冲激噪声环境中LFM信号的特征参数估计

SαS稳定分布是一类非常重要的非高斯随机分布,具有这类分布的噪声称为冲激噪声。在冲激噪声情况下,α阶以上的矩均不存在,导致基于二阶矩的高斯模型算法性能下降,甚至不能正常工作。该文提出了一种在冲激噪声环境下线性调频信号特征参数估计的算法,通过分析冲激噪声的具体特点,给出了修正的低阶矩模糊函数,并结合Radon变换估计了冲激噪声环境下LFM信号的参数。该算法既可应用于冲激噪声下,又可应用于高斯噪声环境,故具有较好的鲁棒性。最后用计算机仿真验证了该算法的有效性。     

On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models

While much used in practice, latent variable models raise challenging estimation problems due to the intractability of their likelihood. Monte Carlo maximum likelihood (MCML), as proposed by Geyer & Thompson (1992 ), is a simulation-based approach to maximum likelihood approximation applicable to general latent variable models. MCML can be described as an importance sampling method in which the likelihood ratio is approximated by Monte Carlo averages of importance ratios simulated from the complete data model corresponding to an arbitrary value of the unknown parameter. This paper studies the asymptotic (in the number of observations) performance of the MCML method in the case of latent variable models with independent observations. This is in contrast with previous works on the same topic which only considered conditional convergence to the maximum likelihood estimator, for a fixed set of observations. A first important result is that when is fixed, the MCML method can only be consistent if the number of simulations grows exponentially fast with the number of observations. If on the other hand, is obtained from a consistent sequence of estimates of the unknown parameter, then the requirements on the number of simulations are shown to be much weaker.     

Bayesian analysis of mixture modelling using the multivariate t distribution

A finite mixture model using the multivariate t distribution has been shown as a robust extension of normal mixtures. In this paper, we present a Bayesian approach for inference about parameters of t-mixture models. The specifications of prior distributions are weakly informative to avoid causing nonintegrable posterior distributions. We present two efficient EM-type algorithms for computing the joint posterior mode with the observed data and an incomplete future vector as the sample. Markov chain Monte Carlo sampling schemes are also developed to obtain the target posterior distribution of parameters. The advantages of Bayesian approach over the maximum likelihood method are demonstrated via a set of real data.     

Estimation of Hazard, Density and Survivor Functions for Randomly Censored Data

Maximum likelihood estimation and goodness-of-fit techniques are used within a competing risks framework to obtain maximum likelihood estimates of hazard, density, and survivor functions for randomly right-censored variables. Goodness-of- fit techniques are used to fit distributions to the crude lifetimes, which are used to obtain an estimate of the hazard function, which, in turn, is used to construct the survivor and density functions of the net lifetime of the variable of interest. If only one of the crude lifetimes can be adequately characterized by a parametric model, then semi-parametric estimates may be obtained using a maximum likelihood estimate of one crude lifetime and the empirical distribution function of the other. Simulation studies show that the survivor function estimates from crude lifetimes compare favourably with those given by the product-limit estimator when crude lifetimes are chosen correctly. Other advantages are discussed.     

On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

Empirical Non-Parametric Control Charts: Estimation Effects and Corrections

Owing to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and non-normality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a large model is inadequate and nothing remains but to consider non- parametric charts. In principle, these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage that seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyse under what conditions non-parametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes that are markedly less huge (but still larger than the customary range). These corrections serve to control the behaviour during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection will clearly be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.     

A study of simulated annealing and a revised cascade algorithm for image reconstruction

We describe an image reconstruction problem and the computational difficulties arising in determining the maximum a posteriori (MAP) estimate. Two algorithms for tackling the problem, iterated conditional modes (ICM) and simulated annealing, are usually applied pixel by pixel. The performance of this strategy can be poor, particularly for heavily degraded images, and as a potential improvement Jubb and Jennison (1991) suggest the cascade algorithm in which ICM is initially applied to coarser images formed by blocking squares of pixels. In this paper we attempt to resolve certain criticisms of cascade and present a version of the algorithm extended in definition and implementation. As an illustration we apply our new method to a synthetic aperture radar (SAR) image. We also carry out a study of simulated annealing, with and without cascade, applied to a more tractable minimization problem from which we gain insight into the properties of cascade algorithms.     

Estimation of noncentrality parameters

We propose some estimators of noncentrality parameters which improve upon usual unbiased estimators under quadratic loss. The distributions we consider are the noncentral chi-square and the noncentral F. However, we give more general results for the family of elliptically contoured distributions and propose a robust dominating estimator.     

理论实证相印语言文化相融--胡正武《训诂阐微集》评议

胡正武新著《训诂阐微集》在训诂方面所展现的,具有理论与实证相得益彰,语言与文化水乳交融,语料丰富内容广博等特点,这是与其深厚扎实的学术功底,别具一格的研究方法相为表里的。胡君甘于寂寞的治学态度,该书朴实无华的语言风格在当今急功近利、充满躁动的商品经济社会里,尤其显示其现实意义。     

BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.