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量化非平稳函数值过程结构假设偏离的一般框架AI 解读

We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral density operators. The second-order dynamics are well known to be elements of the space of trace class operators, the latter is a Banach space of type 1 and of cotype 2, which makes the development of statistical inference tools more…

基于低频观测的扩散过程一致推断AI 解读

Let (Xt) be a reflected diffusion process in a bounded convex domain in Rd, solving the stochastic differential equation dXt=∇f(Xt)dt+ 2f(Xt)dWt,t≥0, with Wt a d-dimensional Brownian motion. The data X0,XD,…,XND consist of discrete measurements and the time interval D between consecutive observations is fixed so that one cannot ‘zoom’ into the observed path of the process. The goal is to infer the diffusivity f and the associated transition operator Pt,f. We prove…

高维线性模型中 L2-boosting 的早停AI 解读

Increasingly high-dimensional data sets require that estimation methods do not only satisfy statistical guarantees but also remain computationally feasible. In this context, we consider L2-boosting via orthogonal matching pursuit in a high-dimensional linear model and analyze a data-driven early stopping time τ of the algorithm, which is sequential in the sense that its computation is based on the first τ iterations only. This approach is much less costly than established…

灵活函数库下斜切回归树的收敛速度AI 解读

We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned splits involving only a single covariate). While this methodology has garnered significant attention from the computer science and optimization communities since the mid-80s, the advantages they offer over their axis-aligned counterparts…

对抗训练中的过度参数化之弊：随机特征回归的稳健泛化分析AI 解读

Successful deep learning models often involve training neural network architectures that contain more parameters than the number of training samples. Such overparametrized models have recently been extensively studied, and the virtues of overparametrization have been established from both the statistical perspective, via the double-descent phenomenon, and the computational perspective via the structural properties of the optimization landscape. Despite this success, it is…

动态处理效应的高维推断AI 解读

Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders. Doubly robust (DR) approaches have emerged as promising tools for estimating treatment effects due to their flexibility. However, we showcase that the traditional DR approaches that only focus on the DR representation of the expected outcomes may fall short of delivering optimal results. In this paper, we propose a novel DR…

异质性因果效应估计的极小极大收敛率AI 解读

Estimation of heterogeneous causal effects - i.e., how effects of policies and treatments vary across subjects - is a fundamental task in causal inference. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but questions surrounding optimality have remained largely unanswered. In particular, a minimax theory of optimality has yet to be developed, with the minimax rate of convergence and construction of rate-optimal…

度量统计：利用距离剖面探索随机对象并进行推断AI 解读

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain structural conditions and features a probability measure. We refer to the random elements of such spaces as random objects and to the emerging field that deals with their statistical analysis as metric statistics. Metric statistics provides…

缺失数据下异方差主成分分析的统计推断AI 解读

This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly underexplored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in general difficult in high dimension, the challenge is further compounded by the prevalent presence of missing data and heteroskedastic noise. We propose a novel approach to performing valid inference on the principal subspace, on the basis…

尾部风险的度量AI 解读

We comprehensively investigate the usefulness of tail risk measures proposed in the literature. We evaluate their statistical as well as their economic validity. The option-implied measure of Bollerslev and Todorov (2011b) (BT11Q) performs best overall. While some other tail risk measures excel at specialized tasks, BT11Q performs well in all tests: First, BT11Q can predict both future tail events and future tail volatility. Second, it has predictive power for returns in…

短尾数据的极端期望分位数估计AI 解读

The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of expectiles. While the theory of expectile estimation at central levels is substantial, tail estimation at extreme levels has so far only been considered when the tail of the underlying distribution is heavy. This article is the first work…

可能不可逆 SVARMA 模型的识别与估计：规范化典范 WHF 参数化AI 解读

This article focuses on the parametrisation, identifiability, and (quasi-) maximum likelihood (QML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models. SVAR models are routinely adopted due to their well-known implementation strategy. However, for various economic and statistical reasons, multivariate SVARMA settings are often more suitable. These settings introduce complexity in the analysis, primarily due to the presence…

局部趋于单位根的动态 Tobit 模型AI 解读

This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive. Surprisingly, despite the…

