相关论文: Regression and Classification by Zonal Kriging

We present a unifying view on various statistical estimation techniques including penalization, variational and thresholding methods. These estimators will be analyzed in the context of statistical linear inverse problems including…

In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square…

Given data sampled from a number of variables, one is often interested in the underlying causal relationships in the form of a directed acyclic graph. In the general case, without interventions on some of the variables it is only possible…

Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental…

The aim of the paper is to derive the complex-valued least-squares estimator for bias-noise mean and variance.

Let X_1,...., X_n be a collection of iid discrete random variables, and Y_1,..., Y_m a set of noisy observations of such variables. Assume each observation Y_a to be a random function of some a random subset of the X_i's, and consider the…

Optimal linear prediction (aka. kriging) of a random field $\{Z(x)\}_{x\in\mathcal{X}}$ indexed by a compact metric space $(\mathcal{X},d_{\mathcal{X}})$ can be obtained if the mean value function $m\colon\mathcal{X}\to\mathbb{R}$ and the…

In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a…

Choosing a shrinkage method can be done by selecting a penalty from a list of pre-specified penalties or by constructing a penalty based on the data. If a list of penalties for a class of linear models is given, we provide comparisons based…

We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…

Penalized smoothing is a standard tool in regression analysis. Classical approaches often rely on basis or kernel expansions, which constrain the estimator to a fixed span and impose smoothness assumptions that may be restrictive for…

Predictions from machine learning algorithms can vary across random seeds, inducing instability in downstream debiased machine learning estimators. We formalize random seed stability via a concentration condition and prove that subbagging…

This paper deals with a projection least squares estimator of the function $J_0$ computed from multiple independent observations on $[0,T]$ of the process $Z$ defined by $dZ_t = J_0(t)d\langle M\rangle_t + dM_t$, where $M$ is a continuous…

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…

Classical causal models, such as Granger causality and structural equation modeling, are largely restricted to acyclic interactions and struggle to represent cyclic and higher-order dynamics in complex networks. We introduce a causal…

We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected…

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…

Spatial interpolation is a crucial task in geography. As perhaps the most widely used interpolation methods, geostatistical models -- such as Ordinary Kriging (OK) -- assume spatial stationarity, which makes it difficult to capture the…

In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, $\pi(Y,X)$, rather than a purely conditional model, $\pi(Y \mid X)$, where $Y$ is a scalar response variable and…

We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a…