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有限混合 Tobit 模型的贝叶斯估计AI 解读

This paper outlines a Bayesian approach to estimate finite mixtures of Tobit models. The method consists of an MCMC approach that combines Gibbs sampling with data augmentation and is simple to implement. I show through simulations that the flexibility provided by this method is especially helpful when censoring is not negligible. In addition, I demonstrate the broad utility of this methodology with applications to a job training program, labor supply, and demand for medical…

利用 Lempel–Ziv 复杂度开展因果发现与分类AI 解读

Inferring causal relationships in the decision-making processes of machine learning algorithms is a crucial step toward achieving explainable Artificial Intelligence (AI). In this research, we introduce a novel causality measure and a distance metric derived from Lempel-Ziv (LZ) complexity. We explore how the proposed causality measure can be used in decision trees by enabling splits based on features that most strongly \textit{cause} the outcome. We further evaluate the…

利用机器学习构建稀疏区间值时间序列模型AI 解读

By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance estimation, which covers point-based estimators are special cases. We establish the consistency and oracle properties of the proposed penalized estimator, regardless of whether the number of predictors is diverging with the sample size. Monte Carlo…

包容式合成控制法AI 解读

We introduce the inclusive synthetic control method (iSCM), a modification of synthetic control methods that includes units in the donor pool potentially affected, directly or indirectly, by an intervention. This method is ideal for situations where including treated units in the donor pool is essential or where donor units may experience spillover effects. The iSCM is straightforward to implement with most synthetic control estimators. As an empirical illustration, we…

基于左截断右删失数据的反事实生存泛函去偏机器学习AI 解读

Learning causal effects of a binary exposure on time-to-event endpoints can be challenging because survival times may be partially observed due to censoring and systematically biased due to truncation. In this work, we present debiased machine learning-based nonparametric estimators of the joint distribution of a counterfactual survival time and baseline covariates for use when the observed data are subject to covariate-dependent left truncation and right censoring and when…

利用主要进展速率量化和比较研究中的疾病进展AI 解读

In comparative studies of progressive diseases, such as randomized controlled trials (RCTs), the mean Change From Baseline (CFB) of a continuous outcome at a pre-specified follow-up time across subjects in the target population is a standard estimand used to summarize the overall disease progression. Despite its simplicity in interpretation, the mean CFB may not efficiently capture important features of the trajectory of the mean outcome relevant to the evaluation of the…

高维向量自回归模型中的网络格兰杰因果发现AI 解读

This paper proposes novel inferential procedures for discovering the network Granger causality in high-dimensional vector autoregressive models. In particular, we mainly offer two multiple testing procedures designed to control the false discovery rate (FDR). The first procedure is based on the limiting normal distribution of the $t$-statistics with the debiased lasso estimator. The second procedure is its bootstrap version. We also provide a robustification of the first…

多变量空间数据的聚类因子分析AI 解读

Factor analysis has been extensively used to reveal the dependence structures among multivariate variables, offering valuable insight in various fields. However, it cannot incorporate the spatial heterogeneity that is typically present in spatial data. To address this issue, we introduce an effective method specifically designed to discover the potential dependence structures in multivariate spatial data. Our approach assumes that spatial locations can be approximately…

自适应收缩：非参数贝叶斯 LassoAI 解读

Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping relatively intact the important ones. With this task in mind, we develop the nonparametric Bayesian Lasso, an adaptive and flexible shrinkage prior for Bayesian regression and variable selection, particularly useful when the number of…

通过数据自适应借用外部对照改进随机试验分析AI 解读

In recent years, real-world external controls have grown in popularity as a tool to empower randomized placebo-controlled trials, particularly in rare diseases or cases where balanced randomization is unethical or impractical. However, as external controls are not always comparable to the trials, direct borrowing without scrutiny may heavily bias the treatment effect estimator. Our paper proposes a data-adaptive integrative framework capable of preventing unknown biases of…

极端分位数回归神经网络及其洪水风险预测应用AI 解读

Risk assessment for extreme events requires accurate estimation of high quantiles that go beyond the range of historical observations. When the risk depends on the values of observed predictors, regression techniques are used to interpolate in the predictor space. We propose the EQRN model that combines tools from neural networks and extreme value theory into a method capable of extrapolation in the presence of complex predictor dependence. Neural networks can naturally…

由 Lipschitz 函数索引的经验过程强逼近AI 解读

This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general empirical processes indexed by possibly Lipschitz functions, improving on previous results in the literature. In the setting considered by Rio (1994), and if the function class is Lipschitzian, our result improves the approximation rate $n^{-1/(2d)}$…

MSTest：检验马尔可夫转换模型的 R 软件包AI 解读

We present the R package MSTest, which implements hypothesis testing procedures to identify the number of regimes in Markov switching models. These models have wide-ranging applications in economics, finance, and numerous other fields. The MSTest package includes the Monte Carlo likelihood ratio test procedures proposed by Rodriguez-Rondon and Dufour (2024), the moment-based tests of Dufour and Luger (2017), the parameter stability tests of Carrasco, Hu, and Ploberger…

已知有效调整集下高维因果效应估计的 PAC 保证AI 解读

Accurate estimates of causal effects play a key role in decision-making across applications such as healthcare, economics, and operations. In the absence of randomized experiments, a common approach to estimating causal effects uses \textit{covariate adjustment}. In this paper, we study covariate adjustment for discrete distributions from the PAC learning perspective, assuming knowledge of a valid adjustment set $\bZ$, which might be high-dimensional. Our first main result…

交叉验证后自助法选择高维 M 估计的惩罚参数AI 解读

We develop a new method for selecting the penalty parameter for $\ell_{1}$-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross-validation. We derive rates of convergence for the corresponding $\ell_1$-penalized M-estimator and also for the post-$\ell_1$-penalized M-estimator, which refits the non-zero entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not…

灵活的函数型处理效应估计AI 解读

We study treatment effect estimation with functional treatments where the average potential outcome functional is a function of functions, in contrast to continuous treatment effect estimation where the target is a function of real numbers. By considering a flexible scalar-on-function marginal structural model, a weight-modified kernel ridge regression (WMKRR) is adopted for estimation. The weights are constructed by directly minimizing the uniform balancing error resulting…

非凸正则化凸稀疏模型最小范数解映射的分段线性性质AI 解读

It is well known that the minimum $\ell_2$-norm solution of the convex LASSO model, say $\mathbf{x}_{\star}$, is a continuous piecewise linear function of the regularization parameter $λ$, and its signed sparsity pattern is constant within each linear piece. The current study is an extension of this classic result, proving that the aforementioned properties extend to the min-norm solution map $\mathbf{x}_{\star}(\mathbf{y},λ)$, where $\mathbf{y}$ is the observed signal, for…

研发与人工智能投资对经济增长和信用评级的影响AI 解读

The research and development (R&D) phase is essential for fostering innovation and aligns with long-term strategies in both public and private sectors. This study addresses two primary research questions: (1) assessing the relationship between R&D investments and GDP through regression analysis, and (2) estimating the economic value added (EVA) that Georgia must generate to progress from a BB to a BBB credit rating. Using World Bank data from 2014-2022, this analysis found…

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…

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…