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利用方差—均值混合进行非高斯回归的数据增广AI 解读

We use the theory of normal variance-mean mixtures to derive a data-augmentation scheme for a class of common regularization problems. This generalizes existing theory on normal variance mixtures for priors in regression and classification. It also allows variants of the expectation-maximization algorithm to be brought to bear on a wider range of models than previously appreciated. We demonstrate the method on several examples, focusing on the case of binary logistic…

基因与环境交互作用研究中共享遗传对照的使用AI 解读

With the advent of modern genomic methods to adjust for population stratification, the use of external or publicly available controls has become an attractive option for reducing the cost of large-scale case-control genetic association studies. In this article, we study the estimation of joint effects of genetic and environmental exposures from a case-control study where data on genome-wide markers are available on the cases and a set of external controls while data on…

顶点数增长的无向随机图 β 模型中心极限定理AI 解读

Chatterjee et al. (2011) established the consistency of the maximum likelihood estimator in the β-model for undirected random graphs when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we prove asymptotic normality of the maximum likelihood estimator under mild conditions. Simulation studies and a data example illustrate the theoretical results.

信息性抽样下调查分析的权重构造AI 解读

Sampling related to the outcome variable of a regression analysis conditional on covariates is called informative sampling and may lead to bias in ordinary least squares estimation. Weighting by the reciprocal of the inclusion probability approximately removes such bias but may inflate variance. This paper investigates two ways of modifying such weights to improve efficiency while retaining consistency. One approach is to multiply the inverse probability weights by functions…

更易判定符号的同时置信区间AI 解读

Many studies draw inferences about multiple endpoints but ignore the statistical implications of multiplicity. Effects inferred to be positive when there is no adjustment for multiplicity can lose their statistical significance when multiplicity is taken into account, perhaps explaining why such adjustments are so often omitted. We develop new simultaneous confidence intervals that mitigate this problem; these are uniformly more likely to determine signs than are standard…

地统计估计与预测中范围参数的作用AI 解读

Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. We show that asymptotic results for a Gaussian process over a fixed domain with Matérn covariance function, previously proven only in the case of a fixed range parameter, can be extended to the case of jointly estimating the range and the variance of the process. Moreover, we show that intuition and…

删失线性回归模型的有效估计AI 解读

In linear regression or accelerated failure time models, complications in efficient estimation arise from the multiple roots of the efficient score and density estimation. This paper proposes a one-step efficient estimation method based on a counting process martingale, which has several advantages: it avoids the multiple-root problem, the initial estimator is easily available and the variance estimator can be obtained by employing plug-in rules. A simple and effective…

基于距离秩的一致多元关联检验AI 解读

We consider the problem of detecting associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all dimensions and consistent against all alternatives. The test has a simple form, is easy to implement, and has good power.

快速二维 P 样条：三明治平滑器AI 解读

Summary We propose a fast penalized spline method for bivariate smoothing. Univariate P-spline smoothers are applied simultaneously along both co-ordinates. The new smoother has a sandwich form which suggested the name ‘sandwich smoother’ to a referee. The sandwich smoother has a tensor product structure that simplifies an asymptotic analysis and it can be fast computed. We derive a local central limit theorem for the sandwich smoother, with simple expressions for the…

用相依归一化随机测度混合模型比较分布AI 解读

Summary A methodology for the simultaneous Bayesian non-parametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in detail. Efficient slice sampling methods are developed for inference. Various posterior summaries are introduced…

微分几何最小角回归：稀疏广义线性模型方法AI 解读

Summary Sparsity is an essential feature of many contemporary data problems. Remote sensing, various forms of automated screening and other high throughput measurement devices collect a large amount of information, typically about few independent statistical subjects or units. In certain cases it is reasonable to assume that the underlying process generating the data is itself sparse, in the sense that only a few of the measured variables are involved in the process. We…

