共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider a nonparametric regression model where m noise-perturbed functions f
1,…,f
m
are randomly observed. For a fixed ν∈{1,…,m}, we want to estimate f
ν from the observations. To reach this goal, we develop an adaptive wavelet estimator based on a hard thresholding rule. Adopting
the mean integrated squared error over Besov balls, we prove that it attains a sharp rate of convergence. Simulation results
are reported to support our theoretical findings. 相似文献
2.
For estimating an unknown parameter θ, we introduce and motivate the use of balanced loss functions of the form Lr, w, d0(q, d)=wr(d0, d)+ (1-w) r(q, d){L_{\rho, \omega, \delta_0}(\theta, \delta)=\omega \rho(\delta_0, \delta)+ (1-\omega) \rho(\theta, \delta)}, as well as the weighted version q(q) Lr, w, d0(q, d){q(\theta) L_{\rho, \omega, \delta_0}(\theta, \delta)}, where ρ(θ, δ) is an arbitrary loss function, δ
0 is a chosen a priori “target” estimator of q, w ? [0,1){\theta, \omega \in[0,1)}, and q(·) is a positive weight function. we develop Bayesian estimators under Lr, w, d0{L_{\rho, \omega, \delta_0}} with ω > 0 by relating such estimators to Bayesian solutions under Lr, w, d0{L_{\rho, \omega, \delta_0}} with ω = 0. Illustrations are given for various choices of ρ, such as absolute value, entropy, linex, and squared error type losses. Finally, under various robust Bayesian analysis criteria
including posterior regret gamma-minimaxity, conditional gamma-minimaxity, and most stable, we establish explicit connections
between optimal actions derived under balanced and unbalanced losses. 相似文献
3.
《统计学通讯:理论与方法》2013,42(11):2105-2113
ABSTRACT The study of r-out-of-n systems is of utmost importance in reliability theory. In this note, we study closure of different partial orders under the formation of r-out-of-N and (N ? s)-out-of-N systems when the number of components N, forming the system, is a random variable having support {k, k + 1,…}, where k is a fixed positive integer, r ∈ {1,…, k} and s ∈ {0, 1,…, k ? 1}. This generalizes quite a few results already known in the literature. We also study the closure of different partial orders when two systems are formed out of different random number of components. 相似文献
4.
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
5.
Mariusz Bieniek 《统计学通讯:理论与方法》2013,42(1):59-72
Let X ? (r), r ≥ 1, denote generalized order statistics based on an arbitrary distribution function F with finite pth absolute moment for some 1 ≤ p ≤ ∞. We present sharp upper bounds on E(X ? (s) ? X ? (r)), 1 ≤ r < s, for F being either general or life distribution. The bounds are expressed in various scale units generated by pth central absolute or raw moments of F, respectively. The distributions achieving the bounds are specified. 相似文献
6.
Let Z
1, Z
2, . . . be a sequence of independent Bernoulli trials with constant success and failure probabilities p = Pr(Z
t
= 1) and q = Pr(Z
t
= 0) = 1 − p, respectively, t = 1, 2, . . . . For any given integer k ≥ 2 we consider the patterns E1{\mathcal{E}_{1}}: two successes are separated by at most k−2 failures, E2{\mathcal{E}_{2}}: two successes are separated by exactly k −2 failures, and E3{\mathcal{E}_{3}} : two successes are separated by at least k − 2 failures. Denote by Nn,k(i){ N_{n,k}^{(i)}} (respectively Mn,k(i){M_{n,k}^{(i)}}) the number of occurrences of the pattern Ei{\mathcal{E}_{i}} , i = 1, 2, 3, in Z
1, Z
2, . . . , Z
n
when the non-overlapping (respectively overlapping) counting scheme for runs and patterns is employed. Also, let Tr,k(i){T_{r,k}^{(i)}} (resp. Wr,k(i)){W_{r,k}^{(i)})} be the waiting time for the r − th occurrence of the pattern Ei{\mathcal{E}_{i}}, i = 1, 2, 3, in Z
1, Z
2, . . . according to the non-overlapping (resp. overlapping) counting scheme. In this article we conduct a systematic study
of Nn,k(i){N_{n,k}^{(i)}}, Mn,k(i){M_{n,k}^{(i)}}, Tr,k(i){T_{r,k}^{(i)}} and Wr,k(i){W_{r,k}^{(i)}} (i = 1, 2, 3) obtaining exact formulae, explicit or recursive, for their probability generating functions, probability mass
functions and moments. An application is given. 相似文献
7.
《Journal of statistical planning and inference》1997,58(2):371-387
In this paper we consider the heteroscedastic regression model defined by the structural relation Y = r(V, β) + s(W)ε, where V is a p-dimensional random vector, W is a q-dimensional random vector, β is an unknown vector in some open subset B of Rm, r is a known function from Rp × B into R, s is an unknown function on Rq, and ε is an unobservable random variable that is independent of the pair (V, W). We construct asymptotically efficient estimates of the regression parameter β under mild assumptions on the functions r and s and on the distributions of ε and (V, W). 相似文献
8.
Summary We consider a lotL formed byN apparently similar unitsW
1,…,W
N, where each of theW
i may come from one of two different populationsP
1 andP
2;T
1,…,T
N denote the corresponding lifetimes. The units fromP
i
undergo a failure of kindi and their survival function isS
i
(t).
We assume that the failure rate function
are known and that the units fromP
1 are ?substandard?: λ
1
(t)≥λ
2
(t), ∀t≥0.
We want to putW
1,…,W
N under a pre-operational test (burn-in test) in order to eliminate at least a great part of the substandard units and we face
the problem of obtaining a rule for stopping the test under the assumption that, with the failure of a unit, it is possible
to recognize the population from which the unit comes.
