论文检索

具有随机未观测异质性的持续期模型非参数分析AI 解读

This paper develops nonparametric identification and estimation results for a single-spell hazard model, where the unobserved heterogeneity is specified as a Lévy subordinator. The identification approach solves a nonlinear Volterra integral equation of the first kind with an unknown kernel function. Both the kernel of the integral operator, which models the distribution of the unobserved heterogeneity, and the functions that enter it are identified given regularity…

结构突变模型中的相关参数变化AI 解读

Structural break time series models, which are commonly used in macroeconomics and finance, capture unknown structural changes by allowing for abrupt changes to model parameters. However, many specifications suffer from an over-parametrization issue, since typically all parameters have to change when a break occurs. We introduce a sparse change-point model to detect which parameters change over time. We propose a shrinkage prior distribution, which controls model parsimony…

高维工具变量回归的统计推断AI 解读

This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear model for the dependent variable, we develop a novel adaptation of the parametric one-step update to a generic second-stage estimator. We provide conditions under which the scaled update is asymptotically normal. We then introduce a…

高频交易者与价格过程AI 解读

Using a dataset that uniquely identifies counterparties to each S&P500 eMini transaction, we classify each market participant as high or low frequency, and each transaction, by the speed of the traders involved. We investigate empirically the comparative influence of high and low frequency traders on the price process, and conversely the influence of the price process on the trading of high and low frequency traders. We find that high frequency traders have a particularly…

一类矩条件模型中函数值参数的导数估计AI 解读

We develop a general approach to estimating the derivative of a function-valued parameter θo(u) that is identified for every value of u as the solution to a moment condition. This setup in particular covers interesting models for conditional distributions, such as quantile regression or distribution regression. Exploiting that θo(u) solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and then estimate the…

对《通过边抽样进行网络交叉验证》的讨论AI 解读

We congratulate the authors for their exciting paper (Li et al., 2020) on the difficult problem of network model selection. The authors have proposed an interesting cross-validation procedure that selects the best network model according to the criterion ... One of the main novelties of the method is the use of matrix completion to reconstruct a full network |$\{\skew6\hat{A}_{ij}\}_{1\leq i\neq j\leq n}$| from the partial set of observations |$\{A_{ij}\}_{(i,\,j)\in\Omega}$|…

《基于边抽样的网络交叉验证》讨论回复AI 解读

We thank the editor for organizing this discussion and giving us the opportunity to read experts’ perspectives on our work. We are grateful to all the discussants for their insightful contributions, which raise many important points and offer suggestions for potential improvements and generalizations of our method. In this rejoinder we provide some clarifications, remarks and selected numerical results in response to these comments. Lei & Lin (2020) conjecture, and we agree,…

《通过边抽样进行网络交叉验证》的讨论AI 解读

We congratulate the authors for a nice contribution to the literature on model selection and assessment for complex network data. The article of Li et al. (2020) enriches the collection of tools available for network data analysis, bringing together different fields such as low-rank matrix estimation, cross-validation and network modelling. This discussion will focus on the |$V$|-fold variant of the edge sampling cross-validation method and its combination with other…

训练标签不完美时的分类AI 解读

Summary We study the effect of imperfect training data labels on the performance of classification methods. In a general setting, where the probability that an observation in the training dataset is mislabelled may depend on both the feature vector and the true label, we bound the excess risk of an arbitrary classifier trained with imperfect labels in terms of its excess risk for predicting a noisy label. This reveals conditions under which a classifier trained with…

半参数截断模型下基于横截面数据的估计AI 解读

Summary Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their…

通过边抽样进行网络交叉验证AI 解读

Summary While many statistical models and methods are now available for network analysis, resampling of network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but it is not directly applicable to networks since splitting network nodes into groups requires deleting edges and destroys some of the network structure. In this paper we propose a new network resampling strategy, based on splitting node pairs…

用于离散参数与不连续似然的非连续哈密顿蒙特卡洛AI 解读

Summary Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables efficient sampling from ordinal parameters through the embedding of probability mass functions into continuous spaces. We motivate our approach through a theory of discontinuous Hamiltonian dynamics and develop a corresponding…

本质直方图AI 解读

Summary The histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the…

特征值的 Lasso 收缩AI 解读

Summary The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

高维双重函数型图模型AI 解读

Summary We consider estimating a functional graphical model from multivariate functional observations. In functional data analysis, the classical assumption is that each function has been measured over a densely sampled grid. However, in practice the functions have often been observed, with measurement error, at a relatively small number of points. We propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a…

放宽容差并作事后校正的近似贝叶斯计算马尔可夫链蒙特卡洛AI 解读

Summary Approximate Bayesian computation enables inference for complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We propose an approach that involves using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure…

基于密度幂散度的稳健经验贝叶斯小区域估计AI 解读

Summary A two-stage normal hierarchical model called the Fay–Herriot model and the empirical Bayes estimator are widely used to obtain indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator can be poor when the assumed normal distribution is misspecified. This article presents a simple modification that makes use of density power divergence and proposes a new robust empirical Bayes small area estimator. The mean…

利用 K 近邻融合套索的自适应非参数回归AI 解读

Summary The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the $K$-nearest-neighbours fused lasso, involves computing the $K$-nearest-neighbours graph of the design points and then performing the fused lasso…

边际似然与交叉验证的关系AI 解读

Summary In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation on held-out data, either through $k$-fold partitioning or leave-$p$-out subsampling. We show that the marginal likelihood is formally equivalent to exhaustive leave-$p$-out crossvalidation averaged over all values of $p$…

高维 Hotelling T² 检验的自适应推广AI 解读

We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling’s $T^{2}$. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the…

局部最近邻分类及其半监督学习应用AI 解读

We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution to the excess risk comes from the decision boundary of the optimal Bayes classifier, but we also show that if these conditions are not satisfied, then the dominant contribution may arise from the tails of the marginal distribution of the…

We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression operators as a special case. We show the optimality of our reconstruction operator and demonstrate that the usually considered regression operators generally cannot be optimal reconstruction operators. Our estimation theory allows for…

通过乘子自助法进行稳健推断AI 解读

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With heavy-tailed observation noise, finite sample properties of the least squares-based methods, typified by the sample mean, are suboptimal both theoretically and empirically. In this paper, we demonstrate that the adaptive Huber regression,…

变点模型的分割与估计：假阳性控制和置信区域AI 解读

To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to…