Daniel Rost

On Random Measure Processes with Application to Smoothed Empirical Processes

We consider function-indexed so-called Random Measure Processes (RMP’s) and focus especially on a uniform law of large numbers (ULLN) for RMP’s. Demonstrating both its power and its generality we apply it to derive a ULLN for smoothed empirical processes covering a former result by Yukich (1989). Finally we also present a functional central limit theorem (FCLT) for smoothed empirical processes under conditions different from those found in the literature.

Brückenkurs für Studierende des Lehramts an Grund-, Haupt- oder Realschulen der Ludwig-Maximilians-Universität München

In folgendem Artikel sollen Struktur und Charakter, Adressaten, Inhalte sowie zentrale Ziele des Bruckenkurses fur Studierende des Lehramts an Grund-, Haupt- oder Realschulen der Ludwig-Maximilians-Universitat Munchen geschildert werden. Das Hauptaugenmerk liegt dabei auf den Inhalten des Kursszenarios, welche anhand von ausgewahlten Beispielaufgaben thematisiert werden. Ein abschliesendes Resumee kommentiert den Gesamteindruck des Kurses und bietet in einem Ausblick Vorschlage zur Optimierung des Angebots.

On Uniform Laws of Large Numbers for Smoothed Empirical Measures

We consider function-indexed smoothed empirical measures on linear metric spaces and focus on uniform laws of large numbers (ULLN) comparable with Glivenko-Cantelli results in the non-smoothed case. Using the random measure process approach we are able to give a set of sufficient conditions for a ULLN which are different from the ones known in the literature and are more close to being necessary.

Smoothed Empirical Processes and the Bootstrap

Based on a uniform functional central limit theorem (FCLT) for unbiased smoothed empirical processes indexed by a class.F of measurable functions defined on a linear metric space we present a consistency theorem for smoothed bootstrapped empirical processes. Our approach and the results are comparable with those in Gine and Zinn [8], and Gine [10], respectively, in the case of empirical processes; especially, our Theorem 2.2 below is comparable with the main result stated as Theorem 2.3 in Gine and Zinn [8].

A note on compact differentiability and theδ-method

AbstractLetηn,n ∈ ℕ, be arbitrary functions defined on a probability space (ω,A,P) with values in a normed vector spaceB1,μ ∈ B1 andξ0 a separable random element inB1 such thatξn:=√n(ηn−μ) converges weakly toξ0 in the sense of Hoffmann-Jørgensen. Then with (B2, ∥·∥2) being another normed vector space andφ:B1→B2 compactly differentiable atμ with derivateDμ, the random variable

On Continuity and Strict Increase of the CDF for the Sup-Functional of a Gaussian Process with Applications to Statistics

\parallel \sqrt n (\phi (n_n ) - \phi (\mu )) - D_\mu (\sqrt n (n_n - \mu ))\parallel 2*

Fachwissenschaftliche mathematische Kompetenzen von Studierenden für das Lehramt an Grund-, Haupt- oder Realschulen zu Studienbeginn

converges to 0P-stochastically where “*” denotes the measurable cover. We show that the classicalδ — method extends to the non-measurable case where in the proof we shall not make use of any representation theorems but only of a slight refinement of the usual characterisation of compact differentiability, due to the fact that we will not assume {ξn:n ∈ ℕ} being tight.

Probability and quantile estimation from individually micro-aggregated data

AbstractThis paper establishes the representation of the generalizedN-dimensional Wasserstein distance (Kantorovich-Functional)