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函数型数据的阶数确定AI 解读

Dimension reduction is often necessary in functional data analysis, with functional principal component analysis being one of the most widely used techniques. A key challenge in applying these methods is determining the number of eigen-pairs to retain, a problem known as order determination. When a covariance function admits a finite representation, the challenge becomes estimating the rank of the associated covariance operator. While this problem is straightforward when the…

基于预测综合的贝叶斯投资组合优化AI 解读

Portfolio optimization is a critical task in investment. Most existing portfolio optimization methods require information on the distribution of returns of the assets that make up the portfolio. However, such distribution information is usually unknown to investors. Various methods have been proposed to estimate distribution information, but their accuracy greatly depends on the uncertainty of the financial markets. Due to this uncertainty, a model that could well predict…

聚类工具变量模型中多工具与弱工具下的推断AI 解读

Data clustering reduces the effective sample size from the number of observations towards the number of clusters. For instrumental variable models this reduced effective sample size makes the instruments more likely to be weak, in the sense that they contain little information about the endogenous regressor, and many, in the sense that their number is large compared to the sample size. Consequently, weak and many instrument problems for estimators and tests in instrumental…

高维扩散过程漂移函数 Lasso 估计的抽样效应AI 解读

In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. We consider both a general linear form for the drift function and the particular case of the Ornstein-Uhlenbeck (OU) process. Assuming sparsity of the parameter vector, we examine the statistical behavior of the Lasso estimator for the unknown parameter. Our primary…

成交价格截断下的拍卖识别AI 解读

I establish nonparametric identification results in first- and second-price auctions when transaction prices are truncated by a binding reserve price under a range of information structures. When the number of potential bidders is fixed and known across all auctions, if only the transaction price is observed, the bidders' private-value distribution is identified in second-price auctions but not in first-price auctions. Identification in first-price auctions can be achieved…

HAC 估计的自动阶数与带宽选择及特征值调整缺陷AI 解读

In this paper, we propose a new heteroskedasticity and autocorrelation consistent covariance matrix estimator based on the prewhitened kernel estimator and a localized leave-one-out frequency domain cross-validation (FDCV). We adapt the cross-validated log likelihood (CVLL) function to simultaneously select the order of the prewhitening vector autoregression (VAR) and the bandwidth. The prewhitening VAR is estimated by the Burg method without eigen adjustment as we find the…

利用逐级比率估计对 trawl 过程进行基于模拟的推断AI 解读

The growing availability of large and complex datasets has increased interest in temporal stochastic processes that can capture stylized facts such as marginal skewness, non-Gaussian tails, long memory, and even non-Markovian dynamics. While such models are often easy to simulate from, parameter estimation remains challenging. Simulation-based inference (SBI) offers a promising way forward, but existing methods typically require large training datasets or complex…

Itô 过程的条件局部独立检验及动态因果发现应用AI 解读

Inferring causal relationships from dynamical systems is the central interest of many scientific inquiries. Conditional local independence, which describes whether the evolution of one process is influenced by another process given additional processes, is important for causal learning in such systems. In this paper, we propose a hypothesis test for conditional local independence in Itô processes. Our test is grounded in the semimartingale decomposition of the Itô process,…

未知信息结构下动态博弈的识别与估计AI 解读

We develop an empirical framework for analyzing dynamic games when the underlying information structure is unknown to the analyst. We introduce \textit{Markov correlated equilibrium}, a dynamic analog of Bayes correlated equilibrium, and show that its predictions coincide with the Markov perfect equilibrium predictions attainable when players observe richer signals than the analyst assumes. We provide tractable methods for informationally robust estimation, inference, and…

Bootstrap 诊断检验AI 解读

Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that (a) induce no pre-testing bias, (b) use the same critical values across applications, and (c) are consistent against deviations from asymptotic normality. The tests compare the conditional distribution of a bootstrap statistic with the…

加密货币网络数据中的张量时间序列变点检测AI 解读

Financial fraud has been growing exponentially in recent years. The rise of cryptocurrencies as an investment asset has simultaneously seen a parallel growth in cryptocurrency scams. To detect possible cryptocurrency fraud, and in particular market manipulation, previous research focused on the detection of changes in the network of trades; however, market manipulators are now trading across multiple cryptocurrency platforms, making their detection more difficult. Hence, it…

关于条件异方差时间序列拟极大似然估计的随机递推方法的一则注记AI 解读

Bougerol (1993) and Straumann and Mikosch (2006) gave conditions under which there exists a unique stationary and ergodic solution to the stochastic difference equation $Y_t \overset{a.s.}{=} Φ_t (Y_{t-1}), t \in \mathbb{Z}$ where $(Φ_t)_{t \in \mathbb{Z}}$ is a sequence of stationary and ergodic random Lipschitz continuous functions from $(Y,|| \cdot ||)$ to $(Y,|| \cdot ||)$ where $(Y,|| \cdot ||)$ is a complete subspace of a real or complex separable Banach space. In the…

