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1.
The L1 and L2-errors of the histogram estimate of a density f from a sample X1,X2,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938). 相似文献
2.
Chong Gu 《Revue canadienne de statistique》2004,32(4):347-358
The author proposes some simple diagnostics for assessing the necessity of selected terms in smoothing spline ANOVA models. The elimination of practically insignificant terms generally enhances the interpretability of the estimates and sometimes may also have inferential implications. The diagnostics are derived from Kullback‐Leibler geometry and are illustrated in the settings of regression, probability density estimation, and hazard rate estimation. 相似文献
3.
It is often of interest to find the maximum or near maxima among a set of vector‐valued parameters in a statistical model; in the case of disease mapping, for example, these correspond to relative‐risk “hotspots” where public‐health intervention may be needed. The general problem is one of estimating nonlinear functions of the ensemble of relative risks, but biased estimates result if posterior means are simply substituted into these nonlinear functions. The authors obtain better estimates of extrema from a new, weighted ranks squared error loss function. The derivation of these Bayes estimators assumes a hidden‐Markov random‐field model for relative risks, and their behaviour is illustrated with real and simulated data. 相似文献
4.
上海第四制药厂在抗生素生产过程系统节能技术研究中对该厂的热能供应系统提出了3个改造方案.本文以该热力系统为例,通过对各方案的技术经济分析比较,以揭示热力系统经济评估的内在含义,并提出了用参数“净年收益”作为评估依据之一的建议. 相似文献
5.
LetX1,X2, ..., be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being either pairwise positively quadrant dependent or pairwise negatively quadrant dependent. LetF^ be the marginal distribution function of theXips, which is estimated by the empirical distribution functionFn and also by a smooth kernel-type estimateFn, by means of the segmentX1, ...,Xn. These estimates are compared on the basis of their mean squared errors (MSE). The main results of this paper are the following. Under certain regularity conditions, the optimal bandwidth (in the MSE sense) is determined, and is found to be the same as that in the independent identically distributed case. It is also shown thatn MSE(Fn(t)) andnMSE (F^n(t)) tend to the same constant, asn→∞ so that one can not discriminate be tween the two estimates on the basis of the MSE. Next, ifi(n) = min {k∈{1, 2, ...}; MSE (Fk(t)) ≤ MSE (Fn(t))}, then it is proved thati(n)/n tends to 1, asn→∞. Thus, once again, one can not choose one estimate over the other in terms of their asymptotic relative efficiency. If, however, the squared bias ofF^n(t) tends to 0 sufficiently fast, or equivalently, the bandwidthhn satisfies the requirement thatnh3n→ 0, asn→∞, it is shown that, for a suitable choice of the kernel, (i(n) ?n)/(nhn) tends to a positive number, asn→∞ It follows that the deficiency ofFn(t) with respect toF^n(t),i(n) ?n, is substantial, and, actually, tends to ∞, asn→∞. In terms of deficiency, the smooth estimateF^n(t) is preferable to the empirical distribution functionFn(t) 相似文献
6.
7.
A multivariate modified histogram density estimate depending on a reference density g and a partition P has been proved to have good consistency properties according to several information theoretic criteria. Given an i.i.d. sample, we show how to select automatically both g and P so that the expected L 1 error of the corresponding selected estimate is within a given constant multiple of the best possible error plus an additive term which tends to zero under mild assumptions. Our method is inspired by the combinatorial tools developed by Devroye and Lugosi [Devroye, L. and Lugosi, G., 2001, Combinatorial Methods in Density Estimation (New York, NY: Springer–Verlag)] and it includes a wide range of reference density and partition models. Results of simulations are also presented. 相似文献
8.
Mohammad Jafari Jozani 《Statistics》2013,47(3):552-557
In this note, we consider the problem of estimating an unknown parameter θ in the sense of the Pitman's measure of closeness (PMC) using the balanced loss function (BLF). We show that the PMC comparison of estimators under the BLF can be reduced to the PMC comparison under the usual absolute error loss. The Pitman-closest estimators of the location and scale parameters under BLF are also characterized. Illustrative examples are given to show the broad range applications of the obtained results. 相似文献
9.
Md. Ershadul Islam Ulrike Grote 《Journal of Statistical Computation and Simulation》2013,83(6):1179-1187
The geographical location and the monsoon climate render Bangladesh highly vulnerable to natural hazards, deteriorating the country's socio-economic stability. This study is based on 500 randomly chosen rural households from the Household Income and Expenditure Survey [Bangladesh Bureau of Statistics, Planning Division, Ministry of Planning, Government of the People's Republic of Bangladesh, Dhaka, 2006]. The objectives are to estimate the income vulnerability of rural households and to check whether the Bayesian approaches (natural conjugate prior and non-informative prior estimates) have any superiority over the classical (feasible generalized least square (FGLS)) method. The poverty level, measured from the data, is 24%; whereas the vulnerability estimates, using FGLS, natural conjugate prior and non-informative prior are 31%, 69% and 82%, respectively. Vulnerability estimates by the Bayesian natural conjugate prior approach is found to have greater efficiency compared with FGLS and non-informative prior approaches. 相似文献
10.
Two types of estimates of process level, namely repeated median estimates (Siegel, 1982) and full online estimates (Gather et al., 2006) based on repeated median filters, are used to develop control charts. The distributional properties of the estimates are studied using simulation and these are found to closely follow normal distribution. The repeated median being robust against outliers with asymptotically 50% breakdown value and having small standard deviation is found to be useful as a basis for monitoring process averages. The control charts using repeated median estimates have been recommended for general use. 相似文献