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波动率的函数型数据分析AI 解读

We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets and describe functional representations and data-based recovery of the process from repeated observations. A study of its asymptotic properties, as the frequency of observed trades increases, is complemented by simulations and an application to the analysis of intra-day volatility patterns of the S&P 500 index. The proposed volatility model…

函数型奇异成分分析AI 解读

Summary Aiming at quantifying the dependence of pairs of functional data (X,Y), we develop the concept of functional singular value decomposition for covariance and functional singular component analysis, building on the concept of ‘canonical expansion’ of compact operators in functional analysis. We demonstrate the estimation of the resulting singular values, functions and components for the practically relevant case of sparse and noise-contaminated longitudinal data and…

函数型方差过程AI 解读

We introduce the notion of a functional variance process to quantify variation in functional data. The functional data are modeled as samples of smooth random trajectories observed under additive noise. The noise is assumed to be composed of white noise and a smooth random process—the functional variance process—which gives rise to smooth random trajectories of variance. The functional variance process is a tool for analyzing stochastic time trends in noise variance. As a…

广义函数型线性模型AI 解读

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function, and the expected value of the response is related to this linear predictor via a link function. If, in addition, a variance function is specified, this leads to a functional estimating…

不连续回归与平滑回归的比较AI 解读

Z.Given measurements $(x_i,y_i) = 1,\dots,n$, we discuss methods to assess whether an underlying regression function is smooth (continuous or differentiable) or whether it has discontinuities. The variance of the measurements is assumed to be unknown, and is estimated simultane-ously. By regressing squared differences of the data formed with various span sizes on the span size itself, we obtain an asymptotic linear model with dependent errors. The parameters of this…

地理聚合数据的空间平滑及发病率地图构建AI 解读

We address the commonly encountered situation in spatial statistics where data such as counts of incidences of a certain disease are available only in geographically aggregated form. We develop fairly general models and propose a modified version of the locally weighted least squares method to recover the unknown smooth spatial function that is assumed to generate the observations. In the special case of count data, the target function is the intensity function, conditional…

平滑回归模型中的依赖性检测AI 解读

A class of simple estimators for the correlation of the errors in nonparametric regression models is proposed for the fixed design case. These estimators are based on squared differences of various spans of the data and are consistent so long as the regression function is Lipschitz continuous. The limiting distribution is established and applied to derive asymptotic ‘global’ and ‘local’ tests for different null hypotheses of uncorrelatedness. The finite sample behaviour of…