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分位数格兰杰因果性的度量AI 解读

We consider measures of Granger causality in quantiles, which detect and quantify both linear and nonlinear causal effects between random variables. The measures are based on nonparametric quantile regressions and defined as logarithmic functions of restricted and unrestricted expectations of quantile check loss functions. They can consistently be estimated by replacing the unknown expectations of check loss functions by their nonparametric kernel estimates. We derive a…

具有门槛边界的门槛回归AI 解读

This article studies computation, estimation, inference, and testing for linearity in threshold regression with a threshold boundary. We first put forward a new algorithm to ease the computation of the threshold boundary, and develop the asymptotics for the least squares estimator in both the fixed-threshold-effect framework and the small-threshold-effect framework. We also show that the inverting-likelihood-ratio method is not suitable to construct confidence sets for the…

预测支配关系的一般条件AI 解读

Recent studies have analyzed whether one forecast method dominates another under a class of consistent scoring functions. While the existing literature focuses on empirical tests of forecast dominance, little is known about the theoretical conditions under which one forecast dominates another. To address this question, we derive a new characterization of dominance among forecasts of the mean functional. We present various scenarios under which dominance occurs. Unlike…

含噪声与异步数据的得分驱动条件相关模型：高频协方差动态应用AI 解读

The analysis of the intraday dynamics of covariances among high-frequency returns is challenging due to asynchronous trading and market microstructure noise. Both effects lead to significant data reduction and may severely affect the estimation of the covariances if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a…

环境市场能否优于开放取用？来自加州地下水权的证据AI 解读

Environmental markets are widely prescribed as an alternative to open access regimes for natural resources. We develop a model of dynamic groundwater extraction to demonstrate how a spatial regression discontinuity design that exploits a spatially incomplete market for groundwater rights recovers a lower bound on the market’s net benefit. We apply this estimator to a major aquifer in water-scarce southern California and find that a groundwater market generated substantial…

用 Wasserstein 距离度量贝叶斯非参数模型的依赖性AI 解读

The proposal and study of dependent Bayesian nonparametric models has been one of the most active research lines in the last two decades, with random vectors of measures representing a natural and popular tool to define them. Nonetheless, a principled approach to understand and quantify the associated dependence structure is still missing. We devise a general, and not model-specific, framework to achieve this task for random measure based models, which consists in: (a)…

海量数据的分布式统计推断AI 解读

This paper considers distributed statistical inference for general symmetric statistics in the context of massive data with efficient computation. Estimation efficiency and asymptotic distributions of the distributed statistics are provided, which reveal different results between the nondegenerate and degenerate cases, and show the number of the data subsets plays an important role. Two distributed bootstrap methods are proposed and analyzed to approximation the underlying…

协调高斯似然与 Whittle 似然：频域估计的应用AI 解读

In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussian likelihood and the Whittle likelihood. We derive an exact, interpretable, bound between the Gaussian and Whittle likelihood of a second order stationary time series. The derivation is based on obtaining the transformation which is biorthogonal to…

高阶全变差正则化最小二乘的预测界AI 解读

We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of (k−1)th order differences. Our approach is based on combining a general oracle inequality for the ℓ1-penalized least squares estimator with “interpolating vectors” to upper bound the “effective sparsity.” This allows one to show that the ℓ1-penalty on the kth order differences leads to an estimator that can adapt to the number of jumps in the (k−1)th order…

两阶段富集试验设计的统计推断AI 解读

Two-stage enrichment designs can be used to target the benefiting population in clinical trials based on patients’ biomarkers. In the case of continuous biomarkers, we show that using a bivariate model that treats biomarkers as random variables more accurately identifies a treatment-benefiting enriched population than assuming biomarkers are fixed. Additionally, we show that under the bivariate model, the maximum likelihood estimators (MLEs) follow a randomly scaled mixture…

函数型数据的经验尾部 CopulaAI 解读

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated estimation errors are known to converge weakly to a Gaussian process that is similar in structure to the weak limit of the empirical copula process. We extend this multivariate result to…

非欧几里得响应与预测变量的加性回归AI 解读

Additive regression is studied in a very general setting where both the response and predictors are allowed to be non-Euclidean. The response takes values in a general separable Hilbert space, whereas the predictors take values in general semimetric spaces, which covers a very wide range of nonstandard response variables and predictors. A general framework of estimating additive models is presented for semimetric space-valued predictors. In particular, full details of…

