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核扩展随机神经网络AI 解读

Abstract The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we propose the so-called kernel-expanded stochastic neural network (K-StoNet) model, which incorporates support vector regression as the first hidden layer and reformulates the neural network as a latent variable model. The former maps the…

基于 HSIC 的自适应独立性检验AI 解读

The Hilbert–Schmidt Independence Criterion (HSIC) is a dependence measure based on reproducing kernel Hilbert spaces that is widely used to test independence between two random vectors. Remains the delicate choice of the kernel. In this work, we develop a new HSIC-based aggregated procedure which avoids such a kernel choice, and provide theoretical guarantees for this procedure. To achieve this, on the one hand, we introduce non-asymptotic single tests based on Gaussian…

高维无岭最小二乘插值中的意外现象AI 解读

Interpolators—estimators that achieve zero training error—have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum ℓ2 norm (“ridgeless”) interpolation least squares regression, focusing on the high-dimensional regime in which the number of unknown parameters p is of the same order as the number of samples n. We consider two different models for the feature…

评《具有随机波动率和非共轭先验的大型贝叶斯向量自回归》AI 解读

Fully Bayesian inference in a vector autoregression with stochastic volatility (VAR-SV) typically relies on simulations from a multi-step Markov chain Monte Carlo (MCMC) algorithm. Carriero et al. (2019) propose a new, faster, “triangular” algorithm (TA) to replace the systemwide algorithm (SWA) in the most time-consuming step of the VAR-SV’s standard MCMC algorithm. This paper analytically shows that the TA and SWA generally sample from different distributions, thereby…

时变模型的同时推断AI 解读

A general class of non-stationary time series is considered in this paper. We estimate the time-varying coefficients by using local linear M-estimation. For these estimators, weak Bahadur representations are obtained and are used to construct simultaneous confidence bands. For practical implementation, we propose a bootstrap based method to circumvent the slow logarithmic convergence of the theoretical simultaneous bands. Our results substantially generalize and unify the…

Brenier 映射势函数的收敛速度AI 解读

The theory of optimal transportation has experienced a sharp increase in interest in many areas of economic research such as optimal matching theory and econometric identification. A particularly valuable tool, due to its convenient representation as the gradient of a convex function, has been the Brenier map: the matching obtained as the optimizer of the Monge–Kantorovich optimal transportation problem with the euclidean distance as the cost function. Despite its…

随机前沿模型中尾部行为的非参数检验AI 解读

Summary This article studies tail behavior for the error components in the stochastic frontier model, where one component has bounded support on one side, and the other has unbounded support on both sides. Under weak assumptions on the error components, we derive nonparametric tests for thin‐tailed distributional assumptions imposed on these two components. The tests are useful diagnostic tools for stochastic frontier analysis and kernel deconvolution density estimation. A…

含噪高频数据的占用密度估计AI 解读

This paper studies the nonparametric estimation of occupation densities for semimartingale processes observed with noise. As leading examples we consider the stochastic volatility of a latent efficient price process, the volatility of the latent noise that separates the efficient price from the actually observed price, and nonlinear transformations of these processes. Our estimation methods are decidedly nonparametric and consist of two steps: the estimation of the spot…

利用含截面依赖的函数系数面板模型检验资本资产定价模型AI 解读

This paper proposes a functional-coefficient panel data model with cross-sectional dependence motivated by re-examining the empirical performance of conditional capital asset pricing model. In order to characterize the time-varying property of assets’ betas and alpha, our proposed model allows the betas to be unknown functions of some macroeconomic and financial instruments. Moreover, a common factor structure is introduced to characterize cross-sectional dependence which is…

无浪费序贯蒙特卡洛AI 解读

Abstract A standard way to move particles in a sequential Monte Carlo (SMC) sampler is to apply several steps of a Markov chain Monte Carlo (MCMC) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its…

多变量纵向与生存数据的半参数潜在类别模型AI 解读

In long-term follow-up studies, data are often collected on repeated measures of multivariate response variables as well as on time to the occurrence of a certain event. To jointly analyze such longitudinal data and survival time, we propose a general class of semiparametric latent-class models that accommodates a heterogeneous study population with flexible dependence structures between the longitudinal and survival outcomes. We combine nonparametric maximum likelihood…

置换检验的极小极大最优性AI 解读

Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing popularity and empirical success, theoretical properties of the permutation test, especially its power, have not been fully explored beyond simple cases. In this paper, we attempt to partly fill this gap by presenting a general nonasymptotic…

第一价格拍卖的分位数回归方法AI 解读

The paper proposes a quantile-regression inference framework for first-price auctions with symmetric risk-neutral bidders under the independent private-value paradigm. It is first shown that a private-value quantile regression generates a quantile regression for the bids. The private-value quantile regression can be easily estimated from the bid quantile regression and its derivative with respect to the quantile level. This also allows to test for various specification or…

