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纯跳跃设定下的期权面板推断AI 解读

We develop parametric inference procedures for large panels of noisy option data in a setting, where the underlying process is of pure-jump type, i.e., evolves only through a sequence of jumps. The panel consists of options written on the underlying asset with a (different) set of strikes and maturities available across the observation times. We consider an asymptotic setting in which the cross-sectional dimension of the panel increases to infinity, while the time span…

高维极值依赖的分解AI 解读

Summary We propose two decompositions that help to summarize and describe high-dimensional tail dependence within the framework of regular variation. We use a transformation to define a vector space on the positive orthant and show that transformed-linear operations applied to regularly-varying random vectors preserve regular variation. We summarize tail dependence via a matrix of pairwise tail dependence metrics that is positive semidefinite; eigendecomposition allows one…

高维纵向数据协方差矩阵的同质性检验AI 解读

Summary This paper deals with the detection and identification of changepoints among covariances of high-dimensional longitudinal data, where the number of features is greater than both the sample size and the number of repeated measurements. The proposed methods are applicable under general temporal-spatial dependence. A new test statistic is introduced for changepoint detection, and its asymptotic distribution is established. If a changepoint is detected, an estimate of…

高维线性模型中的误差方差估计AI 解读

Summary The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized likelihood objective. A key aspect of the natural lasso is that the likelihood is expressed in terms of the natural parameterization of the…

高维回归中的条件性原则AI 解读

Summary Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A conditional and an unconditional framework are considered, where conditioning is with respect to the covariates, which are ancillary to the parameter of interest. In recent papers, a consistent estimator was developed in the…

Pearson 卡方统计量：近似理论及其扩展AI 解读

Summary We establish an approximation theory for Pearson’s chi-squared statistics in situations where the number of cells is large, by using a high-dimensional central limit theorem for quadratic forms of random vectors. Our high-dimensional central limit theorem is proved under Lyapunov-type conditions that involve a delicate interplay between the dimension, the sample size, and the moment conditions. We propose a modified chi-squared statistic and introduce an adjusted…

高维线性判别分析：最优性、自适应算法与缺失数据AI 解读

Summary The paper develops optimality theory for linear discriminant analysis in the high dimensional setting. A data-driven and tuning-free classification rule, which is based on an adaptive constrained l1-minimization approach, is proposed and analysed. Minimax lower bounds are obtained and this classification rule is shown to be simultaneously rate optimal over a collection of parameter spaces. In addition, we consider classification with incomplete data under the…

时变系数面板模型中的潜在分组结构估计AI 解读

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients…

通过核范数正则化估计高维广义迹回归AI 解读

We study the generalized trace regression with a near low-rank regression coefficient matrix, which extends notion of sparsity for regression coefficient vectors. Specifically, given a matrix covariate X, the probability density function of the response Y is f(Y|X)=c(Y)exp(ϕ−1−Yη∗+b(η∗)), where η∗=tr(Θ∗TX). This model accommodates various types of responses and embraces many important problem setups such as reduced-rank regression, matrix regression that accommodates a panel…

贝叶斯非参数稀疏向量自回归模型AI 解读

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR models that can improve estimation efficiency and prediction accuracy. Our hierarchical prior overcomes overparametrization and overfitting issues by clustering the VAR coefficients into groups and by shrinking the coefficients of each…

极端典型相关与高维协整分析AI 解读

We prove that the extreme squared sample canonical correlations between a random walk and its own innovations almost surely converge to the upper and lower boundaries of the support of the Wachter distribution when the sample size and the dimensionality go to infinity proportionally. This result is used to derive previously unknown analytic expressions for the Bartlett-type correction coefficients for Johansen’s trace and maximum eigenvalue tests in a high-dimensional…

高维多变量已实现波动率估计AI 解读

We provide a new factor-based estimator of the realized covolatility matrix, applicable in situations when the number of assets is large and the high-frequency data are contaminated with microstructure noises. Our estimator relies on the assumption of a factor structure for the noise component, separate from the latent systematic risk factors that characterize the cross-sectional variation in the frictionless returns. The new estimator provides theoretically more efficient…

高维向量自回归的自适应层级先验AI 解读

This paper proposes a simulation-free estimation algorithm for vector autoregressions (VARs) that allows fast approximate calculation of marginal parameter posterior distributions. We apply the algorithm to derive analytical expressions for independent VAR priors that admit a hierarchical representation and which would typically require computationally intensive posterior simulation methods. The benefits of the new algorithm are explored using three quantitative exercises.…

