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非参数回归的无分布预测带AI 解读

Summary We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of ‘conformal prediction’ with non-parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions…

条件变换模型AI 解读

Summary The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models estimate only the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and…

In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at a slower rate than or the same rate as the sample size, we obtain two types of asymptotic approximations: the small-b asymptotics and the fixed-b asymptotics. Using techniques for…

可能误设的半非参数时间序列模型的筛推断AI 解读

This paper establishes the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi-nonparametric time series models. We show that, even when the sieve score process is not a martingale difference sequence, the asymptotic variance in the case of irregular functionals is the same as those for independent data. Using an orthonormal series long run variance estimator, we construct a “pre-asymptotic” Wald statistic and show that it is…

误设长期记忆模型的估计AI 解读

We consider time series that, possibly after integer differencing or integrating or other detrending, are covariance stationary with spectral density that is regularly varying near zero frequency, and unspecified elsewhere. This semiparametric framework includes series with short, long and negative memory. We consider the consistency of the popular log-periodogram memory estimate that, conventionally but wrongly, assumes the spectral density obeys a pure power law. The…

用于估计与检验的非参数及半参数残差加权和的一致收敛AI 解读

A new uniform expansion is introduced for sums of weighted kernel-based regression residuals from nonparametric or semiparametric models. This expansion is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data-dependent bandwidths, random trimming, and estimated efficiency weights. Provided examples include a new estimator for a binary choice model with selection and an associated directional test for specification of this…

SUMMARY We consider the dynamic factor model and show how smoothness restrictions can be imposed on factor loadings by using cubic spline functions. We develop statistical procedures based on Wald, Lagrange multiplier and likelihood ratio tests for this purpose. The methodology is illustrated by analyzing a newly updated monthly time series panel of US term structure of interest rates. Dynamic factor models with and without smooth loadings are compared with dynamic models…

具有变化平滑参数的平滑样条AI 解读

This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with nonhomogeneous smoothness across the domain. Two challenging issues arising in this context are the evaluation of the equivalent kernel and the determination of a local penalty. The penalty is a function of the design points in order to accommodate local behaviour of the regression function. We show that the spatially adaptive smoothing spline…

构造函数型数据分类器时离散数据平滑带宽的意外性质AI 解读

The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually smooth functions that were not actually observed. Existing literature shows that this approach is effective, and even optimal, when using functional data methods for prediction or hypothesis testing. However, in the present paper we show…

期权隐含通胀概率密度的经济含义AI 解读

Recently a market in options based on consumer price index inflation (inflation caps and floors) has emerged in the US. This paper uses quotes on these derivatives to construct probability densities for inflation. We study how these probability density functions respond to news announcements and find that the implied odds of deflation are sensitive to certain macroeconomic news releases. We also estimate empirical pricing kernels using these option prices along with time…

降秩惩罚样条平滑的边际方法及其多层函数数据应用AI 解读

Multilevel functional data is collected in many biomedical studies. For example, in a study of the effect of Nimodipine on patients with subarachnoid hemorrhage (SAH), patients underwent multiple 4-hour treatment cycles. Within each treatment cycle, subjects' vital signs were reported every 10 minutes. This data has a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles. Most literature on nonparametric analysis of…

通过嵌套高斯过程实现局部自适应贝叶斯非参数回归AI 解读

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function’s mth-order derivative. The nesting comes in through including a local instantaneous mean function, which is drawn from another Gaussian process inducing adaptivity to locally varying smoothness. We discuss the support of the nGP prior in…

含长期存活群体的删失数据治愈率分位数回归AI 解读

Censored quantile regression offers a valuable complement to the traditional Cox proportional hazards model for survival analysis. Survival times tend to be right-skewed, particularly when there exists a substantial fraction of long-term survivors who are either cured or immune to the event of interest. For survival data with a cure possibility, we propose cure rate quantile regression under the common censoring scheme that survival times and censoring times are…

流形上的局部线性回归及其几何解释AI 解读

High-dimensional data analysis has been an active area, and the main focus areas have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear manifold. Under this manifold assumption, one purpose of this article is regression and gradient estimation on the manifold, and another is developing a new tool for manifold learning. As regards the first aim, we suggest directly reducing…

贝叶斯序贯分割的多元密度估计AI 解读

Consider a class of densities that are piecewise constant functions over partitions of the sample space defined by sequential coordinate partitioning. We introduce a prior distribution for a density in this function class and derive in closed form the marginal posterior distribution of the corresponding partition. A computationally efficient method, based on sequential importance sampling, is presented for the inference of the partition from this posterior distribution.…

加权平均导数的广义刀切估计量AI 解读

With the aim of improving the quality of asymptotic distributional approximations for nonlinear functionals of nonparametric estimators, this article revisits the large-sample properties of an important member of that class, namely a kernel-based weighted average derivative estimator. Asymptotic linearity of the estimator is established under weak conditions. Indeed, we show that the bandwidth conditions employed are necessary in some cases. A bias-corrected version of the…

含高维协变量的广义可加部分线性模型AI 解读

This paper studies generalized additive partial linear models with high-dimensional covariates. We are interested in which components (including parametric and nonparametric components) are nonzero. The additive nonparametric functions are approximated by polynomial splines. We propose a doubly penalized procedure to obtain an initial estimate and then use the adaptive least absolute shrinkage and selection operator to identify nonzero components and to obtain the final…

通过平滑似然高效估计内生分层回归AI 解读

This paper presents efficient semiparametric estimators for endogenously stratified regression with two strata, in the case where the error distribution is unknown and the regressors are independent of the error term. The method is based on the use of a kernel-smoothed likelihood function which provides an explicit solution for the maximization problem for the unknown density function without losing information in the asymptotic limit. We consider both standard stratified…

条件估计方程下的平滑最小距离估计与检验：带宽一致理论AI 解读

To study the influence of a bandwidth parameter in inference with conditional moments, we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth, which can vary within a wide range including bandwidths independent of the sample size. We study its behavior under misspecification. We also propose an efficient version of our estimator. We develop a procedure based on a distance metric statistic for…

固定效应线性面板模型中对异方差与时空依赖稳健的推断AI 解读

This paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms. We propose a bivariate kernel covariance estimator that nests existing estimators as special cases. Our estimator improves upon existing estimators in terms of robustness, efficiency, and adaptiveness. For distributional approximations, we considered two types of asymptotics: the increasing-smoothing asymptotics…

长记忆、短记忆与负记忆时间序列中学生化均值的分布理论AI 解读

We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the first-difference of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the…

跳跃是否影响股票风险溢价的动态变化？AI 解读

This paper investigates whether risks associated with time-varying arrival of jumps and their effect on the dynamics of higher moments of returns are priced in the conditional mean of daily market excess returns. We find that jumps and jump dynamics are significantly related to the market equity premium. The results from our time-series approach reinforce the importance of the skewness premium found in cross-sectional studies using lower-frequency data; and offer a potential…

含潜在奇异点的空间非均匀线性逆问题AI 解读

The objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem where the degree of ill-posedness of operator $Q$ depends not only on the scale but also on location. In this case, the rates of convergence are determined by the interaction of four parameters, the smoothness and spatial homogeneity of the unknown function $f$ and degrees of ill-posedness and spatial inhomogeneity of operator $Q$. Estimators obtained in the…

平滑样条模型中的局部与全局渐近推断AI 解读

This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. Statist. Math. 37 (1966) 577–580]. Equipped with this tool, we develop four interconnected procedures for inference: (i) pointwise confidence interval; (ii)…