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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.
If a population contains many zero values and the sample size is not very large, the traditional normal approximation‐based confidence intervals for the population mean may have poor coverage probabilities. This problem is substantially reduced by constructing parametric likelihood ratio intervals when an appropriate mixture model can be found. In the context of survey sampling, however, there is a general preference for making minimal assumptions about the population under study. The authors have therefore investigated the coverage properties of nonparametric empirical likelihood confidence intervals for the population mean. They show that under a variety of hypothetical populations, these intervals often outperformed parametric likelihood intervals by having more balanced coverage rates and larger lower bounds. The authors illustrate their methodology using data from the Canadian Labour Force Survey for the year 2000. 相似文献
3.
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. 相似文献
4.
Craig H. Mallinckrodt Christopher J. Kaiser John G. Watkin Michael J. Detke Geert Molenberghs Raymond J. Carroll 《Pharmaceutical statistics》2004,3(3):171-186
The last observation carried forward (LOCF) approach is commonly utilized to handle missing values in the primary analysis of clinical trials. However, recent evidence suggests that likelihood‐based analyses developed under the missing at random (MAR) framework are sensible alternatives. The objective of this study was to assess the Type I error rates from a likelihood‐based MAR approach – mixed‐model repeated measures (MMRM) – compared with LOCF when estimating treatment contrasts for mean change from baseline to endpoint (Δ). Data emulating neuropsychiatric clinical trials were simulated in a 4 × 4 factorial arrangement of scenarios, using four patterns of mean changes over time and four strategies for deleting data to generate subject dropout via an MAR mechanism. In data with no dropout, estimates of Δ and SEΔ from MMRM and LOCF were identical. In data with dropout, the Type I error rates (averaged across all scenarios) for MMRM and LOCF were 5.49% and 16.76%, respectively. In 11 of the 16 scenarios, the Type I error rate from MMRM was at least 1.00% closer to the expected rate of 5.00% than the corresponding rate from LOCF. In no scenario did LOCF yield a Type I error rate that was at least 1.00% closer to the expected rate than the corresponding rate from MMRM. The average estimate of SEΔ from MMRM was greater in data with dropout than in complete data, whereas the average estimate of SEΔ from LOCF was smaller in data with dropout than in complete data, suggesting that standard errors from MMRM better reflected the uncertainty in the data. The results from this investigation support those from previous studies, which found that MMRM provided reasonable control of Type I error even in the presence of MNAR missingness. No universally best approach to analysis of longitudinal data exists. However, likelihood‐based MAR approaches have been shown to perform well in a variety of situations and are a sensible alternative to the LOCF approach. MNAR methods can be used within a sensitivity analysis framework to test the potential presence and impact of MNAR data, thereby assessing robustness of results from an MAR method. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
5.
Merging information for semiparametric density estimation 总被引:1,自引:0,他引:1
Konstantinos Fokianos 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2004,66(4):941-958
Summary. The density ratio model specifies that the likelihood ratio of m −1 probability density functions with respect to the m th is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt variants of well-established techniques to choose the smoothing parameter for the density estimators proposed. 相似文献
6.
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
7.
Chunming M. Zhang 《Revue canadienne de statistique》2003,31(2):151-171
Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data. 相似文献
8.
Abstract. In this paper, we study the statistical interpretation of forensic DNA mixtures with related contributors in subdivided populations. Compact general formulae for match probabilities are obtained for two situations: a relative of one tested person is an unknown contributor of a DNA mixture; and two related unknowns are contributors. The effect of kinship and population structure is illustrated using a real case example. 相似文献
9.
Peter Hall Qiwei Yao 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2003,65(2):425-442
Summary. We develop a general methodology for tilting time series data. Attention is focused on a large class of regression problems, where errors are expressed through autoregressive processes. The class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression, robust statistical inference and estimation subject to constraints. The method can be viewed as 'empirical likelihood with nuisance parameters'. 相似文献
10.
Craig H. Mallinckrodt John G. Watkin Geert Molenberghs Raymond J. Carroll 《Pharmaceutical statistics》2004,3(3):161-169
Missing data, and the bias they can cause, are an almost ever‐present concern in clinical trials. The last observation carried forward (LOCF) approach has been frequently utilized to handle missing data in clinical trials, and is often specified in conjunction with analysis of variance (LOCF ANOVA) for the primary analysis. Considerable advances in statistical methodology, and in our ability to implement these methods, have been made in recent years. Likelihood‐based, mixed‐effects model approaches implemented under the missing at random (MAR) framework are now easy to implement, and are commonly used to analyse clinical trial data. Furthermore, such approaches are more robust to the biases from missing data, and provide better control of Type I and Type II errors than LOCF ANOVA. Empirical research and analytic proof have demonstrated that the behaviour of LOCF is uncertain, and in many situations it has not been conservative. Using LOCF as a composite measure of safety, tolerability and efficacy can lead to erroneous conclusions regarding the effectiveness of a drug. This approach also violates the fundamental basis of statistics as it involves testing an outcome that is not a physical parameter of the population, but rather a quantity that can be influenced by investigator behaviour, trial design, etc. Practice should shift away from using LOCF ANOVA as the primary analysis and focus on likelihood‐based, mixed‐effects model approaches developed under the MAR framework, with missing not at random methods used to assess robustness of the primary analysis. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献