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Lesław Gajek 《Probability Theory and Related Fields》1989,80(4):601-617
Summary This paper deals with minimum distance (MD) estimators and minimum penalized distance (MPD) estimators which are based on the L
p
distance. Rates of strong consistency of MPD density estimators are established within the family of density functions which have a bounded m-th derivative. For the case p=2, it is also proved that the MPD density estimator achieves the optimum rate of decrease of the mean integrated square error and the L
1 error. Estimation of derivatives of the density is considered as well.In a class parametrized by entire functions, it is proved that the rate of convergence of the MD density estimator (and its derivatives) to the unknown density (its derivatives) is of order
in expected L
1 and L
2 distances. In the same class of distributions, MD estimators of unknown density and its derivatives are proved to achieve an extraordinary rate (log log n/n)1/2 of strong consistency. 相似文献
3.
Pao-sheng Shen 《Computational Statistics》2014,29(3-4):641-659
We consider estimating the bivariate survival function when both components are subject to random left truncation and right censoring. Using the idea of Sankran and Antony (Sankhyã 69:425–447, 2007) in the competing risks set up, we propose two types of estimators as generalizations of the Dabrowska (Ann Stat 18:1475–1489, 1988) and Campbell and Földes (Nonparametric statistical inference, North-Holland, Amsterdam 1982) estimators. The proposed estimators are easy to implement and do not require iteration. The consistency of the proposed estimators is established. Simulation results indicate that the proposed estimators can outperform the estimators of Shen and Yan (J Stat Plan Inference 138:4041–4054, 2008), which require complex iteration. 相似文献
4.
Vyacheslav A. Vasiliev 《Annals of the Institute of Statistical Mathematics》2014,66(1):141-163
This paper presents a truncated estimation method of ratio type functionals by dependent sample of finite size. This method makes it possible to obtain estimators with guaranteed accuracy in the sense of the $L_m$ -norm, $m\ge 2$ . As an illustration, the parametric and non-parametric estimation problems on a time interval of a fixed length are considered. In particular, parameters of linear (autoregressive) and non-linear discrete-time processes are estimated. Moreover, the parameter estimation problem of non-Gaussian Ornstein-Uhlenbeck process by discrete-time observations and the estimation problem of a multivariate logarithmic derivative of a noise density of an autoregressive process with guaranteed accuracy are solved. In addition to non-asymptotic properties, the limit behavior of presented estimators is investigated. It is shown that all the truncated estimators have asymptotic properties of basic estimators. In particular, the asymptotic efficiency in the mean square sense of the truncated estimator of the dynamic parameter of a stable autoregressive process is established. 相似文献
5.
M. C. Fu 《Journal of Optimization Theory and Applications》1990,65(1):149-160
Discrete-event systems to which the technique of infinitesimal perturbation analysis (IPA) is applicable are natural candidates for optimization via a Robbins-Monro type stochastic approximation algorithm. We establish a simple framework for single-run optimization of systems with regenerative structure. The main idea is to convert the original problem into one in which unbiased estimators can be derived from strongly consistent IPA gradient estimators. Standard stochastic approximation results can then be applied. In particular, we consider the GI/G/1 queue, for which IPA gives strongly consistent estimators for the derivative of the mean system time. Convergence (w.p.1) proofs for the problem of minimizing the mean system time with respect to a scalar service time parameter are presented. 相似文献
6.
Modeling the mean and covariance simultaneously is a common strategy to efciently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data.In this article,using generalized estimation equation techniques,we propose a new kind of regression models for parameterizing covariance structures.Using a novel Cholesky factor,the entries in this decomposition have moving average and log innovation interpretation and are modeled as linear functions of covariates.The resulting estimators for the regression coefcients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed.Simulation studies and a real data analysis show that the proposed approach yields highly efcient estimators for the parameters in the mean,and provides parsimonious estimation for the covariance structure. 相似文献
7.
Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only \(n^{1/2}\)-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. 相似文献
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9.
We study the frequency polygon investigated by Scott (J Am Stat Assoc 80: 348–354, 1985) as a nonparametric density estimate for a continuous and stationary real random field \({\left( X_{\mathbf{t}},\mathbf{t}\in\mathbb{R}^{N}\right)}\). We establish the asymptotic expressions for the integrated pointwise squared bias and the integrated pointwise squared variance of the estimate when the field is observed over a rectangular domain of \({\mathbb{R}^{N}}\). Under mild mixing conditions, we show that the estimate achieves the same rate of convergence to zero of the integrated mean squared error as kernel estimators and it can also attain the optimal uniform strong rate of convergence \({\left(\widehat{\mathbf{T}}^{-1} \log \widehat{\mathbf{T}}\right)^{1/3}}\) for appropriate choices of the bin widths. 相似文献
10.
Srivastava and Jhajj (1981) proposed a class of estimators for population mean of a character using auxiliary information and optimum values involving unknown parameters. From the practical point of view, their results have very little utility. In view of practical utility, we propose a class of estimators with estimated optimum values. Further, it is shown that the proposed class with estimated optimum values attains the same minimum mean square error of the class of estimators based on optimum values. 相似文献
11.
We present two families of polygonal estimators of the distribution function: the first family is based on the knowledge of the support while the second addresses the case of an unknown support. Polygonal smoothing is a simple and natural method for regularizing the empirical distribution function \(F_n\) but its properties have not been studied deeply. First, consistency and exponential type inequalities are derived from well-known convergence properties of \(F_n\). Then, we study their mean integrated squared error (MISE) and we establish that polygonal estimators may improve the MISE of \(F_n\). We conclude by some numerical results to compare these estimators globally, and also together with the integrated kernel distribution estimator. 相似文献
12.
