共查询到20条相似文献,搜索用时 31 毫秒
1.
Pawel R. Pordzik 《Statistical Papers》2012,53(2):299-304
Let
[^(\varveck)]{\widehat{\varvec{\kappa}}} and
[^(\varveck)]r{\widehat{\varvec{\kappa}}_r} denote the best linear unbiased estimators of a given vector of parametric functions
\varveck = \varvecKb{\varvec{\kappa} = \varvec{K\beta}} in the general linear models
M = {\varvecy, \varvecX\varvecb, s2\varvecV}{{\mathcal M} = \{\varvec{y},\, \varvec{X\varvec{\beta}},\, \sigma^2\varvec{V}\}} and
Mr = {\varvecy, \varvecX\varvecb | \varvecR \varvecb = \varvecr, s2\varvecV}{{\mathcal M}_r = \{\varvec{y},\, \varvec{X}\varvec{\beta} \mid \varvec{R} \varvec{\beta} = \varvec{r},\, \sigma^2\varvec{V}\}}, respectively. A bound for the Euclidean distance between
[^(\varveck)]{\widehat{\varvec{\kappa}}} and
[^(\varveck)]r{\widehat{\varvec{\kappa}}_r} is expressed by the spectral distance between the dispersion matrices of the two estimators, and the difference between sums
of squared errors evaluated in the model M{{\mathcal M}} and sub-restricted model Mr*{{\mathcal M}_r^*} containing an essential part of the restrictions
\varvecR\varvecb = \varvecr{\varvec{R}\varvec{\beta} = \varvec{r}} with respect to estimating
\varveck{\varvec{\kappa}}. 相似文献
2.
The mixture of Rayleigh random variables X
1and X
2 are identified in terms of relations between the conditional expectation of ( X2:22 -X1:22)r{\left( {X_{2:2}^2 -X_{1:2}^2}\right)^{r}} given X
1:2 (or X2:22k{X_{2:2}^{2k}} given X1:2,"k £ r){X_{1:2},\forall k\leq r)} and hazard rate function of the distribution, where X
1:2 and X
2:2 denote the corresponding order statistics, r is a positive integer. In addition, we also mention some related theorems to characterize the mixtures of Rayleigh distributions.
Finally, we also give an application to Multi-Hit models of carcinogenesis (Parallel Systems) and a simulated example is used
to illustrate our results. 相似文献
3.
Mariusz Grządziel 《Statistical Papers》2008,49(3):399-419
Gnot et al. (J Statist Plann Inference 30(1):223–236, 1992) have presented the formulae for computing Bayes invariant quadratic
estimators of variance components in normal mixed linear models of the form
where the matrices V
i
, 1 ≤ i ≤ k − 1, are symmetric and nonnegative definite and V
k
is an identity matrix. These formulae involve a basis of a quadratic subspace containing MV
1
M,...,MV
k-1
M,M, where M is an orthogonal projector on the null space of X′. In the paper we discuss methods of construction of such a basis. We survey Malley’s algorithms for finding the smallest
quadratic subspace including a given set of symmetric matrices of the same order and propose some modifications of these algorithms.
We also consider a class of matrices sharing some of the symmetries common to MV
1
M,...,MV
k-1
M,M. We show that the matrices from this class constitute a quadratic subspace and describe its explicit basis, which can be
directly used for computing Bayes invariant quadratic estimators of variance components. This basis can be also used for improving
the efficiency of Malley’s algorithms when applied to finding a basis of the smallest quadratic subspace containing the matrices
MV
1
M,...,MV
k-1
M,M. Finally, we present the results of a numerical experiment which confirm the potential usefulness of the proposed methods.
Dedicated to the memory of Professor Stanisław Gnot. 相似文献
4.
We consider the situation where one wants to maximise a functionf(θ,x) with respect tox, with θ unknown and estimated from observationsy
k
. This may correspond to the case of a regression model, where one observesy
k
=f(θ,x
k
)+ε
k
, with ε
k
some random error, or to the Bernoulli case wherey
k
∈{0, 1}, with Pr[y
k
=1|θ,x
k
|=f(θ,x
k
). Special attention is given to sequences given by
, with
an estimated value of θ obtained from (x1, y1),...,(x
k
,y
k
) andd
k
(x) a penalty for poor estimation. Approximately optimal rules are suggested in the linear regression case with a finite horizon,
where one wants to maximize ∑
i=1
N
w
i
f(θ, x
i
) with {w
i
} a weighting sequence. Various examples are presented, with a comparison with a Polya urn design and an up-and-down method
for a binary response problem. 相似文献
5.
