13 papers
Special Dirichlet Processes: Structure, Uniqueness and Stability
Philip Kennerberg
We introduce the class of \emph{Special--Dirichlet processes}, consisting of càdlàg adapted processes admitting a decomposition \[ X=M+Γ, \] where \(M\) is a local martingale and \…
Stability of compensator integrals and nonlinear operators under canonical p-th power variation convergence
Philip Kennerberg
Let \(X\) and \((X^n)_{n\ge1}\) be c`adl`ag processes with predictable compensators \(ν\) and \(ν^n\). For \(p>1\), assume that \([X^n-X]^{(p)}_t\to0\) in probability, where \([\,\…
An Extremal Reconstruction Principle under Covariance Domination
Philip Kennerberg
We identify a structural extremal principle governing residual \(L^2\)-norms over operator-ordered covariance envelopes. In contrast to the centered setting, where such quantities…
Functional structural equation models with out-of-sample guarantees
Philip Kennerberg, Ernst C. Wit
Statistical learning methods typically assume that the training and test data originate from the same distribution, enabling effective risk minimization. However, real-world applic…
Functional worst risk minimization
Philip Kennerberg, Ernst C. Wit
The aim of this paper is to extend worst risk minimization, also called worst average loss minimization, to the functional realm. This means finding a functional regression represe…
Constructive and consistent estimation of quadratic minimax
Philip Kennerberg, Ernst C. Wit
We consider square integrable random variables and random (row) vectors of length , such that is square integrable for …
Stability in quadratic variation
Philip Kennerberg, Magnus Wiktorsson
Consider a sequence of cadlag processes , and some fixed function . If is continuous then under several modes of convergence implies corresponding conv…
Optimal worst-risk minimization in structural equation models with random coefficients
Philip Kennerberg, Ernst Wit
The insight that causal parameters are particularly suitable for out-of-sample prediction has sparked a lot development of causal-like predictors. However, the connection with stri…
Worst-risk minimization in generalized structural equation models
Philip Kennerberg, Ernst C. Wit
We consider rather general structural equation models (SEMs) between a target and its covariates in several shifted environments. Given shifts we consider the set…
Stability in quadratic variation, with applications
Philip Kennerberg, Magnus Wiktorsson
We show that non continuous Dirichlet processes, defined as in \cite{NonCont} are closed under a wide family of locally Lipschitz continuous maps (similar to the time-homogeneous v…
A local barycentric version of the Bak-Sneppen model
Philip Kennerberg, Stanislav Volkov
We study the behaviour of the interacting particle system, arising from the Bak-Sneppen model and Jante's law process. Let vertices be placed on a circle, such that each vertex…
Convergence in the -contest
Philip Kennerberg, Stanislav Volkov
We study asymptotic properties of the following Markov system of points in~. At each time step, the point farthest from the current centre of mass, multiplied by…
Jante's law process
Philip Kennerberg, Stanislav Volkov
Consider the process which starts with distinct points on , and fix a positive integer~. Of the total points keep those which minimize the en…