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彭鼎对《广义线性模型参数的弱假设推断》的讨论AI 解读

I want to congratulate the authors on a thought-provoking paper on statistical inference with misspecified models. It deepens our understanding of the role of models in causal inference. I offer two comments. Comparison of the conditional and marginal estimands based on 105 Monte Carlo samples. The parameters of the distributions of L and Y are all drawn independently from Uniform(0, 1) The authors provide inspiring derivations of the novel average effect and interaction…

《广义线性模型参数的弱假设推断》讨论与致谢附议AI 解读

In my view, one of the most important contributions of the field of causal inference has been to place the target of inference, the desired estimand, at the centre of the analysis. The estimand is chosen in view of the research question, and typically reflects what decision problem we need to solve or what our ideal (target) trial would be. Crucially, the (causal) estimand is not automatically a parameter that happens to parametrise a chosen model. The role of models is…

摘要暂缺

广义线性模型参数的弱假设推断AI 解读

Abstract Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive model selection process, which may induce excess uncertainty that is not usually acknowledged. Moreover, the assumptions encoded in the chosen model rarely represent some a priori known, ground truth, making standard inferences…

难处理似然下的稳健广义贝叶斯推断AI 解读

Abstract Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of the…

基于耦合的高维收缩先验贝叶斯回归 Gibbs 采样收敛评估AI 解读

Abstract We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is critical when each iteration is expensive, as is the case when dealing with modern data sets, such as genome-wide association studies with thousands of rows and up to hundreds of thousands of columns. We develop coupling techniques…

具有多重不连续点的函数型过程AI 解读

Abstract We consider the problem of estimating multiple change points for a functional data process. There are numerous examples in science and finance in which the process of interest may be subject to some sudden changes in the mean. The process data that are not in a close vicinity of any change point can be analysed by the usual nonparametric smoothing methods. However, the data close to change points and contain the most pertinent information of structural breaks need…

用于评估重复研究成功的怀疑贝叶斯因子AI 解读

Abstract Replication studies are increasingly conducted but there is no established statistical criterion for replication success. We propose a novel approach combining reverse-Bayes analysis with Bayesian hypothesis testing: a sceptical prior is determined for the effect size such that the original finding is no longer convincing in terms of a Bayes factor. This prior is then contrasted to an advocacy prior (the reference posterior of the effect size based on the original…

使用 e 值控制错误发现率AI 解读

Abstract E-values have gained attention as potential alternatives to p-values as measures of uncertainty, significance and evidence. In brief, e-values are realized by random variables with expectation at most one under the null; examples include betting scores, (point null) Bayes factors, likelihood ratios and stopped supermartingales. We design a natural analogue of the Benjamini-Hochberg (BH) procedure for false discovery rate (FDR) control that utilizes e-values, called…

多个因果有序中介变量下的因果中介分析半参数估计AI 解读

Abstract Causal mediation analysis concerns the pathways through which a treatment affects an outcome. While most of the mediation literature focuses on settings with a single mediator, a flourishing line of research has examined settings involving multiple mediators, under which path-specific effects (PSEs) are often of interest. We consider estimation of PSEs when the treatment effect operates through K(≥ 1) causally ordered, possibly multivariate mediators. In this…

无限时域强化学习中价值函数的统计推断AI 解读

Abstract Reinforcement learning is a general technique that allows an agent to learn an optimal policy and interact with an environment in sequential decision-making problems. The goodness of a policy is measured by its value function starting from some initial state. The focus of this paper was to construct confidence intervals (CIs) for a policy’s value in infinite horizon settings where the number of decision points diverges to infinity. We propose to model the…

条件矩模型的贝叶斯估计与比较AI 解读

Abstract We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The non-parametric exponentially tilted empirical likelihood function is constructed to satisfy a sequence of unconditional moments based on an increasing (in sample size) vector of approximating functions (such as tensor splines based on the splines of each conditioning variable). For any given sample size,…

