共查询到20条相似文献,搜索用时 62 毫秒
1.
MERVYN J. SILVAPULLE 《Australian & New Zealand Journal of Statistics》1991,33(3):319-333
Consider the linear regression model y =β01 +Xβ+ in the usual notation. It is argued that the class of ordinary ridge estimators obtained by shrinking the least squares estimator by the matrix (X1X + kI)-1X'X is sensitive to outliers in the ^variable. To overcome this problem, we propose a new class of ridge-type M-estimators, obtained by shrinking an M-estimator (instead of the least squares estimator) by the same matrix. Since the optimal value of the ridge parameter k is unknown, we suggest a procedure for choosing it adaptively. In a reasonably large scale simulation study with a particular M-estimator, we found that if the conditions are such that the M-estimator is more efficient than the least squares estimator then the corresponding ridge-type M-estimator proposed here is better, in terms of a Mean Squared Error criteria, than the ordinary ridge estimator with k chosen suitably. An example illustrates that the estimators proposed here are less sensitive to outliers in the y-variable than ordinary ridge estimators. 相似文献
2.
3.
X1, X2, …, Xk are k(k ? 2) uniform populations which each Xi follows U(0, θi). This note shows the test statistic for the null hypothesis H0: θ1 = θ2 = ??? = θk by using the order statistics. 相似文献
4.
Saul Blumenthal 《统计学通讯:理论与方法》2013,42(4):297-308
Let X1, X2,…,Xn be independent, indentically distributed random variables with density f(x,θ) with respect to a σ-finite measure μ. Let R be a measurable set in the sample space X. The value of X is observable if X ? (X?R) and not otherwise. The number J of observable X’s is binomial, N, Q, Q = 1?P(X ? R). On the basis of J observations, it is desired to estimate N and θ. Estimators considered are conditional and unconditional maximum likelihood and modified maximum likelihood using a prior weight function to modify the likelihood before maximizing. Asymptotic expansions are developed for the [Ncirc]’s of the form [Ncirc] = N + α√N + β + op(1), where α and β are random variables. All estimators have the same α, which has mean 0, variance σ2 (a function of θ) and is asymptotically normal. Hence all are asymptotically equivalent by the usual limit distributional theory. The β’s differ and Eβ can be considered an “asymptotic bias”. Formulas are developed to compare the asymptotic biases of the various estimators. For a scale parameter family of absolutely continuous distributions with X = (0,∞) and R = (T,∞), special formuli are developed and a best estimator is found. 相似文献
5.
Let X1X2,.be i.i.d. random variables and let Un= (n r)-1S?(n,r) h (Xi1,., Xir,) be a U-statistic with EUn= v, v unknown. Assume that g(X1) =E[h(X1,.,Xr) - v |X1]has a strictly positive variance s?2. Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S2n be the Jackknife estimator of n Var Un. Consider the stopping times N(d)= min {n: S2n: + n-1≤2a-2},d > 0, and a confidence interval for v of length 2d,of the form In,d= [Un,-d, Un + d]. We assume that Var Un is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let IN(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. limd → 0P(v ∈ IN(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ IN(d),d) converges to α is investigated. We obtain that |P(v ∈ IN(d),d) - α| = 0 (d1/2-(1+k)/2(1+m)), d → 0, where K = max {0,4 - m}, under the condition that E|h(X1, Xr)|m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981). 相似文献
6.
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
7.
AbstractWe introduce here the truncated version of the unified skew-normal (SUN) distributions. By considering a special truncations for both univariate and multivariate cases, we derive the joint distribution of consecutive order statistics X(r, ..., r + k) = (X(r), ..., X(r + K))T from an exchangeable n-dimensional normal random vector X. Further we show that the conditional distributions of X(r + j, ..., r + k) given X(r, ..., r + j ? 1), X(r, ..., r + k) given (X(r) > t)?and X(r, ..., r + k) given (X(r + k) < t) are special types of singular SUN distributions. We use these results to determine some measures in the reliability theory such as the mean past life (MPL) function and mean residual life (MRL) function. 相似文献
8.
