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函数型数据的自由结点样条平滑AI 解读

Summary The paper introduces free-knot regression spline estimators for the mean and the variance components of a sample of curves. The asymptotic distribution of the mean estimator is derived, and asymptotic confidence bands are constructed. A comparative simulation study shows that free-knot splines estimate salient features of the functions (such as sharp peaks) more accurately than smoothing splines. This adaptive behaviour is also illustrated by an analysis of weather…

曲线样本结构均值的非参数最大似然估计AI 解读

A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) = Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean μ(t) = E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose…

自建模变形函数AI 解读

Summary The paper introduces a semiparametric model for functional data. The warping functions are assumed to be linear combinations of q common components, which are estimated from the data (hence the name ‘self-modelling’). Even small values of q provide remarkable model flexibility, comparable with nonparametric methods. At the same time, this approach avoids overfitting because the common components are estimated combining data across individuals. As a convenient…

一类稳健且具有完全渐近效率的回归估计量AI 解读

This paper introduces a new class of robust estimators for the linear regression model. They are weighted least squares estimators, with weights adaptively computed using the empirical distribution of the residuals of an initial robust estimator. It is shown that under certain general conditions the asymptotic breakdown points of the proposed estimators are not less than that of the initial estimator, and the finite sample breakdown point can be at most $1/n$ less. For the…