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乘性随机波动率驱动随机微分方程的线性乘子非参数估计AI 解读

We study the problem of nonparametric estimation of the linear multiplier function $θ(t)$ for processes satisfying stochastic differential equations of the type $$dX_t= θ(t)X_t dt+ ε\; σ_1(t,X_t)σ_2(t,Y_t)dW_t, X_0=x_0, 0 \leq t \leq T$$ where $\{W_t, t\geq 0\}$ is a standard Brownian motion, $\{Y_t, t\geq 0\}$ is a process adapted to the filtration generated by the Brownian motion. We study the problem of estimation of the unknown function $θ(.)$ as $ε\rightarrow 0$ based…

高维迁移学习中的非凸惩罚同步估计与数据集选择AI 解读

In this paper, we propose to estimate model parameters and identify informative source datasets simultaneously for high-dimensional transfer learning problems with the aid of a non-convex penalty, in contrast to the separate useful dataset selection and transfer learning procedures in the existing literature. To numerically solve the non-convex problem with respect to two specific statistical models, namely the sparse linear regression and the generalized low-rank trace…

非平稳时间序列对白噪声假设的实质性偏离检测AI 解读

We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non-stationary time series. Second, we address the problem that a white noise test, for example checking the residuals of a model fit, is usually not performed because one believes in this hypothesis, but thinks that the white noise hypothesis may be…

乘性随机波动率驱动随机微分方程的趋势非参数估计AI 解读

We discuss nonparametric estimation of the trend coefficient in models governed by a stochastic differential equation driven by a multiplicative stochastic volatility.

重归一化 Bernstein-von Mises 定理下的线性泛函有效可信椭球AI 解读

We consider an infinite-dimensional Gaussian regression model, equipped with a high-dimensional Gaussian prior. We address the frequentist validity of posterior credible sets for a vector of linear functionals. We specify conditions for a 'renormalized' Bernstein-von Mises theorem (BvM), where the posterior, centered at its mean, and the posterior mean, centered at the ground truth, have the same normal approximation. This requires neither a solution to the information…

多重纳什均衡下的稳健网络干预配置AI 解读

Many policy problems involve designing individualized treatment allocation rules to maximize the equilibrium social welfare of interacting agents. Focusing on large-scale simultaneous decision games with strategic complementarities, we develop a method to estimate an optimal treatment allocation rule that is robust to the presence of multiple equilibria. Our approach remains agnostic about changes in the equilibrium selection mechanism under counterfactual policies, and we…

部分正则化普通最小二乘插值器的代数与统计性质AI 解读

Modern deep learning has revealed a surprising statistical phenomenon known as benign overfitting, with high-dimensional linear regression being a prominent example. This paper contributes to ongoing research on the ordinary least squares (OLS) interpolator, focusing on the partial regression setting, where only a subset of coefficients is implicitly regularized. On the algebraic front, we extend Cochran's formula and the leave-one-out residual formula for the partial…

用非参数非平稳空间模型正则化集合卡尔曼滤波AI 解读

The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in high dimensions the Ensemble Kalman Filter's (EnKF) ensemble does not contain enough information to specify the prior covariance matrix accurately. This necessitates the need for regularization of the analysis (observation update) problem. We…

基于 Wasserstein 距离的多元正则变动极值依赖极小极大估计AI 解读

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are derived for the multivariate Peak-over-Threshold estimator in terms of the $p$-th order Wasserstein distance, and information-theoretic lower bounds for the minimax risks are established. The convergence rate of the estimator is shown to be…

高维数据的高效子抽样AI 解读

In the field of big data analytics, the search for efficient subdata selection methods that enable robust statistical inferences with minimal computational resources is of high importance. A procedure prior to subdata selection could perform variable selection, as only a subset of a large number of variables is active. We propose an approach when both the size of the full dataset and the number of variables are large. This approach firstly identifies the active variables by…

统计不可知回归：验证回归模型的机器学习方法AI 解读

Regression analysis is a central topic in statistical modeling, aimed at estimating the relationships between a dependent variable, commonly referred to as the response variable, and one or more independent variables, i.e., explanatory variables. Linear regression is by far the most popular method for performing this task in various fields of research, such as data integration and predictive modeling when combining information from multiple sources. Classical methods for…

当市场摩擦具有分数性：高频数据中的粗糙噪声AI 解读

The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time stochastic process that locally behaves as fractional Brownian motion. Assuming that the underlying efficient price process follows a continuous Itô semimartingale, we derive consistent estimators and asymptotic confidence intervals for…

