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链接函数与方差函数未知的拟似然回归AI 解读

We consider the multiple regression model E(y) = μ, μ = g(x T β), var(y) — [sgrave]2(μ) with predictors x, link function g, and variance function [sgrave]2(·). The aim is to reduce the assumptions in a fully parametric generalized linear model or a quasi-likelihood model by allowing the link and the variance functions to be unknown but smooth. These functions are then estimated nonparametrically, and the estimates are substituted into the quasi-likelihood function. We…

响应曲线的加速时间模型AI 解读

We propose a nonparametric method of data analysis for situations where the data consist of a sample of curves and a covariate is present. We assume the observed curves to be time-accelerated versions of a basic underlying stochastic process and assume the time acceleration factor for each observed process, determining the “eigenzeit,” to be a smooth function of the covariate. We discuss an iterative procedure to estimate the components of the model nonparametrically, using…

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半参数方差函数模型与异方差检验AI 解读

We propose a general semiparametric variance function model in a fixed design regression setting. In this model, the regression function is assumed to be smooth and is modelled nonparametrically, whereas the relation between the variance and the mean regression function is assumed to follow a generalized linear model. Almost all variance function models that were considered in the literature emerge as special cases. Least-squares-types estimates for the parameters of this…

用于曲面平滑与偏导估计的预平均局部正交多项式估计量AI 解读

We propose a multivariate smoothing method based on products of localized orthogonal polynomial series estimators for a smooth regression surface in the fixed-design regression model. The estimation of partial derivatives is included. The proposed method provides for automatic and efficient boundary modifications near the edges of the surface, assuming that the boundary of the support of the regression function satisfies some regularity conditions. By allowing for a…

谱密度峰值位置的弱收敛与自适应估计AI 解读

Adaptive nonparametric kernel estimators for the location of a peak of the spectral density of a stationary time series are proposed and investigated. They are based on direct smoothing of the periodogram where the amount of smoothing is determined automatically in an asymptotically optimal fashion. These adaptive estimators minimize the asymptotic mean squared error. Adaptivity is derived from the weak convergence of a two-parameter stochastic process in a deviation and a…

非参数回归分析中的变化点AI 解读

Estimators for location and size of a discontinuity or change-point in an otherwise smooth regression model are proposed. The assumptions needed are much weaker than those made in parametric models. The proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change-points of slope and of higher order curvature. The proposed estimators are based on a comparison of left and right one-sided kernel smoothers. Weak…

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自适应非参数峰值估计AI 解读

It is shown that consistent estimates of the optimal bandwidths for kernel estimators of location and size of a peak of a regression function are available. Such estimates yield the same joint asymptotic distribution of location and size of a peak as the optimal bandwidths themselves. Therefore data-adaptive efficient estimation of peaks is possible. In order to prove this result, the weak convergence of a two-dimensional stochastic process with appropriately scaled…

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回归分析中的异方差估计AI 解读

Consider the regression model $Y_i = g(t_i) + \varepsilon_i, 1 \leq i \leq n$, with nonrandom design variables $(t_i)$ and measurements $(Y_i)$ for the unknown regression function $g(\cdot)$. We assume that the data are heteroscedastic, i.e., $E(\varepsilon^2_i) = \sigma^2_i \not\equiv \operatorname{const.}$ and investigate how to estimate $\sigma^2_i$. If $\sigma^2_i = \sigma^2(t_i)$ with a smooth function $\sigma^2(\cdot)$, initial estimators $\tilde{\sigma}^2_i$ can be…

回归曲线的可变带宽核估计AI 解读

In the model $Y_i = g(t_i) + \varepsilon_i,\quad i = 1,\cdots, n,$ where $Y_i$ are given observations, $\varepsilon_i$ i.i.d. noise variables and $t_i$ nonrandom design points, kernel estimators for the regression function $g(t)$ with variable bandwidth (smoothing parameter) depending on $t$ are proposed. It is shown that in terms of asymptotic integrated mean squared error, kernel estimators with such a local bandwidth choice are superior to the ordinary kernel estimators…

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密度、回归曲线与众数的光滑最优核估计AI 解读

Several criteria concerning the choice of kernels for the nonparametric estimation of functions and their derivatives are discussed. A specific optimality criterion is described which applies to kernels of compact support and of different orders of smoothness. The solutions of the corresponding variational problems are explicitly given. Many kernels discussed previously are obtained as special cases.

生长曲线的非参数回归分析AI 解读

In recent years, nonparametric curve estimates have been extensively explored in theoretical work. There has, however, been a certain lack of convincing applications, in particular involving comparisons with parametric techniques. The present investigation deals with the analysis of human height growth, where longitudinal measurements were collected for a sample of boys and a sample of girls. Evidence is presented that kernel estimates of acceleration and velocity of height,…