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复杂区域上的非参数密度估计AI 解读

Abstract We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements. This ensures high computational efficiency and enables great flexibility.…

分数阶 d=1/2 与弱非平稳过程下的估计和推断AI 解读

We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity—what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional processes with d=1/2, and arrays of autoregressive processes with roots drifting slowly towards unity. We first apply the theory to study inference in parametric and nonparametric regression models involving WNPs as covariates. We then use…

非参数单调回归中可信区间的覆盖率AI 解读

For nonparametric univariate regression under a monotonicity constraint on the regression function f, we study the coverage of a Bayesian credible interval for f(x0), where x0 is an interior point. Analysis of the posterior becomes a lot more tractable by considering a “projection-posterior” distribution based on a finite random series of step functions with normal basis coefficients as a prior for f. A sample f from the resulting conjugate posterior distribution is…

安全自适应重要性抽样：混合分布方法AI 解读

This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous particles), and a “safe” heavy-tailed density. When the share of samples generated according to the safe density goes to zero but not too quickly, two results are established: (i) uniform convergence rates are derived for the policy toward…

基于层次依赖混合风险率的生存分析AI 解读

Hierarchical nonparametric processes are popular tools for defining priors on collections of probability distributions, which induce dependence across multiple samples. In survival analysis problems, one is typically interested in modeling the hazard rates, rather than the probability distributions themselves, and the currently available methodologies are not applicable. Here, we fill this gap by introducing a novel, and analytically tractable, class of multivariate mixtures…

通过完全单调性与Hardy–Krause变差推广多元保序回归和总变差去噪AI 解读

We consider the problem of nonparametric regression when the covariate is d dimensional, where d≥1. In this paper, we introduce and study two nonparametric least squares estimators (LSEs) in this setting—the entirely monotonic LSE and the constrained Hardy–Krause variation LSE. We show that these two LSEs are natural generalizations of univariate isotonic regression and univariate total variation denoising, respectively, to multiple dimensions. We discuss the…

最优数据披露风险评估AI 解读

Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size n from a finite population of size n¯=n+λn, with λ>0, such that each sample record contains two disjoint types of information: identifying categorical information and sensitive information. Any decision about releasing data is supported by the estimation of measures of disclosure risk, which are defined as discrete…

利用对称性与形状约束的高维非参数密度估计AI 解读

We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on Rp and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and can mitigate the curse of dimensionality. Our main symmetry assumption is that the super-level sets of the density are K-homothetic (i.e., scalar multiples of a convex body K⊆Rp). When K is known, we prove that the K-homothetic log-concave maximum…

多维分布函数、分位数函数、秩与符号：测度运输方法AI 解读

Unlike the real line, the real space Rd, for d≥2, is not canonically ordered. As a consequence, such fundamental univariate concepts as quantile and distribution functions and their empirical counterparts, involving ranks and signs, do not canonically extend to the multivariate context. Palliating that lack of a canonical ordering has been an open problem for more than half a century, generating an abundant literature and motivating, among others, the development of…

时间一致、非参数、非渐近的置信序列AI 解读

A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. Our work develops confidence sequences whose widths go to zero, with nonasymptotic coverage guarantees under nonparametric conditions. We draw connections between the Cramér–Chernoff method for exponential concentration, the law of the iterated logarithm (LIL) and the sequential probability ratio test—our confidence sequences are time-uniform extensions of the…

扩散Copula：识别与估计AI 解读

We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class of semiparametric Markov diffusion models with parametric dynamic copulas and nonparametric marginal distributions. We provide primitive conditions for the identification of the UPD parameters together with the unknown transformations…

变随机系数模型AI 解读

This paper analyzes unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of observed regressors and additively separable unobservables. This paper proposes a novel estimator of the VRC density based on weighted sieve minimum distance. The main example of sieve bases are Hermite functions which yield a numerically stable estimation procedure.…

非参数部分识别下部分线性工具变量模型的稳健与最优估计AI 解读

This paper studies robust and optimal estimation of the slope coefficients in a partially linear instrumental variables model with nonparametric partial identification. We establish the root-n asymptotic normality of a penalized sieve minimum distance estimator of the slope coefficients. We show that the asymptotic normality holds regardless of whether the nonparametric function is point identified or only partially identified. However, in the presence of nonparametric…

期权观测误差中的空间依赖AI 解读

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau…

稳健化的期望最大生产前沿AI 解读

The aim of this paper is to construct a robust nonparametric estimator for the production frontier. We study this problem under a regression model with one-sided errors, where the regression function defines the achievable maximum output, for a given level of inputs-usage, and the regression error defines the inefficiency term. The main tool is a concept of partial regression boundary defined as a special probability-weighted moment. This concept motivates a robustified…

级数项数设定搜索下的非参数级数估计推断AI 解读

Nonparametric series regression often involves specification search over the tuning parameter, that is, evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences for conditional mean functions in nonparametric series estimations that are uniform in the number of series terms. As a result, this paper constructs confidence intervals and confidence bands with possibly data-dependent series terms…

回归不连续设计下条件处理效应的单调性检验AI 解读

Summary Researchers are often interested in the relationship between treatment effects and observed individual heterogeneity. This paper proposes the first nonparametric monotonicity test for conditional treatment effects under the popular regression discontinuity framework. The proposed test examines whether the average treatment effect or the local average treatment effect has a monotonic relationship with some of the observed individual characteristics. We show…

一类指数模型的识别：拓扑方法AI 解读

Summary We establish nonparametric identification in a class of so-called index models by using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions characterising the model than those required by existing strategies; in particular, it does not require any large-support conditions on the regressors of our model. We apply the general identification result to additive random…

条件分位数限制识别的非参数工具变量模型中的外生性检验AI 解读

Summary This paper presents a test for exogeneity of explanatory variables in a nonparametric instrumental variables (IV) model whose structural function is identified through a conditional quantile restriction. Quantile regression models are increasingly important in applied econometrics. As with mean-regression models, an erroneous assumption that the explanatory variables in a quantile regression model are exogenous can lead to highly misleading results. In addition, a…

用半参数非线性动力系统建模时变生物标志物AI 解读

Summary Dynamical systems based on differential equations are useful for modelling the temporal evolution of biomarkers. Such systems can characterize the temporal patterns of biomarkers and inform the detection of interactions between biomarkers. Existing statistical methods for dynamical systems deal mostly with single time-course data based on a linear model or generalized additive model. Hence, they cannot adequately capture the complex interactions between biomarkers;…

具有混合偏差性质的参数刻画AI 解读

Summary We study a class of parameters with the so-called mixed bias property. For parameters with this property, the bias of the semiparametric efficient one-step estimator is equal to the mean of the product of the estimation errors of two nuisance functions. In nonparametric models, parameters with the mixed bias property admit so-called rate doubly robust estimators, i.e., estimators that are consistent and asymptotically normal when one succeeds in estimating both…

大样本平滑样条 ANOVA 模型的渐近与经验平滑参数选择AI 解读

Summary Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection method for…

含污染观测的流形上函数型回归AI 解读

Summary We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold, but is observable only in an infinite-dimensional space. Contamination of the predictor due to discrete or noisy measurements is also accounted for. By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the contamination level.…

战略互动与理性预期离散选择模型的半参数效率界AI 解读

This paper computes semiparametric efficiency bounds for finite-dimensional parameters in discrete choice models with nonparametric regressors in the form of conditional expectations. These can include expectations about exogenous events as well as expectations about the choices of other agents. Thus, the models studied here include incomplete-information games, social-interactions models as well as single-agent discrete choice models with uncertainty as special cases. Our…