粗糙波动率下特征函数的短时展开及其应用AI 解读

We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an Itô semimartingale over a shrinking time interval. The spot characteristics of the Itô semimartingale are allowed to have dynamics of general form. In particular, their paths can be rough, that is, exhibit local behavior like that of a fractional Brownian motion, while at the same time have jumps with arbitrary degree of activity. The expansion result shows the…

部分聚类随机试验中的因果推断AI 解读

Clustering and dependence are common in trials. For example, in some cluster randomized trials (CRTs), pre-existing clusters are enrolled, randomized, and serve as the basis of intervention delivery. Such CRTs are "fully clustered": participants are dependent within clusters. In contrast, "partially clustered" trials contain a mix of participants that are dependent within clusters and participants that are completely independent. One example of this design is a trial where…

分布的即时预测：函数型 MIDAS 模型AI 解读

We propose a functional MIDAS model to leverage high-frequency information for forecasting and nowcasting distributions observed at a lower frequency. We approximate the low-frequency distribution using Functional Principal Component Analysis and consider a group lasso spike-and-slab prior to identify the relevant predictors in the finite-dimensional SUR-MIDAS approximation of the functional MIDAS model. In our application, we use the model to nowcast the U.S. households'…

层级断点回归设计：估计子群体处理效应AI 解读

Regression discontinuity design (RDD) is widely adopted for causal inference under intervention determined by a continuous variable. While one is interested in treatment effect heterogeneity by subgroups in many applications, RDD typically suffers from small subgroup-wise sample sizes, which makes the estimation results highly instable. To solve this issue, we introduce hierarchical RDD (HRDD), a hierarchical Bayes approach for pursuing treatment effect heterogeneity in RDD.…

卡尺合成匹配：结合局部合成控制的广义半径匹配AI 解读

Matching promises transparent causal inferences for observational data, making it an intuitive approach for many applications. In practice, however, standard matching methods often perform poorly compared to modern approaches such as response-surface modeling and optimizing balancing weights. We propose Caliper Synthetic Matching (CSM) to address these challenges while preserving simple and transparent matches and match diagnostics. CSM extends Coarsened Exact Matching by…

厚尾高维时间序列的稳健估计AI 解读

We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $α$-th moment with $α\in (1,2]$. To handle the heavy-tailed dependent data, we propose a Catoni type truncated minimization problem framework and obtain an $\mathcal{O}\big( \big( (d_1+d_2) (d_1\land d_2) \log^2 n / n \big)^{(α- 1)/α} \big)$ order excess risk, where $d_1$ and $d_2$ are the dimensionality and $n$ is the number of…

两阶段极值估计量的推断AI 解读

We present a simulation-based inference approach for two-stage estimators, focusing on extremum estimators in the second stage. We accommodate a broad range of first-stage estimators, including extremum estimators, high-dimensional estimators, and other types of estimators such as Bayesian estimators. The key contribution of our approach lies in its ability to estimate the asymptotic distribution of two-stage estimators, even when the distributions of both the first- and…

主成分分析能否保留稀疏弱因子模型的稀疏性？AI 解读

This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the approximately upper triangular (block) structure of the rotation matrix. It implies an asymmetric relationship among factors: the rotated loadings for a stronger factor can be contaminated by those from a weaker one, but the loadings for a weaker…

信息型MCMC采样的几何方法AI 解读

A Riemannian geometric framework for Markov chain Monte Carlo (MCMC) is developed where using the Fisher-Rao metric on the manifold of probability density functions (pdfs), informed proposal densities for Metropolis-Hastings (MH) algorithms are constructed. We exploit the square-root representation of pdfs under which the Fisher-Rao metric boils down to the standard $L^2$ metric on the positive orthant of the unit hypersphere. The square-root representation allows us to…

利用 Copula 相等假设部分识别面板数据中的分布处理效应AI 解读

This paper aims to partially identify the distributional treatment effects (DTEs) that depend on the unknown joint distribution of treated and untreated potential outcomes. We construct the DTE bounds using panel data and allow individuals to switch between the treated and untreated states more than once over time. Individuals are grouped based on their past treatment history, and DTEs are allowed to be heterogeneous across different groups. We provide two alternative…

非参数工具变量模型中的自适应最优速率假设检验AI 解读

We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve two-stage least squares estimators. We provide computationally simple, data-driven choices of sieve tuning…

基于调查权重正则化的差分隐私有限总体估计AI 解读

In general, it is challenging to release differentially private versions of survey-weighted statistics with low error for acceptable privacy loss. This is because weighted statistics from complex sample survey data can be more sensitive to individual survey response and weight values than unweighted statistics, resulting in differentially private mechanisms that can add substantial noise to the unbiased estimate of the finite population quantity. On the other hand, simply…