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71.
P. Miziuła 《Statistics》2017,51(4):862-877
In the paper we consider mixtures of unknown stochastically ordered distribution functions according to known mixing distribution functions. We provide optimal lower and upper bounds on ratios of general dispersion measures of such mixtures. The bounds do not depend on the particular form of dispersion measure. We present applications of the results in reliability theory, insurance mathematics, Bayesian statistics, and regression analysis. 相似文献
72.
Marica Manisera 《统计学通讯:模拟与计算》2017,46(7):5723-5739
The analysis of human perceptions is often carried out by resorting to surveys and questionnaires, where respondents are asked to express ratings about the objects being evaluated. A class of mixture models, called CUB (Combination of Uniform and shifted Binomial), has been recently proposed in this context. This article focuses on a model of this class, the Nonlinear CUB, and investigates some computational issues concerning parameter estimation, which is performed by Maximum Likelihood. More specifically, we consider two main approaches to optimize the log-likelihood: the classical numerical methods of optimization and the EM algorithm. The classical numerical methods comprise the widely used algorithms Nelder–Mead, Newton–Raphson, Broyden–Fletcher–Goldfarb–Shanno (BFGS), Berndt–Hall–Hall–Hausman (BHHH), Simulated Annealing, Conjugate Gradients and usually have the advantage of a fast convergence. On the other hand, the EM algorithm deserves consideration for some optimality properties in the case of mixture models, but it is slower. This article has a twofold aim: first we show how to obtain explicit formulas for the implementation of the EM algorithm in nonlinear CUB models and we formally derive the asymptotic variance–covariance matrix of the Maximum Likelihood estimator; second, we discuss and compare the performance of the two above mentioned approaches to the log-likelihood maximization. 相似文献
73.
A mixture experiment is an experiment in which the response is assumed to depend on the relative proportions of the ingredients present in the mixture and not on the total amount of the mixture. In such experiment process, variables do not form any portion of the mixture but the levels changed could affect the blending properties of the ingredients. Sometimes, the mixture experiments are costly and the experiments are to be conducted in less number of runs. Here, a general method for construction of efficient mixture experiments in a minimum number of runs by the method for projection of efficient response surface design onto the constrained region is obtained. The efficient designs with a less number of runs have been constructed for 3rd, 4th, and 5th component of mixture experiments with one process variable. 相似文献
74.
This article presents a review and comparison of the most important expanded families of distributions. We set the essential requirements by which an expanding family can fit any dataset successfully. A new method is proposed to construct families, which fulfill these essential requirements. Consequently, two families are suggested, which are more tractable than many other known families and possess very wide range of the indices of skewness and kurtosis. The article is motivated by two applications to real dataset. 相似文献
75.
In this article, the effects of mixtures of two normal distributions on the fraction non-conforming are studied in the context of capability analysis. When the output from several processes is mixed, the quality characteristic variables of the resulting mix may result in a normal mixture distribution. This can happen in cases such as monitoring an output from several suppliers, several machines, or several workers. This study considered the independence case and autocorrelated processes for a mixture of two normal distributions, using an autoregressive model of order one, AR(1). It is shown that the true attained process fraction non-conforming (corresponding to specific values for some capability index) can be very different from what is expected when the data are independent normal random variables. 相似文献
76.
Olivier Cappé Randal Douc Arnaud Guillin Jean-Michel Marin Christian P. Robert 《Statistics and Computing》2008,18(4):447-459
In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture
importance sampling density so as to optimise the performance of importance sampling, as measured by an entropy criterion.
The method, called M-PMC, is shown to be applicable to a wide class of importance sampling densities, which includes in particular
mixtures of multivariate Student t distributions. The performance of the proposed scheme is studied on both artificial and real examples, highlighting in particular
the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.
This work has been supported by the Agence Nationale de la Recherche (ANR) through the 2006–2008 project
’
. Both last authors are grateful to the participants to the BIRS
meeting on “Bioinformatics, Genetics and Stochastic Computation: Bridging the Gap”, Banff, for their comments on an earlier
version of this paper. The last author also acknowledges an helpful discussion with Geoff McLachlan. The authors wish to thank
both referees for their encouraging comments. 相似文献
77.
In the analysis of competing risks data, cumulative incidence function is a useful summary of the overall crude risk for a failure type of interest. Mixture regression modeling has served as a natural approach to performing covariate analysis based on this quantity. However, existing mixture regression methods with competing risks data either impose parametric assumptions on the conditional risks or require stringent censoring assumptions. In this article, we propose a new semiparametric regression approach for competing risks data under the usual conditional independent censoring mechanism. We establish the consistency and asymptotic normality of the resulting estimators. A simple resampling method is proposed to approximate the distribution of the estimated parameters and that of the predicted cumulative incidence functions. Simulation studies and an analysis of a breast cancer dataset demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use. 相似文献
78.
A marginal regression approach for correlated censored survival data has become a widely used statistical method. Examples
of this approach in survival analysis include from the early work by Wei et al. (J Am Stat Assoc 84:1065–1073, 1989) to more
recent work by Spiekerman and Lin (J Am Stat Assoc 93:1164–1175, 1998). This approach is particularly useful if a covariate’s
population average effect is of primary interest and the correlation structure is not of interest or cannot be appropriately
specified due to lack of sufficient information. In this paper, we consider a semiparametric marginal proportional hazard
mixture cure model for clustered survival data with a surviving or “cure” fraction. Unlike the clustered data in previous
work, the latent binary cure statuses of patients in one cluster tend to be correlated in addition to the possible correlated
failure times among the patients in the cluster who are not cured. The complexity of specifying appropriate correlation structures
for the data becomes even worse if the potential correlation between cure statuses and the failure times in the cluster has
to be considered, and thus a marginal regression approach is particularly attractive. We formulate a semiparametric marginal
proportional hazards mixture cure model. Estimates are obtained using an EM algorithm and expressions for the variance–covariance
are derived using sandwich estimators. Simulation studies are conducted to assess finite sample properties of the proposed
model. The marginal model is applied to a multi-institutional study of local recurrences of tonsil cancer patients who received
radiation therapy. It reveals new findings that are not available from previous analyses of this study that ignored the potential
correlation between patients within the same institution. 相似文献
79.
Babies born live under 2,500 g or with a gestational age under 37 weeks are often inadequately developed and have elevated
risks of infant mortality, congenital malformations, mental retardation, and other physical and neurological impairments.
In this paper, we model birth weight as a first hitting time (FHT) of a birthing boundary in a Wiener process representing
fetal development. We associate the parameters of the process and boundary with covariates describing maternal characteristics
and the birthing environment using a relatively new regression methodology called threshold regression. Two FHT models for birth weight are developed. One is a mixture model and the other a competing risks model. These models
are tested in a case demonstration using a 4%-systematic sample of the more than four million live births in the United States
in 2002. An extensive data set for these births was provided by the National Center for Health Statistics. The focus of this
paper is on the conceptual framework, models and methodology. A full empirical study is deferred to a later occasion. 相似文献
80.
Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction
of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood
estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood
bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of
Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed
and the estimators illustrated. Problems using the mixture model-based estimators are highlighted. 相似文献