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高斯有序模型选择中的自助法调参AI 解读

The paper focuses on the problem of model selection in linear Gaussian regression with unknown possibly inhomogeneous noise. For a given family of linear estimators $\{\widetilde{\boldsymbol{{\theta}}}_{m},m\in\mathscr{M}\}$, ordered by their variance, we offer a new “smallest accepted” approach motivated by Lepski’s device and the multiple testing idea. The procedure selects the smallest model which satisfies the acceptance rule based on comparison with all larger models.…

模型误设下的自助法置信集AI 解读

A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension $p$: the bootstrap approximation works if $p^{3}/n$ is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is…

非平稳与尖峰厚尾金融时间序列的建模AI 解读

Financial time series is often assumed to be stationary and has a normal distribution in the literature. Both assumptions are however unrealistic. This paper proposes a new methodology with a focus on volatility estimation that is able to account for nonstationarity and heavy tails simultaneously. In particular, a local exponential smoothing (LES) approach is developed, in which weak estimates with different memory parameters are aggregated in a locally adaptive way. The…

参数估计的有限样本理论AI 解读

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not tend to infinity; (2) the parametric assumption is possibly misspecified and the underlying data distribution can lie beyond the given parametric family. These two features enable to bridge the gap between parametric and nonparametric theory…

利用传播方法调节逐点自适应估计参数AI 解读

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from Lepski [Theory Probab. Appl. 35 (1990) 454–466.] that selects in a data-driven way one estimate out of a given class of estimates ordered by their variability. A serious problem with using this and similar procedures is the choice of some…

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…

利用时变Copula刻画非齐次依赖关系AI 解读

Measuring dependence in multivariate time series is tantamount to modeling its dynamic structure in space and time. In risk management, the nonnormal behavior of most financial time series calls for non-Gaussian dependences. The correct modeling of non-Gaussian dependences is, therefore, a key issue in the analysis of multivariate time series. In this article we use copula functions with adaptively estimated time-varying parameters for modeling the distribution of returns.…

通过预言机估计研究极值统计AI 解读

We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing procedure. Our main result is an oracle type inequality for the Kullback–Leibler loss.

局部似然估计的空间聚合及分类应用AI 解读

This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method is, given a sequence of local likelihood estimates (“weak” estimates), to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all “weak” estimates. We also propose a new approach toward selecting…

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时变波动率模型的统计推断AI 解读

This paper offers a new approach for estimating and forecasting the volatility of financial time series. No assumption is made about the parametric form of the processes. On the contrary, we only suppose that the volatility can be approximated by a constant over some interval. In such a framework, the main problem consists of filtering this interval of time homogeneity; then the estimate of the volatility can be simply obtained by local averaging. We construct a locally…

图像去噪：逐点自适应方法AI 解读

A new method of pointwise adaptation has been proposed and studied in Spokoiny [(1998) Ann. Statist.26 1356-1378] in the context of estimation of piecewise smooth univariate functions. The present paper extends that method to estimation of bivariate grey-scale images composed of large homogeneous regions with smooth edges and observed with noise on a gridded design. The proposed estimator $\hat{f}(x)$ at a point x is simply the average of observations over a window $\widehat{U}(x)$…

结构自适应降维方法AI 解读

We propose a new method of effective dimension reduction for a multi-index model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension $m$ of the index space does not exceed 3, this space can be estimated with the rate $n^{-1/2}$ under rather mild…

加性回归中的结构检验AI 解读

We consider the component analysis problem for a regression model with an additive structure. The problem is to test whether some of the additive components are of polynomial structure (e.g., linear) without specifying the structure of the remaining components. A particular case is the problem of selecting the significant covariates. The method that we present is based on the wavelet transform using the Haar basis, which allows for applications under mild conditions on the…

单指标模型中指标系数的直接估计AI 解读

Single-index modeling is widely applied in,for example,econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models. By such modeling the statistical analysis usually focuses on estimating the index coefficients. The average derivative estimator (ADE) of the index vector is based on the fact that the average gradient of a single index function $f(x^{\top}\beta)$ is proportional to the index vector…