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贝叶斯 CART 的不确定性量化AI 解读

This work affords new insights into Bayesian CART in the context of structured wavelet shrinkage. The main thrust is to develop a formal inferential framework for Bayesian tree-based regression. We reframe Bayesian CART as a g-type prior which departs from the typical wavelet product priors by harnessing correlation induced by the tree topology. The practically used Bayesian CART priors are shown to attain adaptive near rate-minimax posterior concentration in the supremum…

短程依赖下方差恒定性的渐近检验AI 解读

We present a novel approach to test for heteroscedasticity of a nonstationary time series that is based on Gini’s mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic, we establish new limit theorems for U-statistics of dependent triangular arrays. We derive the asymptotic distribution of the test statistic under the null hypothesis of a constant variance and show that the test is consistent against a…

非光滑非凸统计学习中的广义 Bregman 替代算法分析AI 解读

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror descent, iterative thresholding, DC programming and many others as particular instances. The recharacterization via generalized Bregman functions enables us to construct suitable error measures and establish global convergence rates for…

网络检验中带符号多边形统计量的最优自适应性AI 解读

Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed memberships, (c) have a tractable null distribution and (d) adapt automatically to different levels of sparsity, and achieve the optimal phase diagram. How to find such a test is a challenging problem. We propose the Signed Polygon as a class of new tests. Fixing…

凹扩展线性模型中惩罚样条估计量的渐近性质：收敛速率AI 解读

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order and the smoothness of the unknown functions. According to this theory, the…

维度增长下离散选择模型的最优线性判别器AI 解读

Manski’s celebrated maximum score estimator for the discrete choice model, which is an optimal linear discriminator, has been the focus of much investigation in both the econometrics and statistics literatures, but its behavior under growing dimension scenarios largely remains unknown. This paper addresses that gap. Two different cases are considered: p grows with n but at a slow rate, that is, p/n→0; and p≫n (fast growth). In the binary response model, we recast Manski’s…

弱依赖数据半参数回归的 Wilks 定理AI 解读

The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the present and past values of a vector of covariates. A parametric model for the conditional variance of the series is added to capture further nonlinear effects. We propose suitable moment equations which characterize the mean and variance…

增广极小极大线性估计AI 解读

Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this paper, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plug-in estimator by…

低内在维度数据上支持向量机的自适应学习速率AI 解读

We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under some standard regularity assumptions for regression and classification, we prove learning rates, in which the dimension of the ambient space is replaced by the box-counting dimension of the support of the data generating distribution. In…

固定域渐近下具有 Matérn 协方差的各向同性高斯随机场参数估计AI 解读

A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on Rd with isotropic Matérn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under…

多峰似然函数下的在线推断AI 解读

Let (Yt)t≥1 be a sequence of i.i.d. observations and {fθ,θ∈Rd} be a parametric model. We introduce a new online algorithm for computing a sequence (θˆt)t≥1, which is shown to converge almost surely to argmaxθ∈RdE[logfθ(Y1)] at rate O(log(t)(1+ε)/2t−1/2), with ε>0 a user specified parameter. This convergence result is obtained under standard conditions on the statistical model and, most notably, we allow the mapping θ↦E[logfθ(Y1)] to be multi-modal. However, the computational…

通过分组—排序—融合程序估计有限混合模型的成分数AI 解读

Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure—a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous…

In transfer learning, we wish to make inference about a target population when we have access to data both from the distribution itself, and from a different but related source distribution. We introduce a flexible framework for transfer learning in the context of binary classification, allowing for covariate-dependent relationships between the source and target distributions that are not required to preserve the Bayes decision boundary. Our main contributions are to derive…

Expectiles define a least squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last decade. The behaviour and estimation of unconditional extreme expectiles using independent and identically distributed heavy-tailed observations have been investigated in a recent series of papers. We build here a general theory for the estimation of extreme conditional expectiles in…

协变量偏移中的边际奇异性与标签收益AI 解读

Transfer Learning addresses common situations in Machine Leaning where little or no labeled data is available for a target prediction problem—corresponding to a distribution Q, but much labeled data is available from some related but different data distribution P. This work is concerned with the fundamental limits of transfer, that is, the limits in target performance in terms of (1) sample sizes from P and Q, and (2) differences in data distributions P, Q. In particular, we…

一种简单的条件依赖度量AI 解读

We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X1,…,Xp, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0,1], where the limit is 0 if and only if Y and Z are conditionally independent given X1,…,Xp, and is 1 if and only if Y is equal to a measurable function…

少量处理观测与大量对照观测下的匹配估计AI 解读

We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased in this framework. However, when the number of treated observations is fixed, the estimator is not consistent, and it is generally not asymptotically normal. Since standard inference methods are inadequate, we…

含干扰参数的异质性处理效应置换检验AI 解读

This paper proposes an asymptotically valid permutation test for heterogeneous treatment effects in the presence of an estimated nuisance parameter. Not accounting for the estimation error of the nuisance parameter results in statistics that depend on the particulars of the data generating process, and the resulting permutation test fails to control the Type 1 error, even asymptotically.

处理时点存在差异的双重差分AI 解读

The canonical difference-in-differences (DD) estimator contains two time periods, ”pre” and ”post”, and two groups, ”treatment” and ”control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper shows that the two-way fixed effects estimator equals a weighted average of all possible two-group/two-period DD estimators in the data. A causal interpretation of two-way fixed effects DD estimates requires…

针对平均处理效应的协变量调整 Fisher 随机化检验AI 解读

Fisher’s randomization test (frt) delivers exact p-values under the strong null hypothesis of no treatment effect on any units whatsoever and allows for flexible covariate adjustment to improve the power. Of interest is whether the resulting covariate-adjusted procedure could also be valid for testing the weak null hypothesis of zero average treatment effect. To this end, we evaluate two general strategies for conducting covariate adjustment in frts: the pseudo-outcome…

工具变量独立性下潜在结果分布的识别区域AI 解读

This paper examines the identifying power of instrument exogeneity in the treatment effect model. We derive the identification region of the potential outcome distributions, which are the collection of distributions that are compatible with data and with the restrictions of the model. We consider identification when (i) the instrument is independent of each of the potential outcomes (marginal independence), (ii) the instrument is independent of the potential outcomes and…

多时期双重差分的识别、估计与推断AI 解读

In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the “parallel trends assumption” holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create…

异质处理效应下事件研究中的动态效应估计AI 解读

To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment. We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag can be contaminated by effects from other periods, and apparent pretrends can arise solely from treatment effects heterogeneity. We propose an alternative estimator that is free of contamination, and…

动态处理效应非参数模型中的识别AI 解读

This paper develops a nonparametric model that represents how sequences of outcomes and treatment choices influence one another in a dynamic manner. In this setting, we are interested in identifying the average outcome for individuals in each period, had a particular treatment sequence been assigned. The identification of this quantity allows us to identify the average treatment effects (ATE’s) and the ATE’s on transitions, as well as the optimal treatment regimes, namely,…