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识别假设检验的警示：真人秀真的降低了青少年生育率吗？AI 解读

Evaluating policy changes that occur everywhere at the same time is difficult because of the lack of a clear counterfactual. Hoping to address this problem, researchers often proxy for differential exposure using some observed characteristic in the pretreatment period. As a cautionary tale of how difficult identification is in such settings, we re-examine the results of an influential paper by Melissa Kearney and Phillip Levine, who found that the MTV program 16 and Pregnant…

马尔可夫切换三遍回归滤波器AI 解读

We introduce a new approach for the estimation of high-dimensional factor models with regime-switching factor loadings by extending the linear three-pass regression filter to settings where parameters can vary according to Markov processes. The new method, denoted as Markov-switching three-pass regression filter (MS-3PRF), is suitable for datasets with large cross-sectional dimensions, since estimation and inference are straightforward, as opposed to existing…

GARCH 模型中遗漏乘法型长期成分的检验AI 解读

We consider the problem of testing for an omitted multiplicative long-term component in GARCH-type models. Under the alternative, there is a two-component model with a short-term GARCH component that fluctuates around a smoothly time-varying long-term component which is driven by the dynamics of an explanatory variable. We suggest a Lagrange multiplier statistic for testing the null hypothesis that the variable has no explanatory power. We derive the asymptotic theory for…

用于稀疏且具有重叠社区结构图的可交换随机测度AI 解读

Summary We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process and naturally generalizes existing probabilistic models with overlapping block structure to the sparse regime. Our construction builds on vectors of completely random measures and has interpretable parameters, each node being assigned a vector representing its levels of affiliation to some latent…

时变随机对象的函数型模型AI 解读

Summary Functional data analysis provides a popular toolbox of functional models for the analysis of samples of random functions that are real valued. In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global linear structure and therefore common approaches that have been used with great success…

右奇异向量投影图：潜在混杂下的快速高维协方差估计AI 解读

Summary We consider the problem of estimating a high dimensional p × p covariance matrix Σ, given n observations of confounded data with covariance Σ+ΓΓT, where Γ is an unknown p × q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection onto the right singular vectors of the observed data matrix, which we call right singular vector projection (RSVP). Our theoretical analysis of this method reveals that, in contrast with…

Sumca：蒙特卡洛辅助的二阶无偏均方预测误差估计AI 解读

Summary We propose a simple, unified, Monte-Carlo-assisted approach (called ‘Sumca’) to second-order unbiased estimation of the mean-squared prediction error (MSPE) of a small area predictor. The MSPE estimator proposed is easy to derive, has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor, empirical best predictor and post-model-selection empirical best linear unbiased predictor and…

分类未观测混杂下双重负控调整的多重稳健因果推断AI 解读

Summary Unmeasured confounding is a threat to causal inference in observational studies. In recent years, the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a long-standing tradition in laboratory sciences and epidemiology to rule out non-causal explanations, although they have been used primarily for bias detection. Recently, Miao and colleagues have described sufficient conditions under…

高维线性回归解释方差的半监督推断及其应用AI 解读

Summary The paper considers statistical inference for the explained variance βTΣβ under the high dimensional linear model Y = Xβ + ε in the semisupervised setting, where β is the regression vector and Σ is the design covariance matrix. A calibrated estimator, which efficiently integrates both labelled and unlabelled data, is proposed. It is shown that the estimator achieves the minimax optimal rate of convergence in the general semisupervised framework. The optimality result…

近似贝叶斯计算中的模型误设：后果与诊断AI 解读

Summary We analyse the behaviour of approximate Bayesian computation (ABC) when the model generating the simulated data differs from the actual data-generating process, i.e. when the data simulator in ABC is misspecified. We demonstrate both theoretically and in simple, but practically relevant, examples that when the model is misspecified different versions of ABC can yield substantially different results. Our theoretical results demonstrate that even though the model is…

高维数据下合并概率与非概率样本的双重稳健推断AI 解读

Summary We consider integrating a non-probability sample with a probability sample which provides high dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples. In the second step, we focus on a doubly…

多项式时间内实现次高斯速率的均值估计AI 解读

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved by the empirical mean are large compared to the case that $X$ is Gaussian or sub-Gaussian. We offer the first polynomial time algorithm to estimate the mean with sub-Gaussian-size confidence intervals under such mild assumptions. Our…

