Bivariate Function Spaces and the Embedding of Their Marginal Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Bivariate Function Spaces and the Embedding of Their Marginal Spaces

Authors:	J. J. Grobler

Affiliation:	(1) Unit for Business Mathematics and Informatics, North-West University, Potchefstroom, 2520, South Africa

Abstract:	For a probability space we denote the marginal measures of , defined on Σ and Λ respectively, by $user2{mathbb{P}}_1$ and $user2{mathbb{P}}_2$ . If ρ is a function norm defined on $L^0(X, times ,Y,,Sigma , otimes ,Lambda ,,user2{mathbb{P}})$ marginal function norms ρ₁ and ρ₂ are defined on $L^0 (X,,Sigma, ,user2{mathbb{P}}_1 )$ and $L^0 (Y,,Lambda, ,user2{mathbb{P}}_2 )$ . We find conditions which guarantee L_{ρ 1} + L_{ρ 2} to be embedded in L_ρ as a closed subspace. The problem is encountered in Statistics when estimating a bivariate distribution with known marginals. We find a condition which, applied to the binormal distribution in L², improves some known conditions.

Keywords:	Primary 46E30 47G10 47B34 47B38 Secondary 47B80 62H12
本文献已被 SpringerLink 等数据库收录！