Related papers: Nonparametric identification of positive eigenfunc…
We perform an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the one hand we prove that, on many important function spaces,…
Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…
A key goal of unsupervised representation learning is "inverting" a data generating process to recover its latent properties. Existing work that provably achieves this goal relies on strong assumptions on relationships between the latent…
We derive a common mathematical formulation for the eigenfunction statistics of Hermitian operators, represented by a multi-parametric probability density. The system-information in the formulation enters through two parameters only,…
We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically…
Exceptional points associated with non-hermitian operators, i.e. operators being non-hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within…
The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…
Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
Semiparametric inference on average causal effects from observational data is based on assumptions yielding identification of the effects. In practice, several distinct identifying assumptions may be plausible; an analyst has to make a…
To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…
We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the conditional variance function. The tests are based on a sequential marked empirical process and thus combine…
McFadden's random-utility model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions under which multinomial choice-probability functions can be rationalized via random-utility models with…
Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…
Addressing the question of how to achieve optimal decision-making under risk and uncertainty is crucial for enhancing the capabilities of artificial agents that collaborate with or support humans. In this work, we address this question in…
We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties of the so-called Koopman operator, our approach can be regarded as a natural extension of classic linear…
Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Most research has focused on estimating the conditional average treatment…
This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…