Letx i(1)≤x i(2)≤…≤x i(ri) be the right-censored samples of sizesn i from theith exponential distributions $\sigma _i^{ - 1} exp\{ - (x - \mu _i )\sigma _i^{ - 1} \} ,i = 1,2$ where μi and σi are the unknown location and scale parameters respectively. This paper deals with the posteriori distribution of the difference between the two location parameters, namely μ2-μ1, which may be represented in the form $\mu _2 - \mu _1 \mathop = \limits^\mathcal{D} x_{2(1)} - x_{1(1)} + F_1 \sin \theta - F_2 \cos \theta $ where $\mathop = \limits^\mathcal{D} $ stands for equal in distribution,F i stands for the central F-variable with [2,2(r i?1)] degrees of freedom and $\tan \theta = \frac{{n_2 s_{x1} }}{{n_1 s_{x2} }}, s_{x1} = (r_1 - 1)^{ - 1} \left\{ {\sum\limits_{j = 1}^{r_i - 1} {(n_i - j)(x_{i(j + 1)} - x_{i(j)} )} } \right\}$ The paper also derives the distribution of the statisticV=F 1 sin σ?F 2 cos σ and tables of critical values of theV-statistic are provided for the 5% level of significance and selected degrees of freedom. 相似文献
6.
A doubly censoring scheme occurs when the lifetimes T being measured, from a well-known time origin, are exactly observed within a window [L, R] of observational time and are otherwise censored either from above (right-censored observations) or below (left-censored
observations). Sample data consists on the pairs (U, δ) where U = min{R, max{T, L}} and δ indicates whether T is exactly observed (δ = 0), right-censored (δ = 1) or left-censored (δ = −1). We are interested in the estimation of the marginal behaviour of the three random variables T, L and R based on the observed pairs (U, δ). We propose new nonparametric simultaneous marginal estimators [^(S)]T, [^(S)]L{\hat S_{T}, \hat S_{L}} and [^(S)]R{\hat S_{R}} for the survival functions of T, L and R, respectively, by means of an inverse-probability-of-censoring approach. The proposed estimators [^(S)]T, [^(S)]L{\hat S_{T}, \hat S_{L}} and [^(S)]R{\hat S_{R}} are not computationally intensive, generalize the empirical survival estimator and reduce to the Kaplan-Meier estimator in
the absence of left-censored data. Furthermore, [^(S)]T{\hat S_{T}} is equivalent to a self-consistent estimator, is uniformly strongly consistent and asymptotically normal. The method is illustrated
with data from a cohort of drug users recruited in a detoxification program in Badalona (Spain). For these data we estimate
the survival function for the elapsed time from starting IV-drugs to AIDS diagnosis, as well as the potential follow-up time.
A simulation study is discussed to assess the performance of the three survival estimators for moderate sample sizes and different
censoring levels. 相似文献
7.
Milan Merkle 《Statistical Methods and Applications》1996,5(3):323-334
Summary Let
, whereX
i are i.i.d. random variables with a finite variance σ2 and
is the usual estimate of the mean ofX
i. We consider the problem of finding optimal α with respect to the minimization of the expected value of |S
2(σ)−σ2|k for variousk and with respect to Pitman's nearness criterion. For the Gaussian case analytical results are obtained and for some non-Gaussian
cases we present Monte Carlo results regarding Pitman's criteron.
This research was supported by Science Fund of Serbia, grant number 04M03, through Mathematical Institute, Belgrade. 相似文献
8.
Suppose that data {(x l,i,n , y l,i,n ): l?=?1, …, k; i?=?1, …, n} are observed from the regression models: Y l,i,n ?=?m l (x l,i,n )?+?? l,i,n , l?=?1, …, k, where the regression functions {m l } l=1 k are unknown and the random errors {? l,i,n } are dependent, following an MA(∞) structure. A new test is proposed for testing the hypothesis H 0: m 1?=?·?·?·?=?m k , without assuming that {m l } l=1 k are in a parametric family. The criterion of the test derives from a Crámer-von-Mises-type functional based on different distances between {[mcirc]} l and {[mcirc]} s , l?≠?s, l, s?=?1, …, k, where {[mcirc] l } l=1 k are nonparametric Gasser–Müller estimators of {m l } l=1 k . A generalization of the test to the case of unequal design points, with different sample sizes {n l } l=1 k and different design densities {f l } l=1 k , is also considered. The asymptotic normality of the test statistic is obtained under general conditions. Finally, a simulation study and an analysis with real data show a good behavior of the proposed test. 相似文献
9.