载荷机制切换高维因子模型的估计与推断AI 解读

This paper proposes maximum (quasi)likelihood estimation for high dimensional factor models with regime switching in the loadings. The model parameters are estimated jointly by the EM (expectation maximization) algorithm, which in the current context only requires iteratively calculating regime probabilities and principal components of the weighted sample covariance matrix . When regime dynamics are taken into account, smoothed regime probabilities are calculated using a…

利用变化中的变化方法修正样本流失偏差AI 解读

Attrition is a common and potentially important threat to internal validity in treatment effect studies. We extend the changes-in-changes approach to identify the average treatment effect for respondents and the entire study population in the presence of attrition. Our method, which exploits baseline outcome data, can be applied to randomized experiments as well as quasi-experimental difference-in-difference designs. A formal comparison highlights that while widely used…

长记忆下交互固定效应面板模型的稳健推断：频域方法AI 解读

This paper studies a linear panel data model with interactive fixed effects wherein regressors, factors and idiosyncratic error terms are all stationary but with potential long memory. The setup involves a new formulation of panel data models, where weakly dependent regressors, factors and idiosyncratic errors are embedded as a special case. Standard methods based on principal component decomposition and least squares estimation, as in Bai (2009), are found to be biased and…

基于有限对数正态—威布尔混合的参数化风险中性密度估计AI 解读

This paper proposes a new parametric risk-neutral density (RND) estimator based on a finite lognormal-Weibull mixture (LWM) density. We establish the consistency and asymptotic normality of the LWM method in a general misspecified parametric framework. Based on the theoretical results, we propose a sequential test procedure to evaluate the goodness-of-fit of the LWM model, which leads to an adaptive choice for the number and type of mixture components. Our simulation results…

动态偏相关模型AI 解读

We introduce a new scalable model for dynamic conditional correlation matrices based on a recursion of dynamic bivariate partial correlation models. By exploiting the model’s recursive structure and the theory of perturbed stochastic recurrence equations, we establish stationarity, ergodicity, and filter invertibility in the multivariate setting using conditions for bivariate slices of the data only. From this, we establish consistency and asymptotic normality of the maximum…

高维潜变量模型的混合无校正 Langevin 方法AI 解读

The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a novel approximate Bayesian method based on the Langevin diffusion process. The method employs the Fisher identity to integrate out the latent variables, which makes it accurate and computationally feasible when applied to big data. In contrast…

大规模稳定匹配的大数定律AI 解读

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In this paper, we consider a setting in which the researcher observes either all or a nontrivial fraction of outcomes from a stable matching. We establish a concentration inequality for empirical matching probabilities assuming strong…

配对随机实验中的协变量调整AI 解读

This paper studies inference for the average treatment effect (ATE) in experiments in which treatment status is determined according to “matched pairs” and it is additionally desired to adjust for observed, baseline covariates to gain further precision. By a “matched pairs” design, we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates, and finally, within each pair, one unit is selected at random for…

模糊断点回归中局部平均处理效应识别条件的检验AI 解读

This paper derives testable implications of the identifying conditions for the local average treatment effect in fuzzy regression discontinuity designs. We show that the testable implications of these identifying conditions are a finite number of inequality restrictions on the observed data distribution. We then propose a specification test for the testable implications and show that the proposed test controls the size and is asymptotically consistent. We apply our test to…

多个工具变量下的向量单调性假设AI 解读

When a researcher combines multiple instrumental variables for a single binary treatment, the monotonicity assumption of the local average treatment effects (LATE) framework can become restrictive: it requires that all units share a common direction of response even when separate instruments are shifted in opposing directions. What I call vector monotonicity, by contrast, simply assumes treatment uptake to be monotonic in all instruments. I characterize the class of causal…

第一价格拍卖中卖方预期收入的估计与推断AI 解读

I propose an estimator for the seller’s expected revenue function in a first-price sealed-bid auction with independent private values and symmetric bidders, who can exhibit constant relative risk aversion and bid according to the Bayesian Nash equilibrium. I build the proposed estimator from pseudo-private values, which can be estimated from observed bids, and show that it is pointwise and uniformly consistent: the corresponding optimal nonparametric rates of convergence can…