有序时间序列的二元一阶离散自回归模型AI 解读

We present a bivariate vector valued discrete autoregressive model of order $1$ (BDAR($1$)) for discrete time series. The BDAR($1$) model assumes that each time series follows its own univariate DAR($1$) model with dependent random mechanisms that determine from which component the current status occurs and dependent innovations. The joint distribution of the random mechanisms which are expressed by Bernoulli vectors are proposed to be defined through copulas. The same holds…

处理选择的收缩方法AI 解读

This study examines the problem of determining whether to treat individuals based on observed covariates. The most common decision rule is the conditional empirical success (CES) rule proposed by Manski (2004), which assigns individuals to treatments that yield the best experimental outcomes conditional on the observed covariates. Conversely, using shrinkage estimators, which shrink unbiased but noisy preliminary estimates toward the average of these estimates, is a common…

高维时间序列的稀疏组因子分析AI 解读

Factor analysis is a widely used technique for dimension reduction in high-dimensional data. However, a key challenge in factor models lies in the interpretability of the latent factors. One intuitive way to interpret these factors is through their associated loadings. Liu and Wang proposed a novel framework that redefines factor models with sparse loadings to enhance interpretability. In many high-dimensional time series applications, variables exhibit natural group…

机器学习、偏微分方程与统计中的再生核方法AI 解读

This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite kernels; discrete and continuous RKHS; kernel engineering and scaling maps; error assessment via kernel discrepancy/maximum mean discrepancy (MMD); and a systematic operator view of kernels. In this viewpoint, projection, gradient,…

多处理与正值性违背下的因果参数比较AI 解读

Comparing outcomes across treatments is essential in medicine and public policy. To do so, researchers typically estimate a set of parameters, possibly counterfactual, with each targeting a different treatment. Treatment-specific means are commonly used, but their identification requires a positivity assumption, that every subject has a non-zero probability of receiving each treatment. This is often implausible, especially when treatment can take many values. Causal…

风险调整的政策学习与不确定性的社会成本：共同农业政策评估AI 解读

This paper develops a risk-adjusted alternative to standard optimal policy learning (OPL) for observational data by importing Roy's (1952) safety-first principle into the treatment assignment problem. We formalize a welfare functional that maximizes the probability that outcomes exceed a socially required threshold and show that the associated pointwise optimal rule ranks treatments by the ratio of conditional means to conditional standard deviations. We implement the…

图形连续 Lyapunov 模型的结构可识别性AI 解读

We prove two characterizations of model equivalence of acyclic graphical continuous Lyapunov models (GCLMs) with uncorrelated noise. The first result shows that two graphs are model equivalent if and only if they have the same skeleton and equivalent induced 4-node subgraphs. We also give a transformational characterization via structured edge reversals. The two theorems are Lyapunov analogues of celebrated results for Bayesian networks by Verma and Pearl, and Chickering,…

状态空间模型的 MCMC 方法AI 解读

A state-space model is a time-series model that has an unobserved latent process from which we take noisy measurements over time. The observations are conditionally independent given the latent process and the latent process itself is Markovian. These properties lead to simplifications for the conditional distribution of the latent process given the parameters and the observations. This chapter looks at how we can leverage the properties of state-space models to construct…

函数响应模拟器的快速仿真、模块化校准与主动学习AI 解读

Scalable surrogate models enable efficient emulation of computer models (or simulators), particularly when dealing with large ensembles of runs. While Gaussian process (GP) models are commonly employed for emulation, they face limitations in scaling to large datasets. Furthermore, when dealing with dense functional output, such as spatial or time-series data, additional complexities arise, requiring careful handling to ensure fast emulation. This work presents a highly…

比较与评估序贯临床试验中信息性中期决策的信息度量AI 解读

Group sequential designs enable interim analyses and potential early stopping for efficacy or futility. While these adaptations improve trial efficiency and ethical considerations, they also introduce bias into the adapted analyses. We demonstrate how failing to account for informative interim decisions in the analysis can substantially affect posterior estimates of the treatment effect, often resulting in overly optimistic credible intervals aligned with the stopping…

基于去偏组图Lasso的多稀疏精度矩阵统计推断AI 解读

Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates and model selection consistency under irrepresentability conditions. Based on these results, we construct debiased estimators that are asymptotically Gaussian, allowing hypothesis testing for linear combinations of precision matrix entries…

向量 Copula 变分推断与相关分块后验近似AI 解读

The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a common choice is to assume independence between multivariate blocks in a partition of the parameter space. While this simplifies the problem it can reduce accuracy. This paper proposes using vector copulas to capture dependence between the blocks parsimoniously. Tailored multivariate marginals are constructed using learnable transport maps. We call the…