David D. Hanagal 《Statistical Papers》1999,40(1):99-106
In this paper, we estimate the reliability of a system with k components. The system functions when at least s (1≤s≤k) components survive a common random stress. We assume that the strengths of these k components are subjected to a common
stress which is independent of the strengths of these k components. If (X
1,X
2,…,X
k
) are strengths of k components subjected to a common stress (Y), then the reliability of the system or system reliability
is given byR=P[Y<X
(k−s+1)] whereX
(k−s+1) is (k−s+1)-th order statistic of (X
1,…,X
k
). We estimate R when (X
1,…,X
k
) follow an absolutely continuous multivariate exponential (ACMVE) distribution of Hanagal (1993) which is the submodel of
Block (1975) and Y follows an independent exponential distribution. We also obtain the asymptotic normal (AN) distribution
of the proposed estimator. 相似文献
9.
Ghobad Barmalzan Amir T. Payandeh Najafabadi Narayanaswamy Balakrishnan 《统计学通讯:理论与方法》2017,46(20):9869-9880
Let X1, …, Xn be independent random variables with Xi ~ EWG(α, β, λi, pi), i = 1, …, n, and Y1, …, Yn be another set of independent random variables with Yi ~ EWG(α, β, γi, qi), i = 1, …, n. The results established here are developed in two directions. First, under conditions p1 = ??? = pn = q1 = ??? = qn = p, and based on the majorization and p-larger orders between the vectors of scale parameters, we establish the usual stochastic and reversed hazard rate orders between the series and parallel systems. Next, for the case λ1 = ??? = λn = γ1 = ??? = γn = λ, we obtain some results concerning the reversed hazard rate and hazard rate orders between series and parallel systems based on the weak submajorization between the vectors of (p1, …, pn) and (q1, …, qn). The results established here can be used to find various bounds for some important aging characteristics of these systems, and moreover extend some well-known results in the literature. 相似文献
10.
Let X 1, X 2,…, X k be k (≥2) independent random variables from gamma populations Π1, Π2,…, Π k with common known shape parameter α and unknown scale parameter θ i , i = 1,2,…,k, respectively. Let X (i) denotes the ith order statistics of X 1,X 2,…,X k . Suppose the population corresponding to largest X (k) (or the smallest X (1)) observation is selected. We consider the problem of estimating the scale parameter θ M (or θ J ) of the selected population under the entropy loss function. For k ≥ 2, we obtain the Unique Minimum Risk Unbiased (UMRU) estimator of θ M (and θ J ). For k = 2, we derive the class of all linear admissible estimators of the form cX (2) (and cX (1)) and show that the UMRU estimator of θ M is inadmissible. The results are extended to some subclass of exponential family. 相似文献
11.
Rasool Roozegar 《统计学通讯:理论与方法》2017,46(9):4539-4544
In this paper we consider a sequence of independent continuous symmetric random variables X1, X2, …, with heavy-tailed distributions. Then we focus on limiting behavior of randomly weighted averages Sn = R(n)1X1 + ??? + R(n)nXn, where the random weights R(n)1, …, Rn(n) which are independent of X1, X2, …, Xn, are the cuts of (0, 1) by the n ? 1 order statistics from a uniform distribution. Indeed we prove that cnSn converges in distribution to a symmetric α-stable random variable with cn = n1 ? 1/α/Γ1/α(α + 1). 相似文献
12.
《统计学通讯:理论与方法》2012,41(13-14):2405-2418
In this article, we consider two linear models, ?1 = {y, X β, V 1} and ?2 = {y, X β, V 2}, which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of X β under these models. The corresponding problems between the models {y, X β, I n } and {y, X β, V}, i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of X β under ?1 and ?2. This article is an expository one presenting also new results. 相似文献
13.
ABSTRACTIn this article, we consider a (k + 1)n-dimensional elliptically contoured random vector (XT1, X2T, …, XTk, ZT)T = (X11, …, X1n, …, Xk1, …, Xkn, Z1, …, Zn)T and derive the distribution of concomitant of multivariate order statistics arising from X1, X2, …, Xk. Specially, we derive a mixture representation for concomitant of bivariate order statistics. The joint distribution of the concomitant of bivariate order statistics is also obtained. Finally, the usefulness of our result is illustrated by a real-life data. 相似文献
14.
