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查尔斯·斯坦与不变性：从 Hunt–Stein 定理谈起AI 解读

When statistical decision theory was emerging as a promising new paradigm, Charles Stein was to play a major role in the development of minimax theory for invariant statistical problems. In some of his earliest work with Gil Hunt, he set out to prove that, in problems where invariant procedures have constant risk, any best invariant test would be minimax among all tests. Although finding it not quite true in general, this led to the legendary Hunt–Stein theorem, which…

We revisit a paper by Charles Stein, and discuss its follow-up.

连接存在依赖时的社区检测AI 解读

In network analysis, within-community members are more likely to be connected than between-community members, which is reflected in that the edges within a community are intercorrelated. However, existing probabilistic models for community detection such as the stochastic block model (SBM) are not designed to capture the dependence among edges. In this paper, we propose a new community detection approach to incorporate intra-community dependence of connectivities through the…

时间序列中变点的最优估计AI 解读

This paper establishes asymptotic theory for optimal estimation of change points in general time series models under α-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real…

用于α散度最小化的无限维梯度下降AI 解读

This paper introduces the (α,Γ)-descent, an iterative algorithm which operates on measures and performs α-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used variational approximation by adding a prior on the variational parameters in the form of a measure. We prove that for a rich family of functions Γ, this algorithm leads at each step to a systematic decrease in the α-divergence and derive convergence results. Our…

非参数多元有限混合模型的成分数量估计AI 解读

We propose a novel estimator for the number of mixture components (denoted by M) in a nonparametric finite mixture model. The setting that we consider is one where the analyst has repeated observations of K≥2 variables that are conditionally independent given a finitely supported latent variable with M support points. Under a mild assumption on the joint distribution of the observed and latent variables, we show that an integral operator T that is identified from the data…

含时变协变量的非参数风险函数提升估计AI 解读

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent…

扩展可容许决策程序及其非标准贝叶斯风险AI 解读

For finite parameter spaces, among decision procedures with finite risk functions, a decision procedure is extended admissible if and only if it is Bayes. Various relaxations of this classical equivalence have been established for infinite parameter spaces, but these extensions are each subject to technical conditions that limit their applicability, especially to modern (semi and nonparametric) statistical problems. Using results in mathematical logic and nonstandard…

多维保序回归及其他单调模型的置信区间AI 解读

We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, Han and Zhang (2020) obtained a pointwise limit distribution theory for the so-called block max–min and min–max estimators (Fokianos, Leucht and Neumann (2020); Deng and Zhang (2020)) in this model, but inference remains a difficult problem due to the nuisance parameter in the limit distribution that involves multiple unknown partial derivatives of the…

波动率估计的耦合理论AI 解读

This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting.…

二阶 Stein 公式：SURE 的风险估计及高维推断应用AI 解读

Stein’s formula states that a random variable of the form z⊤f(z)−divf(z) is mean-zero for all functions f with integrable gradient. Here, divf is the divergence of the function f and z is a standard normal vector. This paper aims to propose a second-order Stein formula to characterize the variance of such random variables for all functions f(z) with square integrable gradient, and to demonstrate the usefulness of this second-order Stein formula in various applications. In…

重尾稀疏图的一致非参数估计AI 解读

We study graphons as a nonparametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. In contrast to previous work, we relax the usual boundedness assumption for the generating graphon and instead assume only integrability, so that we can handle networks that have long tails in their degree distributions. We also relax the usual assumption that the graphon is defined on the unit…

Lasso 的分布：稀疏球上的一致控制与自适应参数调节AI 解读

The Lasso is a popular regression method for high-dimensional problems in which the number of parameters θ1,…,θN, is larger than the number n of samples: N>n. A useful heuristics relates the statistical properties of the Lasso estimator to that of a simple soft-thresholding denoiser, in a denoising problem in which the parameters (θi)i≤N are observed in Gaussian noise, with a carefully tuned variance. Earlier work confirmed this picture in the limit n,N→∞, pointwise in the…

