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未知误差分布下线性变量误差模型的估计AI 解读

Summary Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based on the phase function, a normalized version of the characteristic…

准平稳蒙特卡洛与 Scale 算法AI 解读

Summary This paper introduces a class of Monte Carlo algorithms which are based on the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current Markov chain Monte Carlo methods which simulate a Markov chain whose stationary distribution is the target. We show how to approximate distributions of interest by carefully combining sequential Monte Carlo methods with methodology for…

含极端观测整数时间序列的贝塔—负二项自回归模型AI 解读

Summary The paper introduces a general class of heavy-tailed auto-regressions for modelling integer-valued time series with outliers. The specification proposed is based on a heavy-tailed mixture of negative binomial distributions that features an observation-driven dynamic equation for the conditional expectation. The existence of a stationary and ergodic solution for the class of auto-regressive processes is shown under general conditions. The estimation of the model can…

采用二元稳定核的积分差分方程时空建模AI 解读

Summary An integro-difference equation can be represented as a hierarchical spatiotemporal dynamic model using appropriate parameterizations. The dynamics of the process defined by an integro-difference equation depends on the choice of a bivariate kernel distribution, where more flexible shapes generally result in more flexible models. Under a Bayesian modelling framework, we consider the use of the stable family of distributions for the kernel, as they are infinitely…

协变量自适应随机化下生存分析中治疗效应的稳健检验AI 解读

Summary Covariate-adaptive randomization is popular in clinical trials with sequentially arrived patients for balancing treatment assignments across prognostic factors that may have influence on the response. However, existing theory on tests for the treatment effect under covariate-adaptive randomization is limited to tests under linear or generalized linear models, although the covariate-adaptive randomization method has been used in survival analysis for a long time.…

临床试验治疗组选择的信息论方法AI 解读

Summary The question of selecting the ‘best’ among different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example, which treatment gives the best response rate. Motivated by recent developments in the theory of context-dependent information measures, we propose a flexible response-adaptive experimental design based on a novel criterion governing treatment arm selections which can be used in adaptive…

利用 Fisher–Gaussian 核估计具有非线性支撑的密度AI 解读

Summary Current tools for multivariate density estimation struggle when the density is concentrated near a non-linear subspace or manifold. Most approaches require the choice of a kernel, with the multivariate Gaussian kernel by far the most commonly used. Although heavy-tailed and skewed extensions have been proposed, such kernels cannot capture curvature in the support of the data. This leads to poor performance unless the sample size is very large relative to the…

高维情形下的修正似然根AI 解读

Summary We examine a higher order approximation to the significance function with increasing numbers of nuisance parameters, based on the normal approximation to an adjusted log-likelihood root. We show that the rate of the correction for nuisance parameters is larger than the correction for non-normality, when the parameter dimension p is O(nα) for α<12. We specialize the results to linear exponential families and location–scale families and illustrate these with…

回归变量选择的新方法及其在遗传精细定位中的应用AI 解读

Summary We introduce a simple new approach to variable selection in linear regression, with a particular focus on quantifying uncertainty in which variables should be selected. The approach is based on a new model—the ‘sum of single effects’ model, called ‘SuSiE’—which comes from writing the sparse vector of regression coefficients as a sum of ‘single-effect’ vectors, each with one non-zero element. We also introduce a corresponding new fitting procedure—iterative Bayesian…

稳健类贝叶斯估计：Rho-Bayes 估计AI 解读

We observe $n$ independent random variables with joint distribution ${\mathbf{P}}$ and pretend that they are i.i.d. with some common density $s$ (with respect to a known measure $\mu $) that we wish to estimate. We consider a density model $\overline{S}$ for $s$ that we endow with a prior distribution $\pi $ (with support in $\overline{S}$) and build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around $s$…

多维空间与图上的保序回归AI 解读

In this paper, we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^{d}$ with ${d\ge2}$ and $N(0,1)$ noise, the minimax rate for the $\ell_{2}$ risk is known to be bounded from below by $n^{-1/d}$ when the unknown mean function $f$ is nondecreasing and its range is bounded by a constant, while the least squares estimator (LSE) is known to nearly achieve the minimax rate up to a factor $(\log n)^{\gamma}$…

