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用于超高维变量选择的惩罚复合准似然AI 解读

Summary In high dimensional model selection problems, penalized least square approaches have been extensively used. The paper addresses the question of both robustness and efficiency of penalized model selection methods and proposes a data-driven weighted linear combination of convex loss functions, together with weighted L1-penalty. It is completely data adaptive and does not require prior knowledge of the error distribution. The weighted L1-penalty is used both to ensure…

黎曼流形上的 Langevin 与 Hamiltonian 蒙特卡洛方法AI 解读

Summary The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed…

剂量—反应研究中实验设计的稳健性AI 解读

Summary We construct experimental designs for dose–response studies. The designs are robust against possibly misspecified link functions; for this they minimize the maximum mean-squared error of the estimated dose required to attain a response in 100p% of the target population. Here p might be one particular value—p = 0.5 corresponds to ED50-estimation—or it might range over an interval of values of interest. The maximum of the mean-squared error is evaluated over a…

计数数据的有效概率预测AI 解读

Summary Efficient probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution non-parametrically over a given broad model class and proving asymptotic (non-parametric) efficiency in that setting. The method is developed within the context of the integer auto-regressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth-and-death process…

相关观测回归模型最优设计的几何刻画AI 解读

Summary We consider the problem of optimal design of experiments for random-effects models, especially population models, where a small number of correlated observations can be taken on each individual, whereas the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving from the case of uncorrelated data can be…

借助降维估计对主要关注参数进行推断AI 解读

Summary As high dimensional data become routinely available in applied sciences, sufficient dimension reduction has been widely employed and its research has received considerable attention. However, with the majority of sufficient dimension reduction methodology focusing on the dimension reduction step, complete analysis and inference after dimension reduction have yet to receive much attention. We couple the strategy of sufficient dimension reduction with a flexible…

具有概周期强度函数的非齐次泊松过程建模AI 解读

Summary We propose a model for the analysis of non-stationary point processes with almost periodic rate of occurrence. The model deals with the arrivals of events which are unequally spaced and show a pattern of periodicity or almost periodicity, such as stock transactions and earthquakes. We model the rate of occurrence of a non-homogeneous Poisson process as the sum of sinusoidal functions plus a baseline. Consistent estimates of frequencies, phases and amplitudes which…

Summary We propose a flexible non-parametric specification of the emission distribution in hidden Markov models and we introduce a novel methodology for carrying out the computations. Whereas current approaches use a finite mixture model, we argue in favour of an infinite mixture model given by a mixture of Dirichlet processes. The computational framework is based on auxiliary variable representations of the Dirichlet process and consists of a forward–backward Gibbs sampling…

经典测量误差模型中的局部与总体拟合优度检验AI 解读

Summary We consider functional measurement error models, i.e. models where covariates are measured with error and yet no distributional assumptions are made about the mismeasured variable. We propose and study a score-type local test and an orthogonal series-based, omnibus goodness-of-fit test in this context, where no likelihood function is available or calculated—i.e. all the tests are proposed in the semiparametric model framework. We demonstrate that our tests have…

半参数广义线性模型中快速稳定的限制极大似然与边际似然估计AI 解读

Summary Recent work by Reiss and Ogden provides a theoretical basis for sometimes preferring restricted maximum likelihood (REML) to generalized cross-validation (GCV) for smoothing parameter selection in semiparametric regression. However, existing REML or marginal likelihood (ML) based methods for semiparametric generalized linear models (GLMs) use iterative REML or ML estimation of the smoothing parameters of working linear approximations to the GLM. Such indirect schemes…

多维对数凹密度的最大似然估计AI 解读

Summary Let X1,…,Xn be independent and identically distributed random vectors with a (Lebesgue) density f. We first prove that, with probability 1, there is a unique log-concave maximum likelihood estimator f^n of f. The use of this estimator is attractive because, unlike kernel density estimation, the method is fully automatic, with no smoothing parameters to choose. Although the existence proof is non-constructive, we can reformulate the issue of computing f^n in terms of…

