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双重因子结构下高维函数型时间序列的协方差函数估计AI 解读

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor structure is imposed on the observed functional processes, whereas a low-dimensional version (via series approximation) is assumed for the latent functional factors. We extend the classic principal component analysis technique for estimating a low-rank structure to the estimation of a large covariance matrix of…

一般非参数回归的集成投影寻踪AI 解读

Projection pursuit regression (PPR) and artificial neural networks (ANNs), both introduced around the same time, share a similar approach to approximating complex structures in data. However, PPR has received far less attention than ANNs and other popular statistical learning methods such as random forests (RF) and support vector machines (SVM). In this paper, we revisit the estimation of PPR and propose an optimal greedy algorithm and an ensemble approach via feature…

存在漏报时的时间序列序列依赖与交叉依赖检验AI 解读

Abstract In practice, it is common for collected data to be underreported, an issue that is particularly prevalent in fields such as the social sciences, ecology and epidemiology. Drawing inferences from such data using conventional statistical methods can lead to incorrect conclusions. In this paper, we study tests for serial or cross dependence in time series data that are subject to underreporting. We introduce new test statistics, develop corresponding group-of-blocks…

梯度外积降维方法及其在高维分类中的应用AI 解读

Sufficient dimension reduction (SDR) has progressed steadily. However, its ability to improve general function estimation or classification has not been well received, especially for high-dimensional data. In this article, we first devise a local linear smoother for high dimensional nonparametric regression and then utilise it in the outer-product-of-gradient (OPG) approach of SDR. We call the method high-dimensional OPG (HOPG). To apply SDR to classification in…

高维白噪声的自助检验AI 解读

The testing of white-noise (WN) is an essential step in time series analysis. In a high dimensional set-up, most existing methods either are computationally infeasible, or suffer from highly distorted Type-I errors, or both. We propose an easy-to-implement bootstrap method for high-dimensional WN test and prove its consistency for a variety of test statistics. Its power properties as well as extensions to WN tests based on fitted residuals are also considered. Simulation…

分析资产收益共同变动的函数型时间序列方法AI 解读

We introduce a new approach for modeling the time varying behavior and time series evolution of asset returns co-movements. Here, the co-movement in each period is captured by a trajectory of returns correlation, then a sequence of this over time and the time series evolution are studied. We rely on functional principal components to achieve dimension reduction and to construct the dynamic space of interest, while introducing a new class of information criteria in order to…

复合决定系数及其在超高维变量筛选中的应用AI 解读

In this article, we propose to measure the dependence between two random variables through a composite coefficient of determination (CCD) of a set of nonparametric regressions. These regressions take consecutive binarizations of one variable as the response and the other variable as the predictor. The resulting measure is invariant to monotonic marginal variable transformation, rendering it robust against heavy-tailed distributions and outliers, and convenient for…

非参数删失分位数回归的一致 Bahadur 表示：质量再分配方法AI 解读

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability , vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local…

具有 ARMA 误差的半变系数时间序列模型估计AI 解读

Serial correlation in the residuals of time series models can cause bias in both model estimation and prediction. However, models with such serially correlated residuals are difficult to estimate, especially when the regression function is nonlinear. Existing estimation methods require strong assumption for the relation between the residuals and the regressors, which excludes the commonly used autoregressive models in time series analysis. By extending the Whittle likelihood…

含移动平均残差的非线性自回归模型的 Whittle 似然估计AI 解读

The Whittle likelihood estimation (WLE) has played a fundamental role in the development of both theory and computation of time series analysis. However, WLE is only applicable to models whose theoretical spectral density function (SDF) is known up to the parameters in the models. In this article, we propose a residual-based WLE, called extended WLE (XWLE), which can estimate models with their SDFs only partially available, including many popular time series models with…

连接函数未指定的广义变系数模型估计AI 解读

In this paper, we study the generalised varying-coefficient models, where the link function is unspecified and the response variable can be either continuous or discrete. As the link function is unspecified, the models under investigation become unidentifiable. In this paper, we derive an identification condition for the generalised varying-coefficient models, which is much weaker and more reasonable than that given by Kuruwita et al. (2011) whose model can be seen as a…