时变参数向量自回归的准贝叶斯局部似然方法AI 解读

The paper establishes a quasi-Bayesian local likelihood (QBLL) estimation methodology for a multivariate model with time varying parameters. The asymptotic validity of the resulting quasi-posterior distributions of the drifting parameters is proven in general and, in the special case of a Gaussian VAR model, a closed form time varying Normal-Wishart expression for the quasi-posterior distribution of the parameters is provided. In addition, this paper develops several Gibbs…

近似因子模型的秩正则化估计AI 解读

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares with ridge regressions turns out to have the effect of removing the contribution of factors associated with small singular values from the common component. The method has been used in the machine learning literature to recover low-rank…

动态预测计量建模中的大数据AI 解读

The modern economic environment is awash in Big Data. The business models of many of today’s largest and most innovative firms, for example, are intimately connected to data collection and processing. Closely related, all of science is now similarly awash in Big Data, due to massive advances in data capture and storage technology, typically in conjunction with the internet.1 Time-series econometrics is no exception, and the time-series community is beginning to confront Big…

存在结构突变的面板模型中的变量选择AI 解读

We develop a Bayesian approach that performs variable selection in panel regression models affected by breaks. Our approach enables deactivation of pervasive regressors and activation of weak regressors for short periods (regimes). We establish theoretical results on the concentration properties of the posterior as well as the rate of convergence for estimating the break dates. Our methodology is demonstrated in simulations and in an empirical application to firms’ choice of…

固定与大时间跨度面板中非线性因子模型的统一推断AI 解读

We provide unifying inference theory for parametric nonlinear factor models based on a panel of noisy observations. The panel has a large cross-section and a time span that may be either small or large. Moreover, we incorporate an additional source of information, provided by noisy observations on some known functions of the factor realizations. The estimation is carried out via penalized least squares, i.e., by minimizing the L2 distance between observations from the panel…

交易成本与模型不确定性下的大规模投资组合配置AI 解读

We theoretically and empirically study portfolio optimization under transaction costs and establish a link between turnover penalization and covariance shrinkage with the penalization governed by transaction costs. We show how the ex ante incorporation of transaction costs shifts optimal portfolios towards regularized versions of efficient allocations. The regulatory effect of transaction costs is studied in an econometric setting incorporating parameter uncertainty and…

Lipschitz 损失正则化方法的估计界与尖锐预言不等式AI 解读

We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*}\hat{f}\in\mathop{\operatorname{argmin}}_{f\in F}\Bigg(\frac{1}{N}\sum_{i=1}^{N}\ell_{f}(X_{i},Y_{i})+\lambda \Vert f\Vert \Bigg)\end{equation*} when $\Vert \cdot \Vert $ is any norm, $F$ is a convex class of functions and $\ell$ is a Lipschitz loss function satisfying a Bernstein condition over $F$. We explore both the bounded and sub-Gaussian stochastic…

自适应 Lasso 的扰动自助法AI 解读

The Adaptive Lasso (Alasso) was proposed by Zou [J. Amer. Statist. Assoc. 101 (2006) 1418–1429] as a modification of the Lasso for the purpose of simultaneous variable selection and estimation of the parameters in a linear regression model. Zou [J. Amer. Statist. Assoc. 101 (2006) 1418–1429] established that the Alasso estimator is variable-selection consistent as well as asymptotically Normal in the indices corresponding to the nonzero regression coefficients in certain…

超高维稀疏数据中基于条件严格凸损失的非参数筛选AI 解读

Sure screening technique has been considered as a powerful tool to handle the ultrahigh dimensional variable selection problems, where the dimensionality $p$ and the sample size $n$ can satisfy the NP dimensionality $\log p=O(n^{a})$ for some $a>0$ [J. R. Stat. Soc. Ser. B. Stat. Methodol. 70 (2008) 849–911]. The current paper aims to simultaneously tackle the “universality” and “effectiveness” of sure screening procedures. For the “universality,” we develop a general and…

密度与高维多项分布的假设检验：精确局部极小极大速率AI 解读

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or unbounded number of categories. In the continuous case, we consider testing a Hölder density with exponent $0

全正性约束下高斯模型的最大似然估计AI 解读

We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_{2}$). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof that the maximum likelihood estimator (MLE) for such distributions exists based on $n\geq2$ observations, irrespective of the underlying dimension. Slawski and Hein [Linear Algebra Appl. 473 (2015) 145–179], who first proved…