Satoshi Kuriki 《Annals of the Institute of Statistical Mathematics》1993,45(4):731-739
The unbiased estimator of risk of the orthogonally invariant estimator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given. 相似文献
13.
Considering absolute log returns as a proxy for stochastic volatility, the influence of explanatory variables on absolute log returns of ultra high frequency data is analysed. The irregular time structure and time dependency of the data is captured by utilizing a continuous time ARMA(p,q) process. In particular, we propose a mixed effect model class for the absolute log returns. Explanatory variable information is used to model the fixed effects, whereas the error is decomposed in a non‐negative Lévy driven continuous time ARMA(p,q) process and a market microstructure noise component. The parameters are estimated in a state space approach. In a small simulation study the performance of the estimators is investigated. We apply our model to IBM trade data and quantify the influence of bid‐ask spread and duration on a daily basis. To verify the correlation in irregularly spaced data we use the variogram, known from spatial statistics. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
M. Ya. Penskaya 《Journal of Mathematical Sciences》1995,75(2):1524-1535
The usual empirical Bayes setting is considered with θ being a shift or a scale parameter. A class of empirical Bayes estimators
of a function b(θ) is proposed. The properties of the estimates are studied and mean square errors are calculated. The lower
bounds are constructed for mean square errors of the empirical Bayes estimators over the class of all empirical Bayes estimators
of b(θ). The results are applied to the case b(θ)=θ. The examples of the upper and lower bounds for mean square error are
presented for the most popular families of conditional distributions.
Added to the English translaion. 相似文献
15.
Didier Chauveau Pierre Vandekerkhove 《Methodology and Computing in Applied Probability》2007,9(1):133-149
We introduce an estimate of the entropy of the marginal density p
t
of a (eventually inhomogeneous) Markov chain at time t≥1. This estimate is based on a double Monte Carlo integration over simulated i.i.d. copies of the Markov chain, whose transition
density kernel is supposed to be known. The technique is extended to compute the external entropy , where the p
1
t
s are the successive marginal densities of another Markov process at time t. We prove, under mild conditions, weak consistency and asymptotic normality of both estimators. The strong consistency is
also obtained under stronger assumptions. These estimators can be used to study by simulation the convergence of p
t
to its stationary distribution. Potential applications for this work are presented: (1) a diagnostic by simulation of the
stability property of a Markovian dynamical system with respect to various initial conditions; (2) a study of the rate in
the Central Limit Theorem for i.i.d. random variables. Simulated examples are provided as illustration.
相似文献
16.
We present a new algorithm for computing motorcycle graphs that runs in \(O(n^{4/3+\varepsilon })\) time for any \(\varepsilon >0\) , improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with \(h\) holes in \(O(n \sqrt{h+1} \log ^2 n+n^{4/3+\varepsilon })\) expected time. If all input coordinates are \(O(\log n)\) -bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with \(h\) holes in \(O(n \sqrt{h+1}\log ^3 n)\) expected time. In particular, it means that we can compute the straight skeleton of a simple polygon in \(O(n\log ^3n)\) expected time if all input coordinates are \(O(\log n)\) -bit rationals, while all previously known algorithms have worst-case running time \(\omega (n^{3/2})\) . 相似文献
17.
In this paper, we consider the problem of making inferences on the common mean of several normal populations when sample sizes and population variances are possibly unequal. We are mainly concerned with testing hypothesis and constructing confidence interval for the common normal mean. Several researchers have considered this problem and many methods have been proposed based on the asymptotic or approximation results, generalized inferences, and exact pivotal methods. In addition, Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) proposed a parametric bootstrap (PB) approach for this problem based on the maximum likelihood estimators. We also propose a PB approach for making inferences on the common normal mean under heteroscedasticity. The advantages of our method are: (i) it is much simpler than the PB test proposed by Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) since our test statistic is not based on the maximum likelihood estimators which do not have explicit forms, (ii) inverting the acceptance region of test yields a genuine confidence interval in contrast to some exact methods such as the Fisher’s method, (iii) it works well in terms of controlling the Type I error rate for small sample sizes and the large number of populations in contrast to Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) method, (iv) finally, it has higher power than recommended methods such as the Fisher’s exact method. 相似文献
18.
In this article, we consider a class of kernel quantile estimators which is the linear combi- nation of order statistics. This class of kernel quantile estimators can be regarded as an extension of some existing estimators. The exact mean square error expression for this class of estimators will be provided when data are uniformly distributed. The implementation of these estimators depends mostly on the bandwidth selection. We then develop an adaptive method for bandwidth selection based on the intersection confidence intervals (ICI) principle. Monte Carlo studies demonstrate that our proposed approach is comparatively remarkable. We illustrate our method with a real data set. 相似文献
19.
Eiichi Isogai 《Annals of the Institute of Statistical Mathematics》1990,42(4):699-708
A somewhat more general class of nonparametric estimators for estimating an unknown regression functiong from noisy data is proposed. The regressor is assumed to be defined on the closed interval [0, 1]. This class of estimators
is shown to be pointwisely consistent in the mean square sense and with probability one. Further, it turns out that these
estimators can be applied to a wide class of noises. 相似文献
20.
Motivated by the problem of labeling maps, we investigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n) time, we can find an O(log n)-factor approximation of the maximum subset in a set of n arbitrary axis-parallel rectangles in the plane. If all rectangles have unit height, we can find a 2-approximation in O(n log n) time. Extending this result, we obtain a (1 + 1/k)-approximation in time O(n log n + n2k−1) time, for any integer k ≥ 1. 相似文献