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1.
LetP be a probability measure on ℝ andI
x be the set of alln-dimensional rectangles containingx. If for allx ∈ ℝn and θ ∈ ℝ the inequality
holds,P is a normal distributioin with mean 0 or the unit mass at 0. The result generalizes Teicher’s (1961) maximum likelihood characterization
of the normal density to a characterization ofN(0, σ2) amongall distributions (including those without density). The m.l. principle used is that of Scholz (1980). 相似文献
2.
3.
4.
Let {X
j
} be a strictly stationary sequence of negatively associated random variables with the marginal probability density function
f(x). The recursive kernel estimators of f(x) are defined by
and the Rosenblatt–Parzen’s kernel estimator of f(x) is defined by , where 0 < b
n
→ 0 are bandwidths and K is some kernel function. In this paper, we study the uniformly Berry–Esseen bounds for these estimators of f(x). In particular, by choice of the bandwidths, the Berry–Esseen bounds of the estimators attain . 相似文献
5.
Prof. Dr. J. Pfanzagl 《Metrika》1970,15(1):141-148
Summary Let (X,A) be a measurable space andP
ϑη |A (ϑη) ∈ Θ x H, ∥A, (θ, η) ∈ Θ×H, a parametrized family of probability measures (for short:p-measures). This paper is concerned with the problem of consistently estimatingθ from realizations governed by
, where ηu ∈ H, v ∈ ℕ, are unknown. 相似文献
6.
Summary Completeness of a family of probability distributions implies its bounded completeness but not conversely. An example of a
family which is boundedly complete but not complete was presented by Lehmann and Scheffe [5]. This appears to be the only
such example quoted in the statistical literature. The purpose of this note is to provide further examples of this type. It
is shown that any given family of power series distributions can be used to construct a class containing infinitely many boundedly
complete, but not complete, families. Furthermore, it is shown that the family of continuous distributions
, is boundedly complete, but not complete, whereU denotes the uniform distribution on [a, b] and {P
ϑ,ϑ ∈ IR}, is a translation family generated by a distributionP
0 with mean value zero, which is continuous with respect to the Lebesgue measure. 相似文献
7.
8.
Prof. Dr. T. J. Terpstra 《Metrika》1989,36(1):63-90
We considerr ×c populations with failure ratesλ
ij(t) satisfying the condition
相似文献
9.
10.
LetX
1,X
2, ...,X
n
(n≥3) be a random sample on a random variableX with distribution functionF having a unique continuous inverseF
−1 over (a,b), −∞≤a<b≤∞ the support ofF. LetX
1:n
<X
2:n
<...<X
n:n
be the corresponding order statistics. Letg be a nonconstant continuous function over (a,b). Then for some functionG over (a, b) and for some positive integersr ands, 1<r+1<s≤n
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