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This paper offers a new approach to modeling and forecasting of nonstationary time series with applications to volatility modeling for financial data. The approach is based on the assumption of local homogeneity: for every time point, there exists a historical interval of homogeneity, in which the volatility parameter can be well approximated by a constant. The proposed procedure recovers this interval from the data using the local change point (LCP) analysis. Afterward, the…

主成分限制最大似然估计量的一致性AI 解读

In this paper we consider two closely related problems: estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and eigenvectors of the covariance matrix for high-dimensional Gaussian vectors. In [A geometric approach to maximum likelihood estimation of covariance kernel from sparse irregular longitudinal data (2007)], a restricted maximum likelihood…

基于已实现测度的日波动率预测密度估计AI 解读

The main objective of this paper is to propose a feasible, model free estimator of the predictive density of integrated volatility. In this sense, we extend recent papers by Andersen et al. [Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., 2003. Modelling and forecasting realized volatility. Econometrica 71, 579-626], and by Andersen et al. [Andersen, T.G., Bollerslev, T., Meddahi, N., 2004. Analytic evaluation of volatility forecasts. International Economic…

风险的Granger因果关系与金融市场极端风险溢出检验AI 解读

Controlling and monitoring extreme downside market risk are important for financial risk management and portfolio/investment diversification. In this paper, we introduce a new concept of Granger causality in risk and propose a class of kernel-based tests to detect extreme downside risk spillover between financial markets, where risk is measured by the left tail of the distribution or equivalently by the Value at Risk (VaR). The proposed tests have a convenient asymptotic…

变系数模型的收缩估计AI 解读

The varying coefficient model is a useful extension of the linear regression model. Nevertheless, how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood. To solve the problem, we propose here a novel method, which combines the ideas of the local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator (LASSO). The new method can do nonparametric estimation and variable selection…

计算高效的非参数重要性抽样AI 解读

The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric estimation of the optimal importance sampling distribution (known as “nonparametric importance sampling”) is a reasonable alternative to parametric approaches. In this article, nonparametric variants of both the self-normalized and the…

稀疏观测函数样本的导数估计及在线拍卖动态应用AI 解读

It is often of interest to recover derivatives of a sample of random functions from sparse and noise-contaminated measurements, especially when the dynamics of underlying processes is of interest. We propose a novel approach based on estimating derivatives of eigenfunctions and expansions of random functions into their eigenfunctions to obtain a representation for derivatives. In combination with estimates for functional principal component scores for sparse data, this leads…

动态 PET 数据的非参数残留函数分析：健康受试者脑部 FDG 研究AI 解读

Kinetic analysis is used to extract metabolic information from dynamic positron emission tomography (PET) uptake data. The theory of indicator dilutions, developed in the seminal work of Meier and Zierler (1954), provides a probabilistic framework for representation of PET tracer uptake data in terms of a convolution between an arterial input function and a tissue residue. The residue is a scaled survival function associated with tracer residence in the tissue. Nonparametric…

逆条件密度加权函数的半参数估计效率界AI 解读

Consider the unconditional moment restriction E[ m ( y , υ , w ; π 0 )/ f V | w ( υ | w ) − s ( w ; π 0 )] = 0, where m (·) and s (·) are known vector-valued functions of data ( y ┬ , υ , w ┬ ) ┬ . The smallest asymptotic variance that $\root \of n $ -consistent regular estimators of π 0 can have is calculated when f V | w (·) is only known to be a bounded, continuous, nonzero conditional density function. Our results show that “plug-in” kernel-based estimators of π 0…

两种长期方差估计量：超越短记忆AI 解读

This paper deals with the estimation of the long-run variance of a stationary sequence. We extend the usual Bartlett-kernel heteroskedasticity and autocorrelation consistent (HAC) estimator to deal with long memory and antipersistence. We then derive asymptotic expansions for this estimator and the memory and autocorrelation consistent (MAC) estimator introduced by Robinson [Robinson, P. M., 2005. Robust covariance matrix estimation: HAC estimates with long…