用于贝叶斯与频率学派推断的默认先验AI 解读

Summary We investigate the choice of default priors for use with likelihood for Bayesian and frequentist inference. Such a prior is a density or relative density that weights an observed likelihood function, leading to the elimination of parameters that are not of interest and then a density-type assessment for a parameter of interest. For independent responses from a continuous model, we develop a prior for the full parameter that is closely linked to the original Bayes…

通过贝叶斯先验—后验转移拟合实现时间扭曲的多分辨率方法AI 解读

Summary Warping is an approach to the reduction and analysis of phase variability in functional observations, by applying a smooth bijection to the function argument. We propose a natural representation of warping functions in terms of a new type of elementary functions named ‘warping component functions’, or ‘warplets’, which are combined into the warping function by composition. The inverse warping function is trivial and explicit to obtain. A sequential Bayesian…

有偏抽样下右删失数据的非参数检验AI 解读

Summary Testing the equality of two survival distributions can be difficult in a prevalent cohort study when non-random sampling of subjects is involved. Owing to the biased sampling scheme, the independent censoring assumption is often violated. Although the issues about biased inference caused by length-biased sampling have been widely recognized in the statistical, epidemiological and economical literature, there is no satisfactory solution for efficient two-sample…

复杂调查的贝叶斯伪经验似然区间AI 解读

Summary Bayesian methods for inference on finite population means and other parameters by using sample survey data face hurdles in all three phases of the inferential procedure: the formulation of a likelihood function, the choice of a prior distribution and the validity of posterior inferences under the design-based frequentist framework. In the case of independent and identically distributed observations, the profile empirical likelihood function of the mean and a…

时变系数线性模型的同时推断AI 解读

Summary The paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models. Using a Gaussian approximation result for non-stationary multiple time series, we show that the constructed simultaneous confidence tubes have asymptotically correct nominal coverage probabilities. Our results are applied to the problem of testing whether the regression coefficients are of certain parametric forms, which is a…

Summary It is possible to implement importance sampling, and particle filter algorithms, where the importance sampling weight is random. Such random-weight algorithms have been shown to be efficient for inference for a class of diffusion models, as they enable inference without any (time discretization) approximation of the underlying diffusion model. One difficulty of implementing such random-weight algorithms is the requirement to have weights that are positive with…

半参数广义线性潜变量模型的显式估计方程AI 解读

Summary We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit…

格点数据空间线性模型的选择AI 解读

Summary Spatial linear models are popular for the analysis of data on a spatial lattice, but statistical techniques for selection of covariates and a neighbourhood structure are limited. Here we develop new methodology for simultaneous model selection and parameter estimation via penalized maximum likelihood under a spatial adaptive lasso. A computationally efficient algorithm is devised for obtaining approximate penalized maximum likelihood estimates. Asymptotic properties…

高斯随机场驱动空间点过程的充分降维AI 解读

Summary We develop a sufficient dimension reduction paradigm for inhomogeneous spatial point processes driven by Gaussian random fields. Specifically, we introduce the notion of the kth-order central intensity subspace. We show that a central subspace can be defined as the combination of all central intensity subspaces. For many commonly used spatial point process models, we find that the central subspace is equivalent to the first-order central intensity subspace. To…

粒子 Markov 链 Monte Carlo 方法AI 解读

Summary Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show…

时间序列置信区间构造的自归一化方法AI 解读

Summary We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent approaches, our method has the attractive convenience of being free of any user-chosen number or smoothing parameter. The interval is constructed on the basis of an asymptotically distribution-free self-normalized statistic, in which the…

非参数贝叶斯分析中的最小信息先验分布AI 解读

Summary We address the problem of how to conduct a minimally informative, non-parametric Bayesian analysis. The central question is how to devise a model so that the posterior distribution satisfies a few basic properties. The concept of ‘local mass’ provides the key to the development of the limiting Dirichlet process model. This model is then used to provide an engine for inference in the compound decision problem and for multiple-comparisons inference in a one-way…

给定 Copula 下相依竞争风险的半参数边际回归AI 解读

Summary Competing risks problems arise in many fields of science, where two or more types of event may occur on a subject, but only the event occurring first is observed together with its occurrence time, and other events are censored. The marginal and joint distributions of event times for competing risks cannot be identified from the observed data without assuming the relationship between events. The commonly adopted independent censoring assumption may be easily violated.…