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1.
OLIVIER CAPPÉ RANDAL DOUC ERIC MOULINES & CHRISTIAN ROBERT 《Scandinavian Journal of Statistics》2002,29(4):615-635
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. 相似文献
2.
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. 相似文献
3.
The robustness of Mauchly's sphericity test criterion when sampling from a mixture of two multivariate normal distributions is studied. The distribution of the sphericity test criterion when the sample covariance matrix has a non-central Wishart density of rank one is derived in terms of Meijer's G-functions; its distribution under the mixture model is then deduced. The robustness is studied by computing actual significance levels of the test under the mixture model using the critical values under the usual normal model. 相似文献
4.
该文考虑一类对角型蜕化抛物组,允许主部系数矩阵的特征值正比例于未知解的模的适当正幂次,也正比例于未知解梯度的模的某个正幂次.对右端项有某种特殊结构的情形得到了解最大模的先验估计. 相似文献
5.
Summary An increase in fish mortality due to fishing can theoretically change the growth and reproduction of fish populations from
the viewpoint of adaptation. We address the issue of how an iteroparous fish should convert surplus energy into somatic growth
and reproduction at each age under given conditions of mortality. A model of life history, which maximizes the net reproductive
rate using the discrete maximum principle, is improved employing a new relationship between body weight and surplus energy
which we have recently proposed. The model is applied to the North Sea plaicePleuronectes platessa, for which it has been reported that the average length of young fish had increased whereas that of old ones had decreased
for some decades. Although the model cannot directly explain the former phenomenon, the two phenomena can be interpreted as
a change in the optimal life history due mainly to an increase in mortality. 相似文献
6.
A Sparse Implementation of the Average Information Algorithm for Factor Analytic and Reduced Rank Variance Models 总被引:1,自引:0,他引:1
Robin Thompson Brian Cullis Alison Smith Arthur Gilmour 《Australian & New Zealand Journal of Statistics》2003,45(4):445-459
Factor analytic variance models have been widely considered for the analysis of multivariate data particularly in the psychometrics area. Recently Smith, Cullis & Thompson (2001) have considered their use in the analysis of multi‐environment data arising from plant improvement programs. For these data, the size of the problem and the complexity of the variance models chosen to account for spatial heterogeneity within trials implies that standard algorithms for fitting factor analytic models can be computationally expensive. This paper presents a sparse implementation of the average information algorithm (Gilmour, Thompson & Cullis, 1995) for fitting factor analytic and reduced rank variance models. 相似文献
7.
Martin Hazelton 《Statistics and Computing》1995,5(4):343-350
Some statistical models defined in terms of a generating stochastic mechanism have intractable distribution theory, which renders parameter estimation difficult. However, a Monte Carlo estimate of the log-likelihood surface for such a model can be obtained via computation of nonparametric density estimates from simulated realizations of the model. Unfortunately, the bias inherent in density estimation can cause bias in the resulting log-likelihood estimate that alters the location of its maximizer. In this paper a methodology for radically reducing this bias is developed for models with an additive error component. An illustrative example involving a stochastic model of molecular fragmentation and measurement is given. 相似文献
8.
It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'. 相似文献
9.
Anirban Dasgupta George Casella Mohan Delampady Christian Genest William E. Strawderman Herman Rubin 《Revue canadienne de statistique》2000,28(4):675-687
The authors consider the correlation between two arbitrary functions of the data and a parameter when the parameter is regarded as a random variable with given prior distribution. They show how to compute such a correlation and use closed form expressions to assess the dependence between parameters and various classical or robust estimators thereof, as well as between p‐values and posterior probabilities of the null hypothesis in the one‐sided testing problem. Other applications involve the Dirichlet process and stationary Gaussian processes. Using this approach, the authors also derive a general nonparametric upper bound on Bayes risks. 相似文献
10.