منابع مشابه
The central limit theorem under random truncation.
Under left truncation, data (X(i), Y(i)) are observed only when Y(i) ≤ X(i). Usually, the distribution function F of the X(i) is the target of interest. In this paper, we study linear functionals ∫ φ dF(n) of the nonparametric maximum likelihood estimator (MLE) of F, the Lynden-Bell estimator F(n). A useful representation of ∫ φ dF(n) is derived which yields asymptotic normality under optimal m...
متن کاملAn Induction Theorem and Nonlinear Regularity
A general nonlinear regularity model for a set-valued mapping F : X × R+ ⇒ Y , where X and Y are metric spaces, is studied using special iteration procedures, going back to Banach, Schauder, Lyusternik and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal. Appl., 118 (1986) and employ it to obtain basic estimates for exploring regularity/openness properties. We also show...
متن کاملCentral Limit Theorem for Maxwellian Molecules and Truncation of the Wild Expansion
We prove an L bound on the error made when the Wild summation for solutions of the Boltzmann equation for a gas of Maxwellian molecules is truncated at the nth stage. This gives quantitative control over the only constructive method known for solving the Boltzmann equation. As such, it has been recently applied to numerical computation, but without control on the approximation made in truncatio...
متن کاملThe Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کاملInduction, bounding, weak combinatorial principles, and the homogeneous model theorem
Goncharov and Peretyat’kin independently gave necessary and sufficient conditions for when a set of types of a complete theory T is the type spectrum of some homogeneous model of T . Their result can be stated as a principle of second order arithmetic, which we call the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2020.02.004