连续函数 Banach 空间中的函数型数据分析AI 解读

Functional data analysis is typically conducted within the $L^{2}$-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data machinery to real-world problems, often based on dimension reduction techniques such as functional principal component analysis. At the same time, there have recently been a number of publications that sidestep dimension reduction steps and focus on a fully functional $L^{2}$…

抛物型随机偏微分方程的高频分析AI 解读

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for multipower variations and related functionals to construct consistent nonparametric estimators and asymptotic confidence bounds for the integrated volatility process. As a byproduct of our analysis, we also obtain feasible estimators for the regularity of the spatial…

Archimax Copula 的统计推断AI 解读

Archimax copula models can account for any type of asymptotic dependence between extremes and at the same time capture joint risks at medium levels. An Archimax copula is characterized by two functional parameters: the stable tail dependence function $\ell $, and the Archimedean generator $\psi $ which distorts the extreme-value dependence structure. This article develops semiparametric inference for Archimax copulas: a nonparametric estimator of $\ell $ and a moment-based…

利用数据子集证明最大似然估计一致性及其在多元混合模型中的应用AI 解读

We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. It requires neither that the data consist of independent observations, nor that the observations can be modeled as a stationary stochastic process. Compared to existing asymptotic theory using the idea of subsets, we substantially weaken…

具有统计保证的 α 变分推断AI 解读

We provide statistical guarantees for a family of variational approximations to Bayesian posterior distributions, called $\alpha $-VB, which has close connections with variational approximations of tempered posteriors in the literature. The standard variational approximation is a special case of $\alpha $-VB with $\alpha =1$. When $\alpha \in (0,1]$, a novel class of variational inequalities are developed for linking the Bayes risk under the variational approximation to the…

Hurst 函数估计AI 解读

This paper considers a wide range of issues concerning the estimation of the Hurst function of a multifractional Brownian motion when the process is observed on a regular grid. A theoretical lower bound for the minimax risk of this inference problem is established for a wide class of smooth Hurst functions. We also propose a new nonparametric estimator and show that it is rate optimal. Implementation issues of the estimator including how to overcome the presence of a…

高维数据下正则化校准估计的处理效应模型辅助推断AI 解读

Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. We develop new methods and theory to obtain not only doubly robust point estimators for average treatment effects, which remain consistent if either the propensity score model or the outcome regression model is correctly specified, but also model-assisted confidence intervals, which…

Ising 模型参数的联合估计AI 解读

We study joint estimation of the inverse temperature and magnetization parameters $(\beta ,B)$ of an Ising model with a nonnegative coupling matrix $A_{n}$ of size $n\times n$, given one sample from the Ising model. We give a general bound on the rate of consistency of the bi-variate pseudo-likelihood estimator. Using this, we show that estimation at rate $n^{-1/2}$ is always possible if $A_{n}$ is the adjacency matrix of a bounded degree graph. If $A_{n}$ is the scaled…

存在干扰的网络中处理效应估计的实验设计AI 解读

In this paper, we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a “quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control…

指数族中的多维多尺度扫描：极限理论与统计结论AI 解读

We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_{i}\}_{i\in \{1,\ldots,n\}^{d}}$, each distributed according to a one-dimensional natural exponential family $\mathcal{F}=\{F_{\theta }\}_{\theta \in \Theta }$. Given some baseline parameter $\theta _{0}\in \Theta $, the field is scanned using local likelihood ratio tests to detect from a (large) given system of regions $\mathcal{R}$ those regions $R\subset \{1,\ldots,n\}^{d}$…

高维最大值统计量的自助法：弱方差衰减下的近参数速率及应用AI 解读

In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of “max statistics” in high-dimensional problems. A leading example of such a statistic is the coordinatewise maximum of a sample average of $n$ random vectors in $\mathbb{R}^{p}$. Existing results for this statistic show that the bootstrap can work when $n\ll p$, and rates of approximation (in Kolmogorov distance) have been obtained with only logarithmic dependence in $p$.…

单调函数非参数推断的统一研究AI 解读

The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the greatest convex minorant or least concave majorant of an estimator of a primitive function. In this paper, we provide general conditions for consistency and pointwise convergence in distribution of a class of generalized Grenander-type…