超越高斯近似：独立随机向量之和最大值的自助法AI 解读

The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme value theory has been proven to provide more accurate multiplicity adjustments in a number of settings, but only on an ad hoc basis. Recently, Gaussian approximation has been used to justify bootstrap adjustments in large scale simultaneous…

通过位移凸性分析两层神经网络AI 解读

Fitting a function by using linear combinations of a large number $N$ of “simple” components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is nonconvex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches. Here,…

随机设计非参数回归中的最优方差估计AI 解读

Consider the heteroscedastic nonparametric regression model with random design \begin{equation*}Y_{i}=f(X_{i})+V^{1/2}(X_{i})\varepsilon _{i},\quad i=1,2,\ldots ,n,\end{equation*} with $f(\cdot )$ and $V(\cdot )$ $\alpha $- and $\beta $-Hölder smooth, respectively. We show that the minimax rate of estimating $V(\cdot )$ under both local and global squared risks is of the order \begin{equation*}n^{-\frac{8\alpha \beta }{4\alpha \beta +2\alpha +\beta }}\vee n^{-\frac{2\beta }{2\beta +1}},\end{equation*}…

高维协方差矩阵检验AI 解读

The paper introduces a new test for testing structures of covariances for high dimensional vectors and the data dimension can be much larger than the sample size. Under proper normalization, central and noncentral limit theorems are established. The asymptotic theory is attained without imposing any explicit restriction between data dimension and sample size. To facilitate the related statistical inference, we propose the balanced Rademacher weighted differencing scheme,…

模型选择与局部几何AI 解读

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases—including common classes of causal or graphical models, as well as time series models—distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than…

结构化、回归及在线场景中错误发现比例的同时高概率界AI 解读

While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (Statist. Sci. 26 (2011) 584–597) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds on the false discovery proportion (FDP) of the chosen set. In this paper, we propose a new class of such simultaneous FDP bounds, tailored for nested sequences of rejection sets. While most existing simultaneous…

预测回归中条件风险价值的统计推断AI 解读

Conditional value-at-risk is a popular risk measure in risk management. We study the inference problem of conditional value-at-risk under a linear predictive regression model. We derive the asymptotic distribution of the least squares estimator for the conditional value-at-risk. Our results relax the model assumptions made in (Oper. Res. 60 (2012) 739–756) and correct their mistake in the asymptotic variance expression. We show that the asymptotic variance depends on the…

通过投影平均构造稳健的多元非参数检验AI 解读

In this work, we generalize the Cramér–von Mises statistic via projection averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed data and minimax rate optimal against a certain class of alternatives. Our test statistic is completely free of tuning parameters and is computationally efficient even in high dimensions. When the dimension tends to infinity, the proposed test…

距离标准差AI 解读

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption of finite second moments. Applications are provided to hypothesis testing on a data set from materials science and to multivariate statistical quality control. The distance standard deviation is compared to classical scale measures for…

高维情形下基于距离与再生核希尔伯特空间的依赖度量AI 解读

In this paper, we study distance covariance, Hilbert–Schmidt covariance (aka Hilbert–Schmidt independence criterion [In Advances in Neural Information Processing Systems (2008) 585–592]) and related independence tests under the high dimensional scenario. We show that the sample distance/Hilbert–Schmidt covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates…

基于独立同分布随机微分方程路径的非参数漂移估计AI 解读

We consider $N$ independent stochastic processes $(X_{i}(t),t\in [0,T])$, $i=1,\ldots ,N$, defined by a one-dimensional stochastic differential equation, which are continuously observed throughout a time interval $[0,T]$ where $T$ is fixed. We study nonparametric estimation of the drift function on a given subset $A$ of ${\mathbb{R}}$. Projection estimators are defined on finite dimensional subsets of ${\mathbb{L}}^{2}(A,dx)$. We stress that the set $A$ may be compact or not…

Fréchet 变点检测AI 解读

We propose a method to infer the presence and location of change-points in the distribution of a sequence of independent data taking values in a general metric space, where change-points are viewed as locations at which the distribution of the data sequence changes abruptly in terms of either its Fréchet mean, Fréchet variance or both. The proposed method is based on comparisons of Fréchet variances before and after putative change-point locations and does not require a…

Lipschitz 球上熵估计的最优收敛速度AI 解读

We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates $(n\ln n)^{-s/(s+d)}+n^{-1/2}$ for $0