Alain Boulanger 《Revue canadienne de statistique》1983,11(4):265-269
For X1, …, XN a random sample from a distribution F, let the process SδN(t) be defined as where K2N = σNi=1(ci ? c?)2 and R xi, + Δd, is the rank of Xi + Δdi, among X1 + Δd1, …, XN + ΔdN. The purpose of this note is to prove that, under certain regularity conditions on F and on the constants ci and di, SΔN (t) is asymptotically approximately a linear function of Δ, uniformly in t and in Δ, |Δ| ≤ C. The special case of two samples is considered. 相似文献
15.
Suppose a subset of populations is selected from k exponential populations with unknown location parameters θ1, θ2, …, θk and common known scale parameter σ. We consider the estimation of the location parameter of the selected population and the average worth of the selected subset under an asymmetric LINEX loss function. We show that the natural estimator of these parameters is biased and find the uniformly minimum risk-unbiased (UMRU) estimator of these parameters. In the case of k = 2, we find the minimax estimator of the location parameter of the smallest selected population. Furthermore, we compare numerically the risk of UMRU, minimax, and the natural estimators. 相似文献
16.
Andrzej Kozek 《Revue canadienne de statistique》1987,15(1):77-85
Let Xi, 1 ≤ i ≤ n, be independent identically distributed random variables with a common distribution function F, and let G be a smooth distribution function. We derive the limit distribution of □{ρα(Fn, G) - α(F, G)}, where Fn is the empirical distribution function based on X1,…,Xn and α is a Kolmogorov-Lévy-type metric between distribution functions. For α ≤ 0 and two distribution functions F and G the metric pα is given by pα(F, G) = inf {? ≤ 0: G(x - α?) - ? F(x) ≤ G(x + α?) + ? for all x ?}. 相似文献
17.
In this note, we derive the exact distribution of S by using the method of generating function and BELL polynomials, where S = X1 + X2 + ??? + Xn, and each Xi follows the negative binomial distribution with arbitrary parameters. As a particular case, we also obtain the exact distribution of the convolution of geometric random variables. 相似文献
18.
Rp
of a linear regression model of the type Y = Xθ + ɛ, where X is the design matrix, Y the vector of the response variable and ɛ the random error vector that follows an AR(1) correlation structure. These estimators
are asymptotically analyzed, by proving their strong consistency, asymptotic normality and asymptotic efficiency. In a simulation
study, a better behaviour of the Mean Squared Error of the proposed estimator with respect to that of the generalized least
squares estimators is observed.
Received: November 16, 1998; revised version: May 10, 2000 相似文献
19.
N. Giri 《Revue canadienne de statistique》1979,7(1):53-60
Let X be a normally distributed p-dimensional column vector with mean μ and positive definite covariance matrix σ. and let X α, α = 1,…, N, be a random sample of size N from this distribution. Partition X as ( X 1, X (2)', X '(3))', where X1 is one-dimension, X(2) is p2- dimensional, and so 1 + p1 + p2 = p. Let ρ1 and ρ be the multiple correlation coefficients of X1 with X(2) and with ( X '(2), X '(3))', respectively. Write ρ2/2 = ρ2 - ρ2/1. We shall cosider the following two problems 相似文献
20.
Changjun Yu 《统计学通讯:理论与方法》2017,46(2):591-601
This paper investigates tail behavior of the randomly weighted sum ∑nk = 1θkXk and reaches an asymptotic formula, where Xk, 1 ? k ? n, are real-valued linearly wide quadrant-dependent (LWQD) random variables with a common heavy-tailed distribution, and θk, 1 ? k ? n, independent of Xk, 1 ? k ? n, are n non-negative random variables without any dependence assumptions. The LWQD structure includes the linearly negative quadrant-dependent structure, the negatively associated structure, and hence the independence structure. On the other hand, it also includes some positively dependent random variables and some other random variables. The obtained result coincides with the existing ones. 相似文献