Such a problem will be formalized as an optimal stopping problem for a suitably defined Markov process. Our study shall evidentiate
some fundamental aspects of the problem and the role of the prior distribution of the (random) numberM
0 of those units inL coming fromP
1 (substandard). The latter distribution has a great influence on the form of the solution.
This research was supported by the C.N.R. Project ?Statistica Bayesiana e Simulazione in Affidalità e Modellistica Biologica?. 相似文献
9.
Summary Let {X
n
} be a sequence of random variables conditionally independent and identically distributed given the random variable Θ. The
aim of this paper is to show that in many interesting situations the conditional distribution of Θ, given (X
1,…,X
n
), can be approximated by means of the bootstrap procedure proposed by Efron and applied to a statisticT
n
(X
1,…,X
n
) sufficient for predictive purposes. It will also be shown that, from the predictive point of view, this is consistent with
the results obtained following a common Bayesian approach. 相似文献
10.
x
1, ..., x
n+r
can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis H
0 that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: ϕ-Divergences. More precisely, if p
a
1 .....,
a
r:
a
r
+1 denotes the transition probability for a r
th
order Markov chain, the hypothesis to be tested is
H
0:p
a
1 .....,
a
r:
a
r
+1 = p
a
2 .....,
a
r:
a
r
+1, a
i
∈{1, ..., s}, i = 1, ..., r + 1
The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based
on the chi-squared statistic.
Received: August 3, 1998; revised version: November 25, 1999 相似文献
11.
12.
Konanur G. Janardan 《Statistical Papers》2005,46(4):587-597
A discrete distribution associated with a pure birth process starting with no individuals, with birth rates λ
n
=λ forn=0, 2, …,m−1 and λ
n
forn≥m is considered in this paper. The probability mass function is expressed in terms of an integral that is very convenient for
computing probabilities, moments, generating functions and others. Using this representation, the mean and the k-th factorial
moments of the distribution are obtained. Some nice characterizations of this distribution are also given. 相似文献
13.
We develop a Bayesian procedure for the homogeneity testing problem of r populations using r × s contingency tables. The posterior probability of the homogeneity null hypothesis is calculated using a mixed prior distribution. The methodology consists of choosing an appropriate value of π0 for the mass assigned to the null and spreading the remainder, 1 ? π0, over the alternative according to a density function. With this method, a theorem which shows when the same conclusion is reached from both frequentist and Bayesian points of view is obtained. A sufficient condition under which the p-value is less than a value α and the posterior probability is also less than 0.5 is provided. 相似文献
14.
Aylin Alin 《Statistical Papers》2009,50(4):711-720
NIPALS and SIMPLS algorithms are the most commonly used algorithms for partial least squares analysis. When the number of
objects, N, is much larger than the number of explanatory, K, and/or response variables, M, the NIPALS algorithm can be time consuming. Even though the SIMPLS is not as time consuming as the NIPALS and can be preferred
over the NIPALS, there are kernel algorithms developed especially for the cases where N is much larger than number of variables. In this study, the NIPALS, SIMPLS and some kernel algorithms have been used to built
partial least squares regression model. Their performances have been compared in terms of the total CPU time spent for the
calculations of latent variables, leave-one-out cross validation and bootstrap methods. According to the numerical results,
one of the kernel algorithms suggested by Dayal and MacGregor (J Chemom 11:73–85, 1997) is the fastest algorithm. 相似文献
15.
16.
In regression analysis, to overcome the problem of multicollinearity, the r ? k class estimator is proposed as an alternative to the ordinary least squares estimator which is a general estimator including the ordinary ridge regression estimator, the principal components regression estimator and the ordinary least squares estimator. In this article, we derive the necessary and sufficient conditions for the superiority of the r ? k class estimator over each of these estimators under the Mahalanobis loss function by the average loss criterion. Then, we compare these estimators with each other using the same criterion. Also, we suggest to test to verify if these conditions are indeed satisfied. Finally, a numerical example and a Monte Carlo simulation are done to illustrate the theoretical results. 相似文献
17.
The density level sets of the two types of measures under consideration are l 2, p -circles with p = 1 and p = 2, respectively. The intersection-percentage function (ipf) of such a measure reflects the percentages which the level set corresponding to the p-radius r shares for each r > 0 with a set to be measured. The geometric measure representation formulae in Richter (2009) is based upon these ipf's and will be used here for evaluating exact cdf's and pdf's for the linear combination, the product, and the ratio of the components of two-dimensional simplicial or spherically distributed random vectors. 相似文献
18.
A. Stepanov 《Statistical Papers》2007,48(1):63-79
LetX
1,X
2, … be a sequence of i.i.d. random variables with some continuous distribution functionF. LetX(n) be then-th record value associated with this sequence and μ
n
−
, μ
n
+
be the variables that count the number of record values belonging to the random intervals(f−(X(n)), X(n)), (X(n), f+(X(n))), wheref−, f+ are two continuous functions satisfyingf−(x)<x, f+(x)>x. Properties of μ
n
−
, μ
n
+
are studied in the present paper. Some statistical applications connected with these variables are also provided. 相似文献
19.
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
20.
We establish strong consistency of the least squares estimates in multiple regression models discarding the usual assumption of the errors having null mean value. Thus, we required them to be i.i.d. with absolute moment of order r, 0<r<2, and null mean value when r>1. Only moderately restrictive conditions are imposed on the model matrix. In our treatment, we use an extension of the Marcinkiewicz–Zygmund strong law to overcome the errors mean value not being defined. In this way, we get a unified treatment for the case of i.i.d. errors extending the results of some previous papers. 相似文献