共查询到20条相似文献,搜索用时 15 毫秒
1.
The rate of convergence in a sample path sense is given for a strongly consistent, recursive estimator. This estimator is for the unknown average return rate of the risky asset that is a parameter in a bilinear stochastic differential equation for the wealth in a portfolio selection and consumption model.This research was partially supported by NSF Grant No. ECS-84-03286-A01 and by University of Kansas General Research Allocation No. 3806-XO-0038. 相似文献
2.
In the present paper we focus on the problem of the bandwidth choice for the kernel density estimates. The problem of finding
the optimal bandwidth belongs to the crucial problems of the kernel estimates. As a criterion of quality of the estimates
the L
2 type measure is used. A special iterative method based on a relevant estimation of mean integrated square error given in
papers Müller and Wang (Prob Theor Relat Fields 85:523–538, 1990), Jones et al. (Ann Stat 19:1919–1932, 1991) is suggested.
Moreover the idea of maximal smoothing principle (Terrell in J Am Stat Assoc 85:470–477, 1990) is extended to the higher order
kernels. A simulation study brings a comparison of the proposed method and the cross-validation method.
Research supported by the GACR:402/04/1308. 相似文献
3.
Elisa María Molanes-López Ricardo Cao 《Annals of the Institute of Statistical Mathematics》2008,60(2):273-300
This paper is focused on two kernel relative density estimators in a two-sample problem. An asymptotic expression for the
mean integrated squared error of these estimators is found and, based on it, two solve- the-equation plug-in bandwidth selectors
are proposed. In order to examine their practical performance a simulation study and a practical application to a medical
dataset are carried out. 相似文献
4.
Jiří Anděl 《Applications of Mathematics》1998,43(5):389-398
Let e
t=(e
t1,...e
tp) be a p-dimensional nonnegative strict white noise with finite second moments. Let h
ij(x) be nondecreasing functions from [0,) onto [0,) such that h
ij(x) x for i, j = 1,...,p. Let U = (u
ij) be a p×p matrix with nonnegative elements having all its roots inside the unit circle. Define a process X
t=(X
t1,...,X
tp) by for
for j=1,..., p A method for estimating U from a realization X
1,...,X
n is proposed. It is proved that the estimators are strongly consistent. 相似文献
5.
We consider an estimation problem with observations from a Gaussian process. The problem arises from a stochastic process modeling of computer experiments proposed recently by Sacks, Schiller, and Welch. By establishing various representations and approximations to the corresponding log-likelihood function, we show that the maximum likelihood estimator of the identifiable parameter θσ2 is strongly consistent and converges weakly (when normalized by √n) to a normal random variable, whose variance does not depend on the selection of sample points. Some extensions to regression models are also obtained. 相似文献
6.
Ian S. Abramson 《Journal of multivariate analysis》1982,12(4):562-567
Consider estimating a smooth p-variate density f at 0 using the classical kernel estimator fn(0) = n−1 Σibn−pw(bn−1Xi) based on a sample {Xi} from f. Under familiar conditions, assigning bn = bn−1/(4 + p) gives the best MSE decay rate O(n−4/(4 + p), but the optimal b, b* say, depends on f through its second derivatives, raising a feasibility objection to its use. By prescribing a pilot estimate of b* based on the same sample, Woodroofe has shown that there need be asymptotically no loss as against knowing the constant exactly, but his proposal is critically dependent on achieving a certain consistency rate for b*. Admitting a minor change in the risk function, we show by a tightness argument applied to the error process that any consistent estimator of b* may be used to achieve the same performance. 相似文献
7.
Alain Le Breton Dinh Tuan Pham 《Annals of the Institute of Statistical Mathematics》1989,41(3):555-563
The paper provides an exact formula for the bias of the parameter estimator of the first order autoregressive process and derives the asymptotic bias. 相似文献
8.
Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L
p
(Q) distance, where 1 ⩽ p < ∞ and Q is a probability measure on [0,A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.
This work was supported by National Science Foundation of USA (Grant No. DMS-0405855, DMS-0804587) 相似文献
9.
