Results 91 to 100 of about 297 (132)
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Local ancillarity in the presence of a nuisance parameter
Biometrika, 1993Let \(S\) be a statistic with density depending on a scale parameter \(\theta\) and nuisance parameter \(\lambda\). If \(S\) can be written as \(S=(T,A)\), then \(A\) is ancillary for \(\theta\) in the presence of \(\lambda\) if the conditional distribution of \(T\) given \(A\) depends only on \(\theta\) and \(A\) contains ``no information about ...
Thomas Severini
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S-Ancillarity and Strong Exogeneity
, 2000 This note analyses the differences and similarities between the concepts of Sancillarity and strong exogeneity. We show that while strong exogeneity of a variable for a parameter implies S-ancillarity of the same variable for the same parameter, the converse is not true. An example illustrates the point.
H. Peter Boswijk
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Risk, Sufficiency, Completeness, and Ancillarity
, 2009 The initial section of this chapter develops a basic framework for inference. Later sections concern the notion of sufficiency that arises when data can be summarized without any loss of information.
Robert W. Keener
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Information, Ancillarity and Conditional Inference
, 1985 The present chapter studies the amount of information carried by a statistic t(x) from the geometrical point of view. The amount of information plays a fundamental role in parameter estimation and statistical hypothesis testing. Higher-order asymptotic sufficiency, higher-order asymptotic ancillarity, and conditional information are defined in the ...
Shun-ichi Amari
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The Structure of a Linear Model: Sufficiency, Ancillarity, Invariance, Equivariance, and the Normal Distribution [PDF]
Journal of Multivariate Analysis, 2000 Consider a general linear model $Y=X\beta+Z$, where $\text{Cov}\,Z$ may be known only partially. We investigate carefully the notions of sufficiency, ancillarity, invariance, and equivariance and related notions for projectors in a general linear model ...
W Bischoff
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Biometrika, 1981
Let p(x, 6) be a probability density function with respect to some measure /, where x E E and 6 E Q, the sample and parameter space. Further, assume that 6 = (61, 62), 62 being a nuisance parameter, where 61 E Ql, 62 E Q2 and Q = Q1 X Q2. In this situation Godambe (1976) defined a statistic t as ancillary for estimating 61 if (a) the conditional ...
P. E. FERREIRA, Ch. E. MINDER
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Let p(x, 6) be a probability density function with respect to some measure /, where x E E and 6 E Q, the sample and parameter space. Further, assume that 6 = (61, 62), 62 being a nuisance parameter, where 61 E Ql, 62 E Q2 and Q = Q1 X Q2. In this situation Godambe (1976) defined a statistic t as ancillary for estimating 61 if (a) the conditional ...
P. E. FERREIRA, Ch. E. MINDER
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Biometrika, 1973
Eine parametrische Familie von Wahrscheinlichkeitsmaßen auf einer endlichen Menge - \(\mathfrak U\) heist universal, wenn für jeden Punkt \(u\in\mathfrak U\) ein Wert des Parameters \(u\) existiert, so daß für die Wahrscheinlichkeitsfunktion \(p(u,\omega)\) \(p(u,\omega)\geq p(\tilde u,\omega)\) \((\tilde u\in\mathfrak U)\) gilt.
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Eine parametrische Familie von Wahrscheinlichkeitsmaßen auf einer endlichen Menge - \(\mathfrak U\) heist universal, wenn für jeden Punkt \(u\in\mathfrak U\) ein Wert des Parameters \(u\) existiert, so daß für die Wahrscheinlichkeitsfunktion \(p(u,\omega)\) \(p(u,\omega)\geq p(\tilde u,\omega)\) \((\tilde u\in\mathfrak U)\) gilt.
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