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GLOBAL ASYMPTOTIC NORMALITY

Statistics & Risk Modeling, 1983
The author generalizes an approximation theorem of \textit{R. Michel} and \textit{J. Pfanzagl} [Metrika 16, 188-205 (1970; Zbl 0218.62023)] for parametric families of probability measures. He proves that a uniform version of \textit{L. LeCam's} [Proc. 3rd Berkeley Sympos. math. Statist.
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Asymptotic Normality of Scaling Functions

SIAM Journal on Mathematical Analysis, 2004
The properties of probability measures are investigated. It is shown that if \(m\) is a probability measure on \(R\) with finite first moment, then the solution of the scaling equation \[ \phi (x) = \int_{R} \alpha \phi (\alpha x - y)\,dm(y),\quad x \in {\mathbb R} , \] is also a probability measure with the scale \(\alpha > 1\).
Goodman, Timothy   +2 more
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