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Asymptotic Normality of Scaling Functions
SIAM Journal on Mathematical Analysis, 2004The 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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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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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 Autoregressive Processes
Acta Applicandae Mathematicae, 2009Using an approximation method along with a central limit theorem for \(m\)-dependent random variables, this paper prove an asymptotic normality for autoregressive processes, and provide the central limit theorems of the least square estimate and the Yule-Walker estimate of the parameters of an autoregressive process.
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Asymptotic Normality of some Estimators
Calcutta Statistical Association Bulletin, 1981This paper uses martingale central limit theorem and continuous mapping theorem to establish asymptotic normality of log-likelihood ratio process, maximum likelihood estimators and the posterior distributions. Illustrative examples are given.
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Matching behaviour is asymptotically normal
Combinatorica, 1981Ak-matching in a graphG is a set ofk edges, no two of which have a vertex in common. The number of these inG is writtenp(G, k). Using an idea due to L. H. Harper, we establish a condition under which these numbers are approximately normally distributed.
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On the asymptotic normality of self-normalized sums
Mathematical Proceedings of the Cambridge Philosophical Society, 1991AbstractLet X1, …, Xn be a sequence of non-degenerate, symmetric, independent identically distributed random variables, and let Sn(rn) denote their sum when the rn largest in modulus have been removed. We obtain necessary and sufficient conditions for asymptotic normality of the studentized version of Sn(rn), and compare this to the condition for ...
Griffin, Philip S., Mason, David M.
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2000
The classical theory of asymptotics in statistics relies heavily on certain local quadratic approximations to the logarithms of likelihood ratios. Such approximations will be studied here but in a restricted framework.
Lucien Le Cam, Grace Lo Yang
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The classical theory of asymptotics in statistics relies heavily on certain local quadratic approximations to the logarithms of likelihood ratios. Such approximations will be studied here but in a restricted framework.
Lucien Le Cam, Grace Lo Yang
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Normal Approximations and Asymptotic Expansions.
Journal of the American Statistical Association, 1977Marius Iosifescu +2 more
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A Note on Asymptotic Normal Structure and Close-to-Normal Structure
Canadian Mathematical Bulletin, 1982AbstractA closed convex subset X of a Banach space E is said to have (i) asymptotic normal structure if for each bounded closed convex subset C of X containing more than one point and for each sequence in C satisfying ‖xn − xn + 1‖ → 0 as n → ∞, there is a point x ∈ C such that ; (ii) close-to-normal structure if for each bounded closed convex subset ...
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