用于充分降维的自适应复合分位数方法AI 解读

Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316–342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an adaptive composite quantile approach. Compared to existing methods, (1) it requires minimal assumptions and is capable of revealing all dimension reduction directions; (2) it is robust against outliers and (3) it is structure-adaptive, thus…

非参数删失回归分位数的全局 Bahadur 表示及其应用AI 解读

This paper is concerned with the nonparametric estimation of regression quantiles of a response variable that is randomly censored. Using results on the strong uniform convergence rate of U-processes, we derive a global Bahadur representation for a class of locally weighted polynomial estimators, which is sufficiently accurate for many further theoretical analyses including inference. Implications of our results are demonstrated through the study of the asymptotic properties…

单指标分位数回归模型及其估计AI 解读

Models with single-index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. This paper focuses on a single-index model for the conditional quantile. We propose an adaptive estimation procedure and an iterative algorithm which, under mild regularity conditions, is proved to converge with probability 1. The resulted estimator of the single-index parametric vector is root- n consistent,…

局部多项式 M 回归估计的一致 Bahadur 表示及其加性模型应用AI 解读

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {( Y i , X i )}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We…

生存模型的降维与半参数估计AI 解读

In this paper, we propose a new dimension reduction method by introducing a nominal regression model with the hazard function as the conditional mean, which naturally retrieves information from complete data and censored data as well. Moreover, without requiring the linearity condition, the new method can estimate the entire central subspace consistently and exhaustively. The method also provides an alternative approach for the analysis of censored data assuming neither the…

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…

多指标模型与进一步降维AI 解读

Dimension reduction can be used as an initial step in statistical modeling. Further specification of model structure is imminent and important when the reduced dimension is still greater than 1. In this article we investigate one method of specification that involves separating the linear component from the nonlinear components, leading to further dimension reduction in the unknown link function and, thus, better estimation and easier interpretation of the model. The…

典型分析的半参数方法AI 解读

Summary Classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables. We propose a method, called semiparametric canonical analysis, to generalize canonical correlation analysis to incorporate the important non-linear association. Semiparametric canonical analysis is easy to implement and interpret. Statistical properties are proved. A consistent estimation method is developed.…

用于降维的切片回归AI 解读

A new dimension-reduction method involving slicing the region of the response and applying local kernel regression to each slice is proposed. Compared with the traditional inverse regression methods [e.g., sliced inverse regression (SIR)], the new method is free of the linearity condition and has much better estimation accuracy. Compared with the direct estimation methods (e.g., MAVE), the new method is much more robust against extreme values and can capture the entire…

降维方向估计的构造性方法AI 解读

In this paper we propose two new methods to estimate the dimension-reduction directions of the central subspace (CS) by constructing a regression model such that the directions are all captured in the regression mean. Compared with the inverse regression estimation methods [e.g., J. Amer. Statist. Assoc. 86 (1991) 328–332, J. Amer. Statist. Assoc. 86 (1991) 316–342, J. Amer. Statist. Assoc. 87 (1992) 1025–1039], the new methods require no strong assumptions on the design of…

单指标模型两种估计量的渐近分布AI 解读

The single-index model is one of the most popular semiparametric models in applied quantitative sciences. Two new estimation methods have been proposed recently by Hristache, Juditski, and Spokoiny (2001, Annals of Statistics 29, 595–623) and Xia, Tong, Li, and Zhu (2002, Journal of the Royal Statistical Society, Series B 64, 363–410), respectively. However, their asymptotic distributions have not been investigated yet. In this paper, alternative versions for the methods are…

降维空间的自适应估计AI 解读

Summary Searching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. We propose an adaptive approach based on semiparametric models, which we call the (conditional) minimum average variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advantages. Most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of…

时间序列瞬时变换的估计AI 解读

Summary We modify Ramsay's algorithm for estimating monotonic transformations in regression and extend it to autoregression, where strict monotonicity is an essential requirement. Compared with other methods, our method can capture some characteristics that are pertinent to the time series and is much easier to implement. An order selection method is introduced and developed. Some real data sets are analysed.