全连接深度神经网络回归估计的收敛速率AI 解读

Recent results in nonparametric regression show that deep learning, that is, neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in these results is that their network architecture has a further constraint, namely the network sparsity. In this paper, we show that we can get similar results…

具有两个有界矩的分布下的稳健 k-means 聚类AI 解读

We consider the robust algorithms for the k-means clustering problem where a quantizer is constructed based on N independent observations. Our main results are median of means based nonasymptotic excess distortion bounds that hold under the two bounded moments assumption in a general separable Hilbert space. In particular, our results extend the renowned asymptotic result of (Ann. Statist. 9 (1981) 135–140) who showed that the existence of two moments is sufficient for…

两样本汇总数据孟德尔随机化中的去偏逆方差加权估计AI 解读

Mendelian randomization (MR) has become a popular approach to study the effect of a modifiable exposure on an outcome by using genetic variants as instrumental variables. A challenge in MR is that each genetic variant explains a relatively small proportion of variance in the exposure and there are many such variants, a setting known as many weak instruments. To this end, we provide a theoretical characterization of the statistical properties of two popular estimators in MR:…

混合首次穿越时间模型的似然计算AI 解读

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent Lévy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of Lévy processes. We use our method to implement a maximum…

递增拍卖中的竞价摩擦AI 解读

This paper develops an approach for identifying and estimating the distribution of valuations in ascending auctions where an indeterminate number of bidders have an unknown number of bidding opportunities. To finesse the complications for identification and estimation due to multiple equilibria, our empirical analysis is based on the fact that bidders play undominated strategies in every equilibrium. We apply the model to a monthly financial market in which local banks…

非法药物使用、教育与劳动力市场结果AI 解读

In this paper we investigate the causal effects of consuming illegal drugs on educational attainment, employment, and wages. To identify these effects we develop and estimate a dynamic structural model to jointly consider decisions of whether to consume drugs, attend school, participate in the labor force, and save.

动态离散选择模型的半参数估计AI 解读

We consider the estimation of dynamic binary choice models in a semiparametric setting, in which the per-period utility functions are known up to a finite number of parameters, but the distribution of utility shocks is left unspecified. This semiparametric setup differs from most of the existing identification and estimation literature for dynamic discrete choice models. To show identification we derive and exploit a new recursive representation for the unknown quantile…

结构动态 Logit 模型中未观测异质性的充分统计量AI 解读

We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is nonparametric, i.e., fixed-effects model. We consider models with two endogenous state variables: the lagged decision variable, and the time duration in the last choice. This class of models includes as particular cases important economic applications…

国际个股收益中的因子与风险溢价AI 解读

We propose an estimation methodology tailored for large unbalanced panels of individual stock returns to study the factor structure and expected returns in international stock markets. We show that the local market is necessary to capture the factor structure in both developed and emerging markets. Neither the presence of multiple world or regional risk factors, systematic currency risk factors, nor a country-specific currency subsumes the importance of the local market…

具有因子结构的多任务分位数回归AI 解读

A multivariate quantile regression model with a factor structure is proposed to study data with multivariate responses with covariates. The factor structure is allowed to vary with the quantile levels, which is more flexible than the classical factor models. Assuming the number of factors is small, and the number of responses and the input variables are growing with the sample size, the model is estimated with the nuclear norm regularization. The incurred optimization…

空间计量模型贝叶斯估计的大样本性质AI 解读

This paper studies asymptotic properties of a posterior probability density and Bayesian estimators of spatial econometric models in the classical statistical framework. We focus on the high-order spatial autoregressive model with spatial autoregressive disturbance terms, due to a computational advantage of Bayesian estimation. We also study the asymptotic properties of Bayesian estimation of the spatial autoregressive Tobit model, as an example of nonlinear spatial models.…