In this paper we introduce the distribution of , with c > 0, where X
i
, i = 1, 2, are independent generalized beta-prime-distributed random variables, and establish a closed form expression of its
density. This distribution has as its limiting case the generalized beta type I distribution recently introduced by Nadarajah
and Kotz (2004). Due to the presence of several parameters the density can take a wide variety of shapes.
相似文献
10.
Deli Li 《Revue canadienne de statistique》1996,24(3):279-292
Let {X, Xn; n ≥ 1} be a sequence of real-valued iid random variables, 0 < r < 2 and p > 0. Let D = { A = (ank; 1 ≤ k ≤ n, n ≥ 1); ank, ? R and supn, k |an,k| < ∞}. Set Sn( A ) = ∑nk=1an, kXk for A ? D and n ≥ 1. This paper is devoted to determining conditions whereby E{supn ≥ 1, |Sn( A )|/n1/r}p < ∞ or E{supn ≥ 2 |Sn( A )|/2n log n)1/2}p < ∞ for every A ? D. This generalizes some earlier results, including those of Burkholder (1962), Choi and Sung (1987), Davis (1971), Gut (1979), Klass (1974), Siegmund (1969) and Teicher (1971). 相似文献
11.
Michael Falk 《统计学通讯:理论与方法》2013,42(7):1729-1755
Consider n independent random variables Zi,…, Zn on R with common distribution function F, whose upper tail belongs to a parametric family F(t) = Fθ(t),t ≥ x0, where θ ∈ ? ? R d. A necessary and sufficient condition for the family Fθ, θ ∈ ?, is established such that the k-th largest order statistic Zn?k+1:n alone constitutes the central sequence yielding local asymptotic normality ( LAN ) of the loglikelihood ratio of the vector (Zn?i+1:n)1 i=kof the k largest order statistics. This is achieved for k = k(n)→n→∞∞ with k/n→n→∞ 0. In the case of vectors of central order statistics ( Zr:n, Zr+1:n,…, Zs:n ), with r/n and s/n both converging to q ∈ ( 0,1 ), it turns out that under fairly general conditions any order statistic Zm:n with r ≤ m ≤s builds the central sequence in a pertaining LAN expansion.These results lead to asymptotically optimal tests and estimators of the underlying parameter, which depend on single order statistics only 相似文献
12.
Consider the regression model Yi= g(xi) + ei, i = 1,…, n, where g is an unknown function defined on [0, 1], 0 = x0 < x1 < … < xn≤ 1 are chosen so that max1≤i≤n(xi-xi- 1) = 0(n-1), and where {ei} are i.i.d. with Ee1= 0 and Var e1 - s?2. In a previous paper, Cheng & Lin (1979) study three estimators of g, namely, g1n of Cheng & Lin (1979), g2n of Clark (1977), and g3n of Priestley & Chao (1972). Consistency results are established and rates of strong uniform convergence are obtained. In the current investigation the limiting distribution of &in, i = 1, 2, 3, and that of the isotonic estimator g**n are considered. 相似文献
13.
Janusz Wywiał 《Statistical Papers》2004,45(3):413-431
LetF(x,y) be a distribution function of a two dimensional random variable (X,Y). We assume that a distribution functionF
x(x) of the random variableX is known. The variableX will be called an auxiliary variable. Our purpose is estimation of the expected valuem=E(Y) on the basis of two-dimensional simple sample denoted by:U=[(X
1, Y1)…(Xn, Yn)]=[X Y]. LetX=[X
1…X
n]andY=[Y
1…Y
n].This sample is drawn from a distribution determined by the functionF(x,y). LetX
(k)be the k-th (k=1, …,n) order statistic determined on the basis of the sampleX. The sampleU is truncated by means of this order statistic into two sub-samples:
% MathType!End!2!1! and
% MathType!End!2!1!.Let
% MathType!End!2!1! and
% MathType!End!2!1! be the sample means from the sub-samplesU
k,1 andU
k,2, respectively. The linear combination
% MathType!End!2!1! of these means is the conditional estimator of the expected valuem. The coefficients of this linear combination depend on the distribution function of auxiliary variable in the pointx
(k).We can show that this statistic is conditionally as well as unconditionally unbiased estimator of the averagem. The variance of this estimator is derived.