正态模型中光滑泛函的估计：偏差降低与渐近效率AI 解读

Let X1,…,Xn be i.i.d. random variables sampled from a normal distribution N(μ,Σ) in Rd with unknown parameter θ=(μ,Σ)∈Θ:=Rd×C+d, where C+d is the cone of positively definite covariance operators in Rd. Given a smooth functional f:Θ↦R1, the goal is to estimate f(θ) based on X1,…,Xn. Let Θ(a;d):=Rd×{Σ∈C+d:σ(Σ)⊂[1/a,a]},a≥1, where σ(Σ) is the spectrum of covariance Σ. Let θˆ:=(μˆ,Σˆ), where μˆ is the sample mean and Σˆ is the sample covariance, based on the observations…

渐近依赖与独立下的秩估计及空间极值应用AI 解读

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing evidence that asymptotic independence is equally important in real world applications. Available statistical methodology in the…

用最优决策树自适应估计多元分段多项式与有界变差函数AI 解读

Proposed by Donoho (Ann. Statist. 25 (1997) 1870–1911), Dyadic CART is a nonparametric regression method which computes a globally optimal dyadic decision tree and fits piecewise constant functions in two dimensions. In this article, we define and study Dyadic CART and a closely related estimator, namely Optimal Regression Tree (ORT), in the context of estimating piecewise smooth functions in general dimensions in the fixed design setup. More precisely, these optimal…

高斯过程回归的变量选择一致性AI 解读

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable selection, are known to also adapt to the unknown intrinsic dimension of a sparse true regression function. But it remains unclear if such extensions offer variable selection consistency, that is, if the true subset of important variables…

基于U统计量置换检验的独立性检验最优速率AI 解读

We study the problem of independence testing given independent and identically distributed pairs taking values in a σ-finite, separable measure space. Defining a natural measure of dependence D(f) as the squared L2-distance between a joint density f and the product of its marginals, we first show that there is no valid test of independence that is uniformly consistent against alternatives of the form {f:D(f)≥ρ2}. We therefore restrict attention to alternatives that impose…

不可忽略无响应数据的半参数最优估计AI 解读

When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have been developed under the parametric model assumptions on the response mechanism. In this paper, a new statistical test is proposed to guarantee model identifiability without using instrumental variable assumption. Furthermore, we develop…

连接稳健主成分分析中的凸与非凸优化：噪声、异常值及缺失数据AI 解读

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers and (3) missing data. This problem, often dubbed as robust principal component analysis (robust PCA), finds applications in various domains. Despite the wide applicability of convex relaxation, the available statistical support (particularly the stability analysis in the presence of random noise)…

隐私的代价：差分隐私参数估计的最优收敛率AI 解读

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low-dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the…

Kronecker 协方差极大似然估计的存在性与唯一性AI 解读

In matrix-valued datasets the sampled matrices often exhibit correlations among both their rows and their columns. A useful and parsimonious model of such dependence is the matrix normal model, in which the covariances among the elements of a random matrix are parameterized in terms of the Kronecker product of two covariance matrices, one representing row covariances and one representing column covariance. An appealing feature of such a matrix normal model is that the…

具有集合结构的全局经验风险最小化估计在一般维度下达到最优速率AI 解读

Entropy integrals are widely used as a powerful empirical process tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimation and regression. The upper bound for the convergence rates thus obtained typically matches the minimax lower bound when the entropy integral converges, but admits a strict gap compared to the lower bound when it diverges. Birgé and Massart (Probab. Theory Related…

大型面板数据模型的递归估计：理论与实践AI 解读

Bai (2009) proposes recursive estimation for panel data models with interactive effects. We study the behaviours of this recursive estimator. The recursive formula is established that shows the behaviours of recursive estimators depend on the initial estimator, the population structure and the iterative steps. Under some general scenarios, we find that the recursive estimator becomes consistent after the first iteration from any initials. We also obtain the optimal number of…

半参数 GARCH 模型的自适应推断AI 解读

This paper considers a semiparametric generalized autoregressive conditional heteroskedasticity (S-GARCH) model. For this model, we first estimate the time-varying long run component for unconditional variance by the kernel estimator, and then estimate the non-time-varying parameters in GARCH-type short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we construct a…