共查询到20条相似文献,搜索用时 15 毫秒
1.
Bernhard Klar 《Metrika》1999,49(1):53-69
This paper presents a new widely applicable omnibus test for discrete distributions which is based on the difference between
the integrated distribution function Ψ(t)=∫t
∞ (1−F(x))dx and its empirical counterpart. A bootstrap version of the test for common lattice models has accurate error rates even for
small samples and exhibits high power with respect to competitive procedures over a large range of alternatives.
Received: July 1998 相似文献
2.
Minimax estimation of a cumulative distribution function by converting to a parametric problem 总被引:2,自引:1,他引:2
Let X = (X
1,...,X
n
) be a sample from an unknown cumulative distribution function F defined on the real line
. The problem of estimating the cumulative distribution function F is considered using a decision theoretic approach. No assumptions are imposed on the unknown function F. A general method of finding a minimax estimator d(t;X) of F under the loss function of a general form is presented. The method of solution is based on converting the nonparametric problem
of searching for minimax estimators of a distribution function to the parametric problem of searching for minimax estimators
of the probability of success for a binomial distribution. The solution uses also the completeness property of the class of
monotone decision procedures in a monotone decision problem. Some special cases of the underlying problem are considered in
the situation when the loss function in the nonparametric problem is defined by a weighted squared, LINEX or a weighted absolute
error. 相似文献
3.
Agnieszka Stępień-Baran 《Metrika》2010,72(1):37-49
The problem of invariant estimation of a continuous distribution function is considered under a general loss function. Minimaxity
of the minimum risk invariant estimator of a continuous distribution function is proved for any sample size n ≥ 2. 相似文献
4.
M. C. Jones 《Metrika》2002,54(3):215-231
Relationships between F, skew t and beta distributions in the univariate case are in this paper extended in a natural way to the multivariate case. The result
is two new distributions: a multivariate t/skew t distribution (on ℜm) and a multivariate beta distribution (on (0,1)m). A special case of the former distribution is a new multivariate symmetric t distribution. The new distributions have a natural relationship to the standard multivariate F distribution (on (ℜ+)m) and many of their properties run in parallel. We look at: joint distributions, mathematically and graphically; marginal
and conditional distributions; moments; correlations; local dependence; and some limiting cases.
Received: March 2001 相似文献
5.
A consistent test for multivariate normality based on the empirical characteristic function 总被引:2,自引:1,他引:1
LetX
1,X
2, …,X
n be independent identically distributed random vectors in IR
d
,d ⩾ 1, with sample mean
and sample covariance matrixS
n. We present a practicable and consistent test for the composite hypothesisH
d: the law ofX
1 is a non-degenerate normal distribution, based on a weighted integral of the squared modulus of the difference between the
empirical characteristic function of the residualsS
n
−1/2
(X
j −
) and its pointwise limit exp (−1/2|t|2) underH
d. The limiting null distribution of the test statistic is obtained, and a table with critical values for various choices ofn andd based on extensive simulations is supplied. 相似文献
6.
In the present paper families of truncated distributions with a Lebesgue density
forx=(x
1,...,x
n
) ε ℝ
n
are considered, wheref
0:ℝ → (0, ∞) is a known continuous function andC
n
(ϑ) denotes a normalization constant. The unknown truncation parameterϑ which is assumed to belong to a bounded parameter intervalΘ=[0,d] is to be estimated under a convex loss function. It is studied whether a two point prior and a corresponding Bayes estimator
form a saddle point when the parameter interval is sufficiently small. 相似文献
7.
Michael Kohler 《Metrika》1998,47(1):147-163
Let (X, Y) be a pair of random variables withsupp(X)⊆[0,1]
l
andEY
2<∞. Letm
* be the best approximation of the regression function of (X, Y) by sums of functions of at mostd variables (1≤d≤l). Estimation ofm
* from i.i.d. data is considered.
For the estimation interaction least squares splines, which are defined as sums of polynomial tensor product splines of at
mostd variables, are used. The knot sequences of the tensor product splines are chosen equidistant. Complexity regularization is
used to choose the number of the knots and the degree of the splines automatically using only the given data.
Without any additional condition on the distribution of (X, Y) the weak and strongL
2-consistency of the estimate is shown. Furthermore, for everyp≥1 and every distribution of (X, Y) withsupp(X)⊆[0,1]
l
,y bounded andm
*
p-smooth, the integrated squared error of the estimate achieves up to a logarithmic factor the (optimal) rate
相似文献
8.
In the reliability studies, k-out-of-n systems play an important role. In this paper, we consider sharp bounds for the mean residual life function of a k-out-of-n system consisting of n identical components with independent lifetimes having a common distribution function F, measured in location and scale units of the residual life random variable X
t
= (X−t|X > t). We characterize the probability distributions for which the bounds are attained. We also evaluate the so obtained bounds
numerically for various choices of k and n. 相似文献
9.
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
相似文献
10.
Peter C. Fishburn 《Journal of Mathematical Economics》1980,7(3):271-285
Let P = {F,G,…} be the set of all probability distribution functions with support (0, ∞). An unrestricted stochastic dominance relation>∞ is defined on P for each real ∞ 1, where F >∞ G means that xy = 0 (x - y)∞ - 1 dG(y) xn = 0(x − y)∞−1 dG(y) for all ∞ 0, with < for some x. These relations are partial orders that increase as ∞ increases with limit relation>∞. A class U∞ of utility functions u on (0, ∞) is defined in such a way that F >∞ G iff udF > udG for all u ε U∞. The U∞ decrease as ∞ increases and have a non-empty intersection U∞. Each u ε U∞ is an increasing function that has derivatives of all orders that alternate in sign. Criteria which tell when F eventually dominates G in the sense of F >∞ G are noted. Comparisons with bounded stochastic dominance results are made in several places. 相似文献
11.