In this paper, we generalize the classical estimator of the reinsurance premium for heavy-tailed loss distributions with a kernel-type estimator. Since this estimator exhibits a bias, we propose its bias-reduced version by using a least-squares method. The asymptotic normality of the proposed estimators is established under suitable assumptions. A small simulation study is carried out to prove the performance of our approach. 相似文献
10.
Let {X(t): t [a, b]} be a Gaussian process with mean μ L2[a, b] and continuous covariance K(s, t). When estimating μ under the loss ∫ab (
(t)−μ(t))2 dt the natural estimator X is admissible if K is unknown. If K is known, X is minimax with risk ∫ab K(t, t) dt and admissible if and only if the three by three matrix whose entries are K(ti, tj) has a determinant which vanishes identically in ti [a, b], i = 1, 2, 3. 相似文献
11.
W. Wefelmeyer 《Annals of the Institute of Statistical Mathematics》1994,46(2):309-315
Consider a stationary first-order autoregressive process, with i.i.d. residuals following an unknown mean zero distribution. The customary estimator for the expectation of a bounded function under the residual distribution is the empirical estimator based on the estimated residuals. We show that this estimator is not efficient, and construct a simple efficient estimator. It is adaptive with respect to the autoregression parameter. 相似文献
12.
13.
考虑半参数回归模型$y_i=x_i\beta+g(t_i)+V_i$ $(1\le i\len)$, 其中$(x_i,t_i)$是已知的设计点, 斜率参数$\beta$是未知的,$g(\cdot)$是未知函数, 误差$V_i=\tsm^\infty_{j=-\infty}c_je_{i-j}$,$\tsm^\infty_{j=-\infty}|c_j|<\infty$并且$e_i$是负相关的随机变量.在适当的条件下, 我们研究了$\beta$与$g(\cdot)$小波估计量的强收敛速度.结果显示$g(\cdot)$的小波估计量达到最优收敛速度. 同时,对$\beta$小波估计量也作了模拟研究. 相似文献
14.
The stationary density of an invertible linear processes can be estimated at the parametric rate by a convolution of residual-based
kernel estimators. We have shown elsewhere that the convergence is uniform and that a functional central limit theorem holds
in the space of continuous functions vanishing at infinity. Here we show that analogous results hold in weighted L
1-spaces. We do not require smoothness of the innovation density.
相似文献
15.
Carla Henriques Paulo Eduardo Oliveira 《Statistical Inference for Stochastic Processes》2008,11(1):77-91
Let X
n
, n ≥ 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X
1,X
k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X
n
, n ≥ 1. Assuming a convenient decrease rate of the covariances Cov(X
1,X
n+1), n ≥ 1, we derive uniform strong convergence rates for these estimators. The condition on the covariance structure of the variables
is satisfied either if Cov(X
1,X
n+1) decreases polynomially or if it decreases geometrically, but as we could expect, under the latter condition we are able
to establish faster convergence rates. For the two-dimensional distribution function the rate of convergence derived under
a geometrical decrease of the covariances is close to the optimal rate for independent samples.
相似文献
16.
Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models 总被引:1,自引:0,他引:1
Quasi-likelihood nonlinear models (QLNM) include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation (MQLE) is obtained in QLNM. In an important case, this rate is O(n-^1/2(loglogn)^1/2), which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore. 相似文献
17.
1.IntroductionTheestimationofpopulationquaillesisofgrestillterestwhenone.isnotpreparedtoassumeaparametricformfortheunderlyingdistribution.Inaddition,quaillesoftenariseasthensturalthingtoestimatewhentheunderlyingdistributionisskewed.LetXIIXZ,')Xubei... 相似文献
18.
《Applied Mathematics Letters》2003,16(3):317-321
The exact expression for the inverse of the correlation matrix for the moving average order one, MA(1) process, is obtained. Its application in the context of longitudinal data analysis is discussed. 相似文献
19.
胡舒合 《中国科学A辑(英文版)》2002,45(2):137-146
We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained. 相似文献
20.
Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval 总被引:3,自引:0,他引:3
Éric Marchand William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2005,57(1):129-143
For location families with densitiesf
0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f
0, ρ), the Bayes estimator δ
U
with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous
dominance results due to Katz and Farrell, we make use of Kubokawa'sIERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and
are characterized in terms of δ
U
. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint
of the form θ∈[a, b].
Research supported by NSERC of Canada. 相似文献