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Comment on "On some statistical paradoxes and non-conglomerability" by Bruce Hill.

Isaac Levi (1981)

Trabajos de Estadística e Investigación Operativa

Those who follow Harold Jeffreys in using improper priors together with likelihoods to determine posteriors have thought of the improper measures as probability measures of a deviant sort. This is a mistake. Probability measures are finite measures. Improper distributions generate σ-finite measures. (...)

Commutative nonstationary stochastic fields

Hatamleh Ra'ed (2002)

Archivum Mathematicum

The present paper is devoted to further development of commutative nonstationary field themes; the first studies in this area were performed by K. Kirchev and V. Zolotarev [4, 5]. In this paper a more complicated variant of commutative field with nonstationary rank 2, carrying into more general situation for correlation function is studied. A condition of consistency (see (7) below) for commutative field is placed in the basis of the method proposed in [4, 5] and developed in this paper. The following...

Commuting functions and simultaneous Abel equations

W. Jarczyk, K. Łoskot, M. C. Zdun (1994)

Annales Polonici Mathematici

The system of Abel equations α(ft(x)) = α(x) + λ(t), t ∈ T, is studied under the general assumption that f t are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.

Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions

Kirchev, K., Borisova, G. (1997)

Serdica Mathematical Journal

* Partially supported by Grant MM-428/94 of MESC.In this paper we present some generalizations of results of M. S. Livšic [4,6], concerning regular colligations (A1, A2, H, Φ, E, σ1, σ2, γ, ˜γ) (σ1 > 0) of a pair of commuting nonselfadjoint operators A1, A2 with finite dimensional imaginary parts, their complete characteristic functions and a class Ω(σ1, σ2) of operator-functions W(x1, x2, z): E → E in the case of an inner function W(1, 0, z) of the class Ω(σ1). ...

Compact convex sets of the plane and probability theory

Jean-François Marckert, David Renault (2014)

ESAIM: Probability and Statistics

The Gauss−Minkowski correspondence in ℝ2 states the existence of a homeomorphism between the probability measures μ on [0,2π] such that 0 2 π e i x d μ ( x ) = 0 ∫ 0 2 π e ix d μ ( x ) = 0 and the compact convex sets (CCS) of the plane with perimeter 1. In this article, we bring out explicit formulas relating the border of a CCS to its probability measure. As a consequence, we show that some natural operations on CCS – for example, the Minkowski sum – have natural translations in terms of probability measure operations,...

Compact hypothesis and extremal set estimators

João Tiago Mexia, Pedro Corte Real (2003)

Discussiones Mathematicae Probability and Statistics

In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when the true...

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