paper we introduce and study two nonparametric least squares estimators (LSEs) in this setting---the entirely monotonic LSE…

Statistics Theory · Mathematics 2020-06-11 Billy Fang , Adityanand Guntuboyina , Bodhisattva Sen

We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…

Statistics Theory · Mathematics 2022-11-24 Kang Wang , Subhashis Ghosal

Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices, the Isotonic Regression of $y$ is a vector $x$ that respects the partial order described by $G,$ and minimizes $||x-y||,$ for a specified norm. This paper gives…

Machine Learning · Computer Science 2015-11-12 Rasmus Kyng , Anup Rao , Sushant Sachdeva

Motivated by models for multiway comparison data, we consider the problem of estimating a coordinate-wise isotonic function on the domain $[0, 1]^d$ from noisy observations collected on a uniform lattice, but where the design points have…

Statistics Theory · Mathematics 2021-06-25 Ashwin Pananjady , Richard J. Samworth

The present paper provides a representation result for monetary risk measures (i.e., monotone translation invariant functionals) satisfying a weak maxitivity property. This result can be understood as a functional analytic generalization of…

Functional Analysis · Mathematics 2022-12-13 José Miguel Zapata

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…

Statistics Theory · Mathematics 2013-04-19 Aboubacar Amiri , Baba Thiam

In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple…

Statistics Theory · Mathematics 2018-11-05 Alexander Giessing , Xuming He

Isotonic regression is a shape-constrained nonparametric regression in which the regression is an increasing step function. For $n$ data points, the number of steps in the isotonic regression may be as large as $n$. As a result, standard…

Computation · Statistics 2014-12-10 Janis Hardwick , Quentin F. Stout

We propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random series priors based on a…

Methodology · Statistics 2018-08-03 Xiuqi Li , Subhashis Ghosal

Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.…

Statistics Theory · Mathematics 2019-03-26 Philippe Rigollet , Jonathan Weed

This article addresses the problem of functional supervised classification of Cox process trajectories, whose random intensity is driven by some exogenous random covariable. The classification task is achieved through a regularized convex…

Statistics Theory · Mathematics 2014-10-16 Gérard Biau , Benoît Cadre , Quentin Paris

We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval.…

Methodology · Statistics 2020-06-08 Zhenhua Lin , Jane-Ling Wang

This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our primary goal is to establish central limit theorems for these functionals when mixed estimators are employed. Our study is relevant to the…

Statistics Theory · Mathematics 2025-01-09 Huihui Chen , Darinka Dentcheva , Yang Lin , Gregory J. Stock

This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…

Statistics Theory · Mathematics 2013-10-24 Natalia Bochkina

The problem of simultaneous estimation of location/scale parameters $\theta_1$ and $\theta_2$ of a general bivariate location/scale model, when the ordering between the parameters is known apriori (say, $\theta_1\leq \theta_2$), has been…

Statistics Theory · Mathematics 2023-01-03 Naresh Garg , Neeraj Misra

In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. In particular, we propose the use of Diebold-Mariano tests, and show how they can be implemented for Expected Shortfall (ES), based on the…

Risk Management · Quantitative Finance 2016-08-10 Tobias Fissler , Johanna F. Ziegel , Tilmann Gneiting

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…

Machine Learning · Statistics 2013-10-04 Peter Kovesarki , Ian C. Brock