Related papers: Osband's Principle for Identification Functions
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
Many statistical estimands of interest (e.g., in regression or causality) are functions of the joint distribution of multiple random variables. But in some applications, data is not available that measures all random variables on each…
Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of…
Identifiability is a structural property of any ODE model characterized by a set of unknown parameters. It describes the possibility of determining the values of these parameters from fusing the observations of the system inputs and…
A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale.…
We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
The paper discusses inference techniques for semiparametric models based on suitable versions of inference functions. The text contains two parts. In the first part, we review the optimality theory for non-parametric models based on the…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
Multidimensional heterogeneity and endogeneity are important features of a wide class of econometric models. With control variables to correct for endogeneity, nonparametric identification of treatment effects requires strong support…
An experimenter seeks to learn a subject's preference relation. The experimenter produces pairs of alternatives. For each pair, the subject is asked to choose. We argue that, in general, large but finite data do not give close…
Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the…
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…
Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, such as the absolute error or the squared error. The individual scores are then averaged over forecast cases, to result in a…
A goodness-of-fit index measures the consistency of consumption data with a given model of utility-maximization. We show that for the class of well-behaved (i.e., continuous and increasing) utility functions there is no goodness-of-fit…
We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal field such that, for any bounded definable function, the germ of the function on an initial segment of the curve can be continuously extended to a closed…