基于相关矩阵的主成分分析的渐近性质AI 解读

It is a common practice to conduct principal component analysis (PCA) using standardized data, which is equivalent to applying PCA to the correlation matrix rather than the covariance matrix. Yet little research has been done about such differences in the context of high frequency data. This paper bridges this gap. We derive the analytical forms of the asymptotic biases and variances for the estimators of the integrated eigenvalues and eigenvectors. Furthermore, we propose a…

稀疏备择下线性因子定价模型 Alpha 的高维检验AI 解读

We consider the problem of testing for the presence of alpha in Linear Factor Pricing Models. We propose a novel test of the max-of-squares type, which is designed to deal with the high dimensionality of the securities and the sparse alternatives. We rigorously show that the proposed test has attractive theoretical properties and demonstrate its superior performance via Monte Carlo experiments. These results are established when the number of securities is larger than the…

多因子误差结构下异质空间面板的估计与推断AI 解读

We develop a unifying econometric framework for the analysis of heterogeneous panel data models that can account for both spatial dependence and common factors. To tackle the challenging issues of endogeneity due to the spatial lagged term and the correlation between the regressors and factors, we propose the CCEX-IV estimation procedure that approximates factors by the cross-section averages of regressors and deals with the spatial endogeneity using the internal…

共同冲击面板中免受附带参数问题影响的推断方法AI 解读

This paper develops a novel Method of Moments approach for panel data models with endogenous regressors and unobserved common factors. The proposed approach does not require estimating explicitly a large number of parameters in either time-series or cross-sectional dimension, T and N respectively. Hence, it is free from the incidental parameter problem. In particular, the proposed approach does not suffer from “Nickell bias” of order O(T−1), nor from bias terms that are of…

高维矩阵因子模型的投影估计AI 解读

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that of a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the…

多资产因子模型：强因子、弱因子与两步估计AI 解读

This paper re-examines the problem of estimating risk premia in unconditional linear factor pricing models. Typically, the data used in the empirical literature are characterized by weakness of some pricing factors, strong cross-sectional dependence in the errors, and (moderately) high cross-sectional dimensionality. Using an asymptotic framework where the number of assets/portfolios grows with the time span of the data while the risk exposures of weak factors are…

高维广义因子模型的极大似然估计与推断：因子扩展回归应用AI 解读

This paper reestablishes the main results in Bai (2003) and Bai and Ng (2006) for generalized factor models, with slightly stronger conditions on the relative magnitude of N (number of subjects) and T (number of time periods). Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear, Logit, Probit, Tobit, Poisson and some other single-index…

大数据时代的市场有效性AI 解读

Modern investors face a high-dimensional prediction problem: thousands of observable variables are potentially relevant for forecasting. We reassess the conventional wisdom on market efficiency in light of this fact. In our equilibrium model, N assets have cash flows that are linear in J characteristics, with unknown coefficients. Risk-neutral Bayesian investors learn these coefficients and determine market prices. If J and N are comparable in size, returns are…

Boosting 与最小 ℓ1 范数插值分类器的精确高维渐近理论AI 解读

This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider a high-dimensional setting where the number of features (weak learners) p scales with the sample size n, in an overparametrized regime. Under a class of statistical models, we provide an exact analysis of the generalization error of boosting when the algorithm interpolates the training data and maximizes the…

大型 VAR 中的协整AI 解读

The paper analyzes cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, N, and the number of time periods, T, are large and of the same order. We propose a way to examine a VAR of order 1 for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from…

具有块结构的大规模统计推断AI 解读

The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing that is inherent in these problems. Here, we show that fundamentally more powerful statistical inference is possible when there is some structure in the signal that can be exploited, for example, if the signal is clustered in…

多元最大稳定分布贝叶斯推断的一致性AI 解读

Predicting extreme events is important in many applications in risk analysis. Extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction. Although various Bayesian inferential procedures have been proposed in the literature of univariate extremes and some for multivariate extremes, the study of their asymptotic properties has been left largely untouched. In this paper we focus on…