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1.
We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data. 相似文献
2.
On Conditional Density Estimation 总被引:1,自引:0,他引:1
With the aim of mitigating the possible problem of negativity in the estimation of the conditional density function, we introduce a so-called re-weighted Nadaraya-Watson (RNW) estimator. The proposed RNW estimator is constructed by a slight modification of the well-known Nadaraya-Watson smoother. With a detailed asymptotic analysis, we demonstrate that the RNW smoother preserves the superior large-sample bias property of the local linear smoother of the conditional density recently proposed in the literature. As a matter of independent statistical interest, the limit distribution of the RNW estimator is also derived. 相似文献
3.
A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations
AXB=C, A∈ℝm×n, B∈ℝp×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case.
An adjusted least squares estimator is constructed, which converges to the true value X, as m →∞, q →∞. A small sample modification of the estimator is presented,
which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical
results are confirmed by a simulation study.
Acknowledgements. We thank two anonymous reviewers for their suggestions and corrections.? A. Kukush is supported by a postdoctoral research
fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration
with Central and Eastern Europe.? S. Van Huffel is a full professor with the Katholieke Universiteit Leuven.? I. Markovsky
is a research assistant with the Katholieke Universiteit Leuven.? This paper presents research results of the Belgian Programme
on Interuniversity Poles of Attraction (IUAP V-22), initiated by the Belgian State, Prime Minister's Office – Federal Office
for Scientific, Technical and Cultural Affairs of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666
(Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) “Predictive
computer models for medical classification problems using patient data and expert knowledge”, of the FWO projects G.0078.01,
G.0200.00, and G0.0270.02.? The scientific responsibility is assumed by its authors. 相似文献
4.
The underidentification of linear models with measurement error does not necessarily extend to panel data models, as has been shown by GAiliches and Hausman (1986). We discuss and extend some of their results for a simple case and address particular issues concerning identification and asymptotic variances. 相似文献
5.
Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and, in a sequel to this paper, prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound. 相似文献
6.
H. P. Lopuhaä 《Statistica Neerlandica》1997,51(2):220-237
By means of a straightforward application of empirical process theory, we show that S-estimators of multivariate location and covariance are asymptotically equivalent to a sum of independent vector and matrix valued random elements respectively. This provides an alternative proof of asymptotic normality of S-estimators and clearly explains the limiting covariance structure. It also leads to a relatively simple proof of asymptotic normality of the length of the shortest α-fraction. 相似文献
7.
In this paper we construct all possible orthogonal arrays OA(18,q, 3,2) with 18 runs and 3 ≤ q ≤ 7 columns and present those that are nonisomorphic. A discussion on the novelty and the superiority of many of the designs
found in terms of isomorphism and generalized minimum aberration has been made.
相似文献
8.
把我国现有知识产权制度与环境保护现状有机地结合起来,针对性地研究了两者的相关性,系统、全面地分析了我国现有知识产权制度对环境保护的影响,指出了现有知识产权制度与环境保护实施不协调的若干具体问题,并就此提出了建设性意见及对策. 相似文献
9.
The Hannah-Kay [1977] generalized concentration index contains the well-known Herfindahl [1950]-Hirschman [1945] and the entropy indices as particular cases. In this papaer we show that the Hannah-Kay class can be regarded as a particular member of a generalized family of indices, which we refer to as self-weighted quasilinear means. We then show that among all self-weighted quasilinear means the Hannah-Kay family is the only class of concentration indices which satisfies the replication principle, a requirement which states that an m-fold replication of the industry, firm by firm, will multiply the concentration index by the factor 1/m.The refereeing process of this paper was handled through N.R. Adam.We are grateful to two anonymous referees for their suggestions. 相似文献
10.
For a balanced two-way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non-negativity requirements of the variance components by L ee and K apadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non-negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense. 相似文献