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高频金融数据大维瞬时波动率矩阵的非参数估计AI 解读

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot…

逆问题泛函的源条件双重稳健推断AI 解读

We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the dual solution can be thought as a generalization of the inverse propensity function. We provide the first source condition double robust inference method that ensures asymptotic normality around the parameter of interest as long as either…

包含算法随机性的两阶段观测模型统计推断AI 解读

Randomized algorithms, such as random sampling, random projections, and stochastic optimization, are increasingly used to reduce the computational cost of modern statistical analysis. These algorithms introduce algorithmic randomness in addition to the sampling randomness in the data, and this extra source of variation complicates statistical inference. We develop a framework for valid inference in such two-stage observation models, where data are first generated from an…

一步平滑样条工具变量回归AI 解读

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique regularization parameter. We derive rates of the convergence for the estimator and its first derivative, which are uniform in the support of the endogenous variable. We also address the issue of imposing monotonicity in estimation and extend the…

高维线性模型的稀疏化同时置信区间AI 解读

Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible and how to embed the inference of the model into the simultaneous inference of the coefficients? To this end, we propose a notion of simultaneous confidence intervals called the sparsified simultaneous confidence intervals. Our intervals…

多元计数时间序列的潜在高斯动态因子建模与预测AI 解读

This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters is based on second-order properties of the count and underlying Gaussian time series, yielding estimators of the underlying covariance matrices for which standard principal component analysis applies. Theoretical consistency results are…

局部因果发现中的结构限制：识别目标变量的直接原因AI 解读

We consider the problem of learning a set of direct causes of a target variable from an observational joint distribution. Learning directed acyclic graphs (DAGs) that represent the causal structure is a fundamental problem in science. Several results are known when the full DAG is identifiable from the distribution, such as assuming a nonlinear Gaussian data-generating process. Here, we are only interested in identifying the direct causes of one target variable (local causal…

病态线性回归的扩展潜在因子框架AI 解读

In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases, hinder both the accurate estimation and meaningful interpretation of the effects of the relevant features on the response. At the same time, the relevant features may also be well-approximated within a low-dimensional linear subspace,…

模型误设下的稳健通用推断AI 解读

In statistical inference, it is rarely realistic that the hypothesized statistical model is well-specified, and consequently it is important to understand the effects of misspecification on inferential procedures. When the hypothesized statistical model is misspecified, the natural target of inference is a projection of the data generating distribution onto the model. We present a general method for constructing valid confidence sets for such projections, under weak…

协变量分布偏移下的自动去偏机器学习AI 解读

We present machine learning estimators for causal and predictive parameters under covariate shift, where covariate distributions differ between training and target populations. One such parameter is the average effect of a policy that alters the covariate distribution, such as a treatment modifying surrogate covariates used to predict long-term outcomes. Another example is the average treatment effect for a population with a shifted covariate distribution, like the effect of…

结合实验与观察数据的双重机器学习方法AI 解读

Experimental and observational studies often lack validity due to untestable assumptions. We propose a double machine learning approach to combine experimental and observational studies, allowing practitioners to test for assumption violations and estimate treatment effects consistently. Our framework proposes a falsification test for external validity and ignorability under milder assumptions. We provide consistent treatment effect estimators even when one of the…

因子模型的典范分解：弱因子无处不在AI 解读

We derive a novel canonical decomposition of factor models encompassing both the static factor model - where factors are loaded only contemporaneously - and the Generalised Dynamic Factor Model - where factors are loaded with lags. This decomposition features a new term: the weak common component, defined as the difference between the dynamic and static common components. It is driven by (possibly infinitely many) non-pervasive weak factors which belong to the dynamically…

惩罚与阈值估计中模式恢复的统一框架及其几何AI 解读

We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO, generalized LASSO, SLOPE, OSCAR, PACS and others. Each of these estimators is defined through an optimization problem and can uncover a different structure or ``pattern'' of the unknown parameter vector. We define a novel and general notion of patterns based on subdifferentials and formalize an approach to measure…