大规模多重检验的扩展似然方法AI 解读

Summary To date, only frequentist, Bayesian and empirical Bayes approaches have been studied for the large-scale inference problem of testing simultaneously hundreds or thousands of hypotheses. Their derivations start with some summarizing statistics without modelling the basic responses. As a consequence testing procedures have been developed without necessarily checking model assumptions, and empirical null distributions are needed to avoid the problem of rejecting all…

高维惩罚似然中的调节参数选择AI 解读

Summary Determining how to select the tuning parameter appropriately is essential in penalized likelihood methods for high dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear models, where the dimensionality of covariates p is allowed to increase exponentially with the sample size n. We propose to select the tuning parameter by optimizing the generalized information criterion with an appropriate model…

SMC²：状态空间模型序贯分析的高效算法AI 解读

Summary We consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter θ. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the θ-dimension, that samples values of θ, reweights iteratively these values by using the likelihood increments pyt∣y1:t−1,θ and rejuvenates the θ-particles…

元分析中异质性方差的估计AI 解读

Summary Several new estimators of the between-study variability in a heterogeneous random effects meta-analysis model are derived. One is the unbiased statistic which is locally optimal for small values of the parameter. Others are Bayes procedures within a class of quadratic statistics for a diffuse prior with different choices of the prior mean. These estimators are compared with the DerSimonian–Laird procedure and the Hedges statistic in particular via the quadratic risk…

固定边际和矩阵的精确抽样与计数AI 解读

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including…

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…

尺度依赖辅助变量的非参数回归AI 解读

The paper is devoted to the problem of estimation of a univariate component in a heteroscedastic nonparametric multiple regression under the mean integrated squared error (MISE) criteria. The aim is to understand how the scale function should be used for estimation of the univariate component. It is known that the scale function does not affect the rate of the MISE convergence, and as a result sharp constants are explored. The paper begins with developing a sharp-minimax…

高频观测遍历 Lévy 驱动随机微分方程的高斯拟似然随机场收敛AI 解读

This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a Lévy driven stochastic differential equation whose coefficients are known except for the finite-dimensional parameters to be estimated, where the diffusion coefficient may be degenerate or even null. We suppose that the process is discretely observed under the rapidly increasing experimental design with step size $h_{n}$…

莱维测度与莱维联结函数的非参数推断AI 解读

In this paper nonparametric methods to assess the multivariate Lévy measure are introduced. Starting from high-frequency observations of a Lévy process $\mathbf{X} $, we construct estimators for its tail integrals and the Pareto–Lévy copula and prove weak convergence of these estimators in certain function spaces. Given $n$ observations of increments over intervals of length $\Delta_{n}$, the rate of convergence is $k_{n}^{-1/2}$ for $k_{n}=n\Delta_{n}$ which is natural…

泊松过程两样本问题：基于非渐近野生自助法的自适应检验AI 解读

Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose testing procedures whose test statistics are $U$-statistics based on single kernel functions. The corresponding critical values are constructed from a nonasymptotic wild bootstrap approach, leading to level $\alpha$ tests. Various choices for the kernel functions are possible, including projection, approximation or reproducing kernels.…

用于最优序贯分配的 Kullback–Leibler 上置信界AI 解读

We consider optimal sequential allocation in the context of the so-called stochastic multi-armed bandit model. We describe a generic index policy, in the sense of Gittins [J. R. Stat. Soc. Ser. B Stat. Methodol. 41 (1979) 148–177], based on upper confidence bounds of the arm payoffs computed using the Kullback–Leibler divergence. We consider two classes of distributions for which instances of this general idea are analyzed: the kl-UCB algorithm is designed for one-parameter…

通过闭式密度展开进行扩散过程最大似然估计AI 解读

This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and accompanied by an algorithm containing only basic and explicit calculations for delivering any arbitrary order of the expansion. The likelihood function is thus approximated explicitly and employed in statistical estimation. The performance of our…

时间序列的固定平滑渐近理论AI 解读

In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based $t$-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order…