利用积分嵌套拉普拉斯近似进行潜在高斯模型的近似贝叶斯推断AI 解读

Summary Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive…

一类半参数线性模型的平滑参数选择AI 解读

Summary Spline-based approaches to non-parametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several…

广义惩罚样条平滑的若干渐近结果AI 解读

Summary The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for non-normal responses. The results are extended in two ways. First, assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models. We consider the asymptotic rates such that the Laplace approximation is…

逆回归降维问题的再生核希尔伯特空间表述AI 解读

Suppose that Y is a scalar and X is a second-order stochastic process, where Y and X are conditionally independent given the random variables ξ1, …, ξp which belong to the closed span LX2 of X. This paper investigates a unified framework for the inverse regression dimension-reduction problem. It is found that the identification of LX2 with the reproducing kernel Hilbert space of X provides a platform for a seamless extension from the finite- to infinite-dimensional settings.…

高维部分线性模型中的 SCAD 惩罚回归AI 解读

We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be…

动态模型的模拟非参数估计AI 解读

This paper introduces a new class of parameter estimators for dynamic models, called simulated non-parametric estimators (SNEs). The SNE minimizes appropriate distances between non-parametric conditional (or joint) densities estimated from sample data and non-parametric conditional (or joint) densities estimated from data simulated out of the model of interest. Sample data and model-simulated data are smoothed with the same kernel, which considerably simplifies bandwidth…

混合类别与连续协变量下平均处理效应的有效估计AI 解读

In this article, we consider the nonparametric estimation of average treatment effects when there exist mixed categorical and continuous covariates. One distinguishing feature of the approach presented herein is the use of kernel smoothing for both the continuous and the discrete covariates. This approach, together with the cross-validation method. which we use for selecting the smoothing parameters, has the ability to automatically remove irrelevant covariates. We establish…

损失分布的局部变换核密度估计AI 解读

We develop a tailor-made semiparametric asymmetric kernel density estimator for the estimation of actuarial loss distributions. The estimator is obtained by transforming the data with the generalized Champernowne distribution initially fitted to the data. Then the density of the transformed data is estimated by use of local asymmetric kernel methods to obtain superior estimation properties in the tails. We find in a vast simulation study that the proposed semiparametric…

利用贝叶斯平滑样条混合进行局部谱分析AI 解读

In many practical problems, time series are realizations of nonstationary random processes. These processes can often be modeled as processes with slowly changing dynamics or as piecewise stationary processes. In these cases, various approaches to estimating the time-varying spectral density have been proposed. Our approach in this article is to estimate the log of the Dahlhaus local spectrum using a Bayesian mixture of splines. The basic idea of our approach is to first…

动态平滑系数模型的非参数分位数估计AI 解读

In this article, quantile regression methods are suggested for a class of smooth coefficient time series models. We use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework. We establish the asymptotic properties of both the local polynomial and local constant estimators for α-mixing time series. Also, a bandwidth selector based on the nonparametric version of the Akaike information criterion is suggested,…

函数型预测变量的贝叶斯半参数联合模型AI 解读

Motivated by the need to understand and predict early pregnancy loss using hormonal indicators of pregnancy health, this paper proposes a semiparametric Bayes approach for assessing the relationship between functional predictors and a response. A multivariate adaptive spline model is used to describe the functional predictors, and a generalized linear model with a random intercept describes the response. Through specifying the random intercept to follow a Dirichlet process…

变量含测量误差问题中适应设计分布的局部多项式估计AI 解读

Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last…

无单调性非可分模型中局部平均导数的识别与估计AI 解读

In many structural economic models there are no good arguments for additive separability of the error. Recently, this motivated intensive research on non-separable structures. For instance, in equation case was considered, and it was established that in the absence of the frequently employed monotonicity assumption local average structural derivatives (LASD) are still identified. In this paper, we introduce an estimator for the LASD. The estimator we propose is based on…

含缺失值估计方程的经验似然推断AI 解读

We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we propose a nonparametric imputation of the missing values from a kernel estimator of the conditional distribution of the missing variable given the always observable variable. The empirical likelihood is used to construct a profile…