The variance of the statistic
% MathType!End!2!1! is compared with the variance of the order sample mean. The generalization of the conditional estimation
of the mean is considered, too. 相似文献
14.
Suppose that Xi are independent random variables, and that Xi has cdf Fi (x), 1 ≤ i ≤ k. Many statistical problems involve the probability Pr{X 1 < X 2 < ··· < Xk }. In this note a numerical method is proposed for computing this probability. 相似文献
15.
Let X1,…, Xn be mutually independent non-negative integer-valued random variables with probability mass functions fi(x) > 0 for z= 0,1,…. Let E denote the event that {X1≥X2≥…≥Xn}. This note shows that, conditional on the event E, Xi-Xi+ 1 and Xi+ 1 are independent for all t = 1,…, k if and only if Xi (i= 1,…, k) are geometric random variables, where 1 ≤k≤n-1. The k geometric distributions can have different parameters θi, i= 1,…, k. 相似文献
16.
Suppose there are k
1 (k
1 ≥ 1) test treatments that we wish to compare with k
2 (k
2 ≥ 1) control treatments. Assume that the observations from the ith test treatment and the jth control treatment follow a two-parameter exponential distribution and , where θ is a common scale parameter and and are the location parameters of the ith test and the jth control treatment, respectively, i = 1, . . . ,k
1; j = 1, . . . ,k
2. In this paper, simultaneous one-sided and two-sided confidence intervals are proposed for all k
1
k
2 differences between the test treatment location and control treatment location parameters, namely , and the required critical points are provided. Discussions of multiple comparisons of all test treatments with the best
control treatment and an optimal sample size allocation are given. Finally, it is shown that the critical points obtained
can be used to construct simultaneous confidence intervals for Pareto distribution location parameters. 相似文献
17.
Junjiro Ogawa 《Journal of statistical planning and inference》1998,70(2):293-360
We are considering the ABLUE’s – asymptotic best linear unbiased estimators – of the location parameter μ and the scale parameter σ of the population jointly based on a set of selected k sample quantiles, when the population distribution has the density of the formwhere the standardized function f(u) being of a known functional form.A set of selected sample quantiles with a designated spacingor in terms of u=(x−μ)/σwhereare given bywhereAsymptotic distribution of the k sample quantiles when n is very large is given bywhereThe relative efficiency of the joint estimation is given bywhereand κ being independent of the spacing
. The optimal spacing is the spacing which maximizes the relative efficiency η(μ,σ).We will prove the following rather remarkable theorem. Theorem. The optimal spacing for the joint estimation is symmetric, i.e.orif the standardized density f(u) of the population is differentiable infinitely many times and symmetric 相似文献
λi=∫−∞uif(t) dt, i=1,2,…,k
x(n1)<x(n2)<<x(nk),
h(x(n1),x(n2),…,x(nk);μ,σ)=(2πσ2)−k/2[λ1(λ2−λ1)(λk−λk−1)(1−λk)]−1/2nk/2 exp(−nS/2σ2),
fi=f(ui), i=0,1,…,k,k+1,
f0=fk+1=0, λ0=0, λk+1=1.
λi+λk−i+1=1,
ui+uk−i+1=0, i=1,2,…,k,
f(−u)=f(u), f′(−u)=−f′(u).
18.
A sequence of independent random variables {Zn:n≥ 1} with unknown probability distributions is considered and the problem of estimating their expectations {Mn+1: n≥ 1} is examined. The estimation of Mn+1 is based on a finite set {zk:1≤k≤n}, each zk being an observed value of Zk, 1 ≤k≤n, and also based on the assumption that {Mn:n≥ 1} follows an unknown trend of a specified form. 相似文献
19.
20.
One of the basic parameters in survival analysis is the mean residual life M
0. For right censored observation, the usual empirical likelihood based log-likelihood ratio leads to a scaled c12{\chi_1^2} limit distribution and estimating the scaled parameter leads to lower coverage of the corresponding confidence interval.
To solve the problem, we present a log-likelihood ratio l(M
0) by methods of Murphy and van der Vaart (Ann Stat 1471–1509, 1997). The limit distribution of l(M
0) is the standard c12{\chi_1^2} distribution. Based on the limit distribution of l(M
0), the corresponding confidence interval of M
0 is constructed. Since the proof of the limit distribution does not offer a computational method for the maximization of the
log-likelihood ratio, an EM algorithm is proposed. Simulation studies support the theoretical result. 相似文献