极值图套索：尾部稀疏相依结构的估计AI 解读

In this paper, we estimate the sparse dependence structure in the tail region of a multivariate random vector, potentially of high dimension. The tail dependence is modeled via a graphical model for extremes embedded in the Hüsler-Reiss distribution. We propose the extreme graphical lasso procedure to estimate the sparsity in the tail dependence, similar to the Gaussian graphical lasso in high dimensional statistics. We prove its consistency in identifying the graph…

Yule–Frisch–Waugh–Lovell 定理AI 解读

This paper traces the historical and analytical development of what is known in the econometrics literature as the Frisch-Waugh-Lovell theorem. This theorem demonstrates that the coefficients on any subset of covariates in a multiple regression is equal to the coefficients in a regression of the residualized outcome variable on the residualized subset of covariates, where residualization uses the complement of the subset of covariates of interest. In this paper, I suggest…

特定计数回归时间序列模型中的变量选择AI 解读

Time series of counts occurring in various applications are often overdispersed, meaning their variance is much larger than the mean. This paper proposes a novel variable selection approach for processing such data. Our approach consists in modelling them using sparse negative binomial GLARMA models. It combines estimating the autoregressive moving average (ARMA) coefficients of GLARMA models and the overdispersion parameter with performing variable selection in regression…

弱依赖下局部经验过程的极大不等式AI 解读

We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}\{x - h \leq X_i \leq x+h\}f(Z_i)$, where $f$ belongs to a class of functions, $x \in \mathbb{R}$ and $h > 0$ is a bandwidth. Our nonasymptotic bounds control estimation error uniformly over the function class, evaluation point $x$ and bandwidth $h$. They are also general enough to…

通过反事实推断识别淀粉样蛋白积累与阿尔茨海默病进展的因果关系AI 解读

Alzheimer's disease (AD) is a neurodegenerative disorder that is beginning with amyloidosis, followed by neuronal loss and deterioration in structure, function, and cognition. The accumulation of amyloid-beta in the brain, measured through 18F-florbetapir (AV45) positron emission tomography (PET) imaging, has been widely used for early diagnosis of AD. However, the relationship between amyloid-beta accumulation and AD pathophysiology remains unclear, and causal inference…

广义自回归条件持续期模型的渐近理论AI 解读

Engle and Russell (1998, Econometrica, 66:1127--1162) apply results from the GARCH literature to prove consistency and asymptotic normality of the (exponential) QMLE for the generalized autoregressive conditional duration (ACD) model, the so-called ACD(1,1), under the assumption of strict stationarity and ergodicity. The GARCH results, however, do not account for the fact that the number of durations over a given observation period is random. Thus, in contrast with Engle and…

函数型时间序列的降噪AI 解读

A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional dynamics of the functional time series to separate the serially dependent dynamical part of the observed curves from the noise. Upon identifying the subspaces of the signal and idiosyncratic components, we construct a projection of the…

高维混合暴露的因果中介路径识别：数据自适应目标参数策略AI 解读

Mediation analysis in causal inference typically concentrates on one binary exposure, using deterministic interventions to split the average treatment effect into direct and indirect effects through a single mediator. Yet, real-world exposure scenarios often involve multiple continuous exposures impacting health outcomes through varied mediation pathways, which remain unknown a priori. Addressing this complexity, we introduce NOVAPathways, a methodological framework that…

面板数据即时预测：以市盈率为例AI 解读

The paper uses structured machine learning regressions for nowcasting with panel data consisting of series sampled at different frequencies. Motivated by the problem of predicting corporate earnings for a large cross-section of firms with macroeconomic, financial, and news time series sampled at different frequencies, we focus on the sparse-group LASSO regularization which can take advantage of the mixed frequency time series panel data structures. Our empirical results show…

高维时间序列的一致因果推断AI 解读

A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian vector autoregressive process. This is tantamount to assume that the dynamics are captured by a Gaussian copula. No knowledge or estimation of the marginal distribution of the data is required. The procedure consistently identifies the…

非欧氏值时间序列的两样本与变点推断AI 解读

Data objects taking value in a general metric space have become increasingly common in modern data analysis. In this paper, we study two important statistical inference problems, namely, two-sample testing and change-point detection, for such non-Euclidean data under temporal dependence. Typical examples of non-Euclidean valued time series include yearly mortality distributions, time-varying networks, and covariance matrix time series. To accommodate unknown temporal…