连续非经典测量误差下非参数单调回归模型的识别AI 解读

This paper provides sufficient conditions for identification of a nonparametric regression model with an unobserved continuous regressor subject to nonclassical measurement error. The measurement error may be directly correlated with the latent regressor in the model. Our identification strategy does not require the availability of additional data information, such as a secondary measurement, an instrumental variable, or an auxiliary sample. Our main assumptions for…

平滑样条半参数密度模型AI 解读

Jiahui Yua, Jian Shib, Anna Liuc & Yuedong Wangd*a Department of Mathematics and Statistics, Boston University, Boston, MAb PayPal, San Jose, CAc Department of Mathematics and Statistics, University of Massachusetts, Amherst, MAd Department Statistics and Applied Probability, University of California, Santa Barbara, CAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are…

半参数因子模型中的同质性与结构识别AI 解读

Factor modeling is an essential tool for exploring intrinsic dependence structures in financial and economic studies through the construction of common latent variables, including the famous Fama–French three factor models for the description of asset returns in finance. However, most of the existing statistical methods for analyzing latent factors have been developed through a linear approach. In this article, we consider a semiparametric factor model and present a…

因子数增长时充分预测的非参数估计与共形推断AI 解读

The sufficient forecasting (SF) provides a nonparametric procedure to estimate forecasting indices from high-dimensional predictors to forecast a single time series, allowing for the possibly nonlinear forecasting function. This article studies the asymptotic theory of the SF with a diverging number of factors and develops its predictive inference. First, we revisit the SF and explore its connections to Fama–MacBeth regression and partial least squares. Second, with a…

高维数据下条件平均处理效应的估计AI 解读

Given the unconfoundedness assumption, we propose new nonparametric estimators for the reduced dimensional conditional average treatment effect (CATE) function. In the first stage, the nuisance functions necessary for identifying CATE are estimated by machine learning methods, allowing the number of covariates to be comparable to or larger than the sample size. The second stage consists of a low-dimensional local linear regression, reducing CATE to a function of the…

反事实处理效应：估计与推断AI 解读

This article proposes statistical methods to evaluate the quantile counterfactual treatment effect (QCTE) if one were to change the composition of the population targeted by a status quo program. QCTE enables a researcher to carry out an ex-ante assessment of the distributional impact of certain policy interventions or to investigate the possible explanations for treatment effect heterogeneity. Assuming unconfoundedness and invariance of the conditional distributions of the…

均值结构与自相关稳健的协方差矩阵估计AI 解读

We consider estimation of the asymptotic covariance matrix in nonstationary time series. A nonparametric estimator that is robust against unknown forms of trends and possibly a divergent number of change points (CPs) is proposed. It is algorithmically fast because neither a search for CPs, estimation of trends, nor cross-validation is required. Together with our proposed automatic optimal bandwidth selector, the resulting estimator is both statistically and computationally…

异方差分数单整时间序列模型中的自适应推断AI 解读

We consider estimation and inference in fractionally integrated time series models driven by shocks which can display conditional and unconditional heteroscedasticity of unknown form. Although the standard conditional sum-of-squares (CSS) estimator remains consistent and asymptotically normal in such cases, unconditional heteroscedasticity inflates its variance matrix by a scalar quantity, λ>1, thereby inducing a loss in efficiency relative to the unconditionally…

符号正则核的低秩逼近AI 解读

Parameterized integrals, q y = ∫ K x , y d P x , are common in economic applications. To optimize a parameterized integral, or to relate one such integral to others, it is helpful to reduce the rank of the kernel K while controlling approximation error. A bound on the uniform approximation error of K x , y ≈ ∑ i = 1 n f i x g i y also bounds the uniform approximation error of q y ≈ ∑ i = 1 n c i g i y = ∑ i = 1 n ∫ f i x d P x g i y over all y and all signed measures P whose…

具有参数化截面依赖的非参数面板回归AI 解读

Summary In this paper, we consider efficiency improvement in a nonparametric panel data model with cross-sectional dependence. A generalised least squares (GLS)-type estimator is proposed by taking into account this dependence structure. Parameterising the cross-sectional dependence, a local linear estimator is shown to be dominated by this type of GLS estimator. Also, possible gains in terms of rate of convergence are studied. Asymptotically optimal bandwidth choice is…

非光滑非凸统计学习中的广义 Bregman 替代算法分析AI 解读

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror descent, iterative thresholding, DC programming and many others as particular instances. The recharacterization via generalized Bregman functions enables us to construct suitable error measures and establish global convergence rates for…