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有限混合模型的拜占庭容错分布式学习AI 解读

Abstract Traditional statistical methods need to be updated to work with modern distributed data storage paradigms. The split-and-conquer framework that learns models on local machines and averaging their parameter estimates is common. However, this does not work for the important problem of learning finite mixture models, because subpopulation indices on each local machine may be arbitrarily permuted (the ‘label switching problem’). Earlier work proposed mixture reduction…

多样本混合模型的似然比检验及其基因印记应用AI 解读

Genomic imprinting is a known aspect of the etiology of many diseases. The imprinting phenomenon depicts differential expression levels of the allele depending on its parental origin. When the parental origin is unknown, the expression level has a finite normal mixture distribution. In such applications, a random sample of expression levels consists of three subsamples according to the number of minor alleles an individual possesses, of which one is the mixture and the other…

用于超高维特征筛选的稀疏最大似然估计AI 解读

Feature selection is fundamental for modeling the high dimensional data, where the number of features can be huge and much larger than the sample size. Since the feature space is so large, many traditional procedures become numerically infeasible. It is hence essential to first remove most apparently non-influential features before any elaborative analysis. Recently, several procedures have been developed for this purpose, which include the sure-independent-screening (SIS)…

密度比模型下的分位数及分位数函数估计AI 解读

Population quantiles and their functions are important parameters in many applications. For example, the lower quantiles often serve as crucial quality indices for forestry products. Given several independent samples from populations satisfying the density ratio model, we investigate the properties of empirical likelihood (EL) based inferences. The induced EL quantile estimators are shown to admit a Bahadur representation that leads to asymptotically valid confidence…

正态混合模型成分数的推断AI 解读

Finite normal mixture models are used in a wide range of applications. Hypothesis testing on the order of the normal mixture is an important yet unsolved problem. Existing procedures often lack a rigorous theoretical foundation. Many are also hard to implement numerically. In this article, we develop a new method to fill the void in this important area. An effective expectation-maximization (EM) test is invented for testing the null hypothesis of arbitrary order m 0 under a…

有限混合模型的阶数检验AI 解读

The order is an important parameter in applications of finite mixture models. Yet designing a valid and easy-to-use statistical test for the order is challenging. To date, most results on hypothesis tests have focused on homogeneity, a special case where the null model has order 1. In this work, we designed an EM test for the general problem of testing the null hypothesis of order m0 versus an alternative hypothesis of order larger than m0. For any positive integer m0, the…

具有高阶精度的调整经验似然AI 解读

Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective…

正态混合模型的假设检验：EM 方法AI 解读

Normal mixture distributions are arguably the most important mixture models, and also the most technically challenging. The likelihood function of the normal mixture model is unbounded based on a set of random samples, unless an artificial bound is placed on its component variance parameter. Moreover, the model is not strongly identifiable so it is hard to differentiate between over dispersion caused by the presence of a mixture and that caused by a large variance, and it…

利用非光滑惩罚选择有限混合模型的阶数AI 解读

Order selection is a fundamental and challenging problem in the application of finite mixture models. In this article, we develop a new penalized likelihood approach. The new method, modified smoothly clipped absolute deviation (MSCAD), deviates from information-based methods such as Akaike information criterion (AIC) and Bayesian information criterion (BIC) by introducing two penalty functions that depend on the mixing proportions and the component parameters. It is…

采用非光滑惩罚的有限混合模型阶数选择AI 解读

Order selection is a fundamental and challenging problem in the application of finite mixture models. We develop a new penalized likelihood approach that we call MSCAD. MSCAD deviates from information-based methods, such as Akaike information criterion and the Bayes information criterion, by introducing two penalty functions that depend on the mixing proportions and the component parameters. It is consistent in estimating both the order of the mixture model and the mixing…

有限混合回归模型中的变量选择AI 解读

In the applications of finite mixture of regression (FMR) models, often many covariates are used, and their contributions to the response variable vary from one component to another of the mixture model. This creates a complex variable selection problem. Existing methods, such as the Akaike information criterion and the Bayes information criterion, are computationally expensive as the number of covariates and components in the mixture model increases. In this article we…

有限混合模型中两组分假设的检验AI 解读

Summary We consider a finite mixture model with k components and a kernel distribution from a general one-parameter family. The problem of testing the hypothesis k=2 versusk⩾3 is studied. There has been no general statistical testing procedure for this problem. We propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function. It is shown that estimators of the…

最近邻插补的刀切法方差估计AI 解读

Nearest-neighbor imputation is a popular hot deck imputation method used to compensate for nonresponse in sample surveys. Although this method has a long history of application, the problem of variance estimation after nearest-neighbor imputation has not been fully investigated. Because nearest-neighbor imputation is a nonparametric method, a nonparametric variance estimation technique, such as the jackknife, is desired. We show that the naive jackknife that treats imputed…

有限混合模型同质性的修正似然比检验AI 解读

Summary Testing for homogeneity in finite mixture models has been investigated by many researchers. The asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to use in practice. We propose a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family. The modified LRT has a χ-type of null limiting distribution and is asymptotically most powerful under local alternatives. Simulations show…

有限混合模型的最优收敛速率AI 解读

In finite mixture models, we establish the best possible rate of convergence for estimating the mixing distribution. We find that the key for estimating the mixing distribution is the knowledge of the number of components in the mixture. While a $\sqrt n$-consistent rate is achievable when the exact number of components is known, the best possible rate is only $n^{-1/4}$ when it is unknown. Under a strong identifiability condition, it is shown that this rate is reached by…

迭代加权最小二乘估计量AI 解读

In a heteroscedastic linear model, we establish the asymptotic normality of the iterative weighted least squares estimators with weights constructed by using the within-group residuals obtained from the previous model fitting. An adaptive procedure is proposed which ensures that the iterative process stops after a finite number of iterations and produces an estimator asymptotically equivalent to the best estimator that can be obtained by using the iterative procedure.…

有限总体经验似然估计与辅助信息的有效利用AI 解读

SUMMARY In finite population inference problems, auxiliary population information is often available. We show in this paper that the empirical likelihood method can be naturally applied to such problems to make effective use of the auxiliary information. We prove that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information. A Bahadur-type representation for empirical likelihood sample quantiles is given.…