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期权隐含状态价格密度的筛估计AI 解读

This paper proposes a nonparametric estimator for the state price density implied by a single cross-section of European options with different strikes and the same maturity. The proposed estimator has two distinctive features. First, it extracts information from both call and put options, as opposed to only call options. Second, it does not require estimating any second-order derivative; instead, it solves a constrained and penalized linear regression. The asymptotic…

利用平滑聚类标准误进行时间序列模型推断AI 解读

This paper proposes a long run variance estimator for conducting inference in time series regression models that combines the nonparametric approach with a cluster approach. The basic idea is to divide the time periods into non-overlapping clusters. The long run variance estimator is constructed by first aggregating within clusters and then kernel smoothing across clusters or applying the nonparametric series method to the clusters with Type II discrete cosine transform. We…

时变参数高维预测回归的 Boosting 估计AI 解读

High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for parameter instability in economic time series, but theories for parameter instability are mainly developed for models with a small number of covariates. In this paper, we present two L2 boosting algorithms for estimating high dimensional…

存在中间混杂变量时的非参数有效因果中介分析AI 解读

Summary Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence function in the nonparametric statistical model. We use the efficient influence function to develop two…

刀切经验似然：小带宽、稀疏网络与高维渐近AI 解读

Summary This article aims to shed light on inference problems for statistical models under alternative or nonstandard asymptotic frameworks from the perspective of the jackknife empirical likelihood. Examples include small-bandwidth asymptotics for semiparametric inference and goodness-of-fit testing, sparse-network asymptotics, many-covariates asymptotics for regression models, and many-weak-instruments asymptotics for instrumental variable regression. We first establish…

利用 ROC 曲线评估生存数据中的治愈状态预测AI 解读

Summary Survival analysis relies on the hypothesis that, if the follow-up is long enough, the event of interest will eventually be observed for all observations. This assumption, however, is often not realistic. The survival data then contain a cure fraction. A common approach to modelling and analysing this type of data consists in using cure models. Two types of information can therefore be obtained: the survival at a given time and the cure status, both possibly modelled…

移动健康中二元结局的时变因果偏离效应估计AI 解读

Summary Advances in digital technology and wearables have made it possible to deliver behavioural mobile health interventions to individuals in their everyday lives. Micro-randomized trials are increasingly used to provide data to inform the construction of these interventions. In a micro-randomized trial, each individual is repeatedly randomized among multiple intervention options, often hundreds or even thousands of times over the course of the trial. The work reported in…

We revisit a paper by Charles Stein, and discuss its follow-up.

高斯过程建模中参考后验分布的正常性AI 解读

In a seminal article, Berger, De Oliveira and Sansó [J. Amer. Statist. Assoc. 96 (2001) 1361–1374] compare several objective prior distributions for the parameters of Gaussian process models with isotropic correlation kernel. The reference prior distribution stands out among them insofar as it always leads to a proper posterior. They prove this result for rough correlation kernels: Spherical, Exponential with power ρ<2, Matérn with smoothness ν<1. This paper provides a proof…

非参数多元有限混合模型的成分数量估计AI 解读

We propose a novel estimator for the number of mixture components (denoted by M) in a nonparametric finite mixture model. The setting that we consider is one where the analyst has repeated observations of K≥2 variables that are conditionally independent given a finitely supported latent variable with M support points. Under a mild assumption on the joint distribution of the observed and latent variables, we show that an integral operator T that is identified from the data…

含时变协变量的非参数风险函数提升估计AI 解读

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent…

扩展可容许决策程序及其非标准贝叶斯风险AI 解读

For finite parameter spaces, among decision procedures with finite risk functions, a decision procedure is extended admissible if and only if it is Bayes. Various relaxations of this classical equivalence have been established for infinite parameter spaces, but these extensions are each subject to technical conditions that limit their applicability, especially to modern (semi and nonparametric) statistical problems. Using results in mathematical logic and nonstandard…

波动率估计的耦合理论AI 解读

This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting.…

二阶 Stein 公式：SURE 的风险估计及高维推断应用AI 解读

Stein’s formula states that a random variable of the form z⊤f(z)−divf(z) is mean-zero for all functions f with integrable gradient. Here, divf is the divergence of the function f and z is a standard normal vector. This paper aims to propose a second-order Stein formula to characterize the variance of such random variables for all functions f(z) with square integrable gradient, and to demonstrate the usefulness of this second-order Stein formula in various applications. In…

重尾稀疏图的一致非参数估计AI 解读

We study graphons as a nonparametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. In contrast to previous work, we relax the usual boundedness assumption for the generating graphon and instead assume only integrability, so that we can handle networks that have long tails in their degree distributions. We also relax the usual assumption that the graphon is defined on the unit…

全连接深度神经网络回归估计的收敛速率AI 解读

Recent results in nonparametric regression show that deep learning, that is, neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in these results is that their network architecture has a further constraint, namely the network sparsity. In this paper, we show that we can get similar results…

利用平滑与筛方法求解动态离散选择模型AI 解读

We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce smoothed versions of the random…

动态离散选择模型的半参数估计AI 解读

We consider the estimation of dynamic binary choice models in a semiparametric setting, in which the per-period utility functions are known up to a finite number of parameters, but the distribution of utility shocks is left unspecified. This semiparametric setup differs from most of the existing identification and estimation literature for dynamic discrete choice models. To show identification we derive and exploit a new recursive representation for the unknown quantile…

结构动态 Logit 模型中未观测异质性的充分统计量AI 解读

We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is nonparametric, i.e., fixed-effects model. We consider models with two endogenous state variables: the lagged decision variable, and the time duration in the last choice. This class of models includes as particular cases important economic applications…

一般波动率动态下积分波动率泛函的有效估计AI 解读

We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric…

测量误差模型的设定检验AI 解读

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the methods proposed by Hall and Ma (2007, Annals of Statistics , 35, 2620–2638) and Song (2008, Journal of Multivariate Analysis , 99, 2406–2443), our test allows general nonlinear regression models and possesses complementary local power…

基于边际化脆弱性的疾病—死亡模型：英国生物样本库应用AI 解读

The UK Biobank is a large-scale health resource comprising genetic, environmental, and medical information on approximately 500,000 volunteer participants in the United Kingdom, recruited at ages 40–69 during the years 2006–2010. The project monitors the health and well-being of its participants. This work demonstrates how these data can be used to yield the building blocks for an interpretable risk-prediction model, in a semiparametric fashion, based on known genetic and…

成人声调学习的贝叶斯半参数纵向漂移扩散混合模型AI 解读

Understanding how adult humans learn nonnative speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions using longitudinal learning experiments under a multi-category decision making paradigm. Drift-diffusion processes are popular in such contexts for their ability to mimic underlying neural mechanisms. Motivated by these problems, we develop…

利用双重 Lasso 惩罚非参数估计星系团辐射率并检测点源AI 解读

Astrophysicists are interested in recovering the three-dimensional gas emissivity of a galaxy cluster from a two-dimensional telescope image. Blurring and point sources make this inverse problem harder to solve. The conventional approach requires in a first step to identify and mask the point sources. Instead we model all astrophysical components in a single Poisson generalized linear model. To enforce sparsity on the parameters, maximum likelihood estimation is regularized…