Based on the exponential and Poisson characteristics of the Poisson process, in this work we present some characterizations
of the Poisson process as a renewal process. More precisely, let γt be the residual life at time t of the renewal process A={A(t),t≥0 }, under suitable condition, we prove that if Var(γt)=E
2 (γt),∀t≥0, then A is a Poisson process. Secondly, we show that if Var (A(t)) is proportional to E (A(t)), then A is a Poisson process also, and Var (A(t))=E (A(t)).
Received: August 1999 相似文献
12.
Pearn et al. (1999) considered a capability index C
′′
pmk, a new generalization of C
pmk, for processes with asymmetric tolerances. In this paper, we provide a comparison between C
′′
pmk and other existing generalizations of C
pmk on the accuracy of measuring process performance for processes with asymmetric tolerances. We show that the new generalization
C
′′
pmk is superior to other existing generalizations of C
pmk. Under the assumption of normality, we derive explicit forms of the cumulative distribution function and the probability
density function of the estimated index . We show that the cumulative distribution function and the probability density function of the estimated index can be expressed in terms of a mixture of the chi-square distribution and the normal distribution. The explicit forms of
the cumulative distribution function and the probability density function considerably simplify the complexity for analyzing
the statistical properties of the estimated index .
Received April 2000 相似文献
13.
In this paper we generalize the quality and cost trade-off problem of Chang and Hung (Qual Quant 41: 291–301, 2007) under
the LINEX loss function. We consider the general input characteristic given by the random variable X with moment generating function m
X
(t) and output characteristic given by the deterministic transformation Y = g(X). The two cases we consider are when g(X) is an affine function of X and X follows (1) the gamma distribution, and (2) the double exponential distribution. 相似文献
14.
A bandit problem consisting of a sequence of n choices (n) from a number of infinitely many Bernoulli arms is considered. The parameters of Bernoulli arms are independent and identically distributed random variables from a common distribution F on the interval [0,1] and F is continuous with F(0)=0 and F(1)=1. The goal is to investigate the asymptotic expected failure rates of k-failure strategies, and obtain a lower bound for the expected failure proportion over all strategies presented in Berry et al. (1997). We show that the asymptotic expected failure rates of k-failure strategies when 0<b1 and a lower bound can be evaluated if the limit of the ratio F(1)–F(t) versus (1–t)b exists as t1– for some b>0. 相似文献
15.
LetX
1,…,X
m
andY
1,…,Y
n
be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S
(1),…,S
(n)), whereS
(j)=# (X
i
’s≤Y
(j)) andY
(j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the
Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test.
We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests
based onS
(1) andS
(n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c). 相似文献
16.
Dr. Werner Goldmann 《Metrika》1987,34(1):25-30
Summary Letx
1,x
2,x
3, ... be a sequence of independent identically distributed random variables andτ an estimable parameter of their distribution. We want to estimateτ by the correspondingU-statisticu
n
with loss function (u
n
−τ)2 +cn. We derive a stopping time and prove its risk-efficiency in the sense of Starr (1966) without any assumption on the nature
of the distribution function other than the existence of some moments.
Research supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 72, at the Universit?t Bonn. 相似文献
17.
Let (W
n
,n ≥ 0) denote the sequence of weak records from a distribution with support S = { α0,α1,...,α
N
}. In this paper, we consider regression functions of the form ψ
n
(x) = E(h(W
n
) |W
n+1 = x), where h(·) is some strictly increasing function. We show that a single function ψ
n
(·) determines F uniquely up to F(α0). Then we derive an inversion formula which enables us to obtain F from knowledge of ψ
n
(·), ψ
n-1(·), h(·) and F(α0). 相似文献
18.
In the present paper, we consider a (n − k + 1)-out-of-n system with identical components where it is assumed that the lifetimes of the components are independent and have a common
distribution function F. We assume that the system fails at time t or sometime before t, t > 0. Under these conditions, we are interested in the study of the mean time elapsed since the failure of the components.
We call this as the mean past lifetime (MPL) of the components at the system level. Several properties of the MPL are studied.
It is proved that the relation between the proposed MPL and the underlying distribution is one-to-one. We have shown that
when the components of the system have decreasing reversed hazard then the MPL of the system is increasing with respect to
time. Some examples are also provided. 相似文献
19.
Summary LetX andY be two random vectors with values in ℝ
k
and ℝ∝, respectively. IfZ=(X
T,Y
T)
T
is multivariate normal thenX givenY=y andY givenX=x are (multivariate) normal; the converse is wrong. In this paper simple additional conditions are stated such that the converse
is true, too. Furthermore, the case is treated that the random vectorZ=(X
1
T
, …,X
t
T
)
T
is splitted intot≥3 partsX
1, …,X
t. 相似文献
20.
A new location invariant loss function is considered and the best invariant estimator of normal mean is obtained. This estimator is a function of the moment generating function of the lognormal distribution. The admissibility is studied of a class of linear estimators of the form cX+d, where X~N(/,C2), with / unknown and C2 known. This yields the admissibility of the best invariant estimator of /. 相似文献
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