论文检索

自动选择平滑参数的非线性平滑 EM 反卷积密度估计AI 解读

We study a nonparametric deconvolution density estimation problem. The estimator is obtained by an EM algorithm for a smoothed maximum likelihood estimation problem, which has a unique continuous solution. We present an implementation of the procedure incorporating a data-driven discrepancy principle for selecting the smoothing parameter. Simulations illustrate the good properties of the resulting estimator when the unknown distribution is smooth and has regularly varying…

利用核方法非参数估计混合密度AI 解读

Editor's note: This manuscript was first submitted in May 1996, and a first review with a request for revision was completed in September 1996. Costas Goutis lost his life in a scuba diving accident in July 1996. The associate editor, Jianqing Fan, graciously offered to carry out the required revisions. This article presents a method for estimating the latent distribution of a mixture model. The method is motivated by the standard kernel density estimation, but instead of…

基于粗糙度度量的拟合优度检验AI 解读

A test for the one-sample goodness-of-fit problem is proposed. The test is based on a distance that measures the difference, in terms of roughness, between the underlying density function and the hypothesized density function. One advantage of using a roughness measure is high power in detecting high-frequency alternatives and densities with sharp features. The test statistic that estimates the distance is derived from the viewpoint of kernel density estimation, and a…

卷积核未完全确定时的反卷积及其在 FDG PET 血液曲线建模中的应用AI 解读

Camouflaged deconvolution arises when the kernel in a simple convolution model is not completely specified. We consider a situation in which the same fixed signal is repeatedly measured by separate convolutions with imprecisely known kernels. We develop a regularization methodology for application to these problems. The method involves simultaneous estimation of the target signal and the unknown parameters of the convolution kernels. Cross-validation is used to determine the…

随机删失观测下风险函数估计的半参数方法AI 解读

One method for estimating the hazard function is to use a parametric estimator, provided that the underlying distribution of the data can be assumed to belong to some well known family of distributions depending on an unknown, possibly vector-valued parameter. Another approach is to use nonparametric estimators, such as Cox's proportional hazard models, kernel hazard estimators, and so on. However, nonparametric estimators are less efficient than suitably chosen parametric…

利用U统计量无偏估计中心矩AI 解读

Summary We obtain an estimator of the rth central moment of a distribution, which is unbiased for all distributions for which the first r moments exist. We do this by finding the kernel which allows the rth central moment to be written as a regular statistical functional. The U-statistic associated with this kernel is the unique symmetric unbiased estimator of the rth central moment, and, for each distribution, it has minimum variance among all estimators which are unbiased…

利用核平滑改善自助法置信区间AI 解读

Summary Some studies of the bootstrap have assessed the effect of smoothing the estimated distribution that is resampled, a process usually known as the smoothed bootstrap. Generally, the smoothed distribution for resampling is a kernel estimate and is often rescaled to retain certain characteristics of the empirical distribution. Typically the effect of such smoothing has been measured in terms of the mean-squared error of bootstrap point estimates. The reports of these…

摘要暂缺

相关误差下非参数回归的大样本推断AI 解读

A central limit theorem is given for certain weighted partial sums of a covariance stationary process, assuming it is linear in martingale differences, but without any restriction on its spectrum. We apply the result to kernel nonparametric fixed-design regression, giving a single central limit theorem which indicates how error spectral behavior at only zero frequency influences the asymptotic distribution and covers long-range, short-range and negative dependence. We show…

带宽选择、预白化与 Phillips–Perron 检验的功效AI 解读

This study examines several important practical issues concerning nonparametric estimation of the innovation variance for the Phillips-Perron (PP) test. A Monte Carlo study is conducted to evaluate the potential effects of kernel choice, databased bandwidth selection, and prewhitening on the power property of the PP test in finite samples. The Monte Carlo results are instructive. Although the kernel choice is found to make little difference, data-based bandwidth selection…

扩散过程的非参数估计及其在短期利率模型中的应用AI 解读

In this paper, we propose a nonparametric identification and estimation procedure for an ltd diffusion process based on discrete sampling observations. The nonparametric kernel estimator for the diffusion function developed in this paper deals with general ltd diffusion processes and avoids any functional form specification for either the drift function or the diffusion function. It is shown that under certain regularity conditions the nonparametric diffusion function…

高阶偏差核密度估计方法的比较AI 解读

We consider many kernel-based density estimators, all theoretically improving bias from O(h 2), as the smoothing parameter h → 0, to O(h 4). Examples include higher-order kernels, variable kernel methods, and transformation and multiplicative bias-correction approaches. We stress the similarities between what appear to be disparate approaches. In particular, we show how the mean squared errors of all methods have the same form. Our main practical contribution is a…

区间删失比例优势失效时间回归模型的筛估计AI 解读

Estimation of the proportional-odds failure-time regression model with interval censoring is considered. Conditions that allow for positive information for the regression parameter are discussed. The efficient score is characterized by a Fredholm equation of the second kind. The sieve maximum likelihood estimator for the finite-dimensional regression parameter is shown to be asymptotically normal with √n convergence rate and to achieve the information bound. Data analysis…

用 TSMARS 建模海表温度的长程依赖、非线性与周期现象AI 解读

We analyze a time series of 20 years of daily sea surface temperatures measured off the California coast. The temperatures exhibit quite complicated features, such as effects on many different time scales, nonlinear effects, and long-range dependence. We show how a time series version of the multivariate adaptive regression splines (MARS) algorithm, TSMARS, can be used to obtain univariate adaptive spline threshold autoregressive models that capture many of the physical…

局部多项式回归与密度估计的经验偏差带宽AI 解读

A data-based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials. The estimator, called the empirical-bias bandwidth selector (EBBS), is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function. EBBS minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term. The variance term used is exact, not asymptotic, though it…

用 TSMARS 建模海表温度的长程依赖、非线性与周期现象AI 解读

We analyze a time series of 20 years of daily sea surface temperatures measured off the California coast. The temperatures exhibit quite complicated features, such as effects on many different time scales, nonlinear effects, and long-range dependence. We show how a time series version of the multivariate adaptive regression splines (MARS) algorithm, TSMARS, can be used to obtain univariate adaptive spline threshold autoregressive models that capture many of the physical…

REML估计中的Wald一致性与筛方法AI 解读

We prove that for all unconfounded balanced mixed models of the analysis of variance, estimates of variance components parameters that maximize the (restricted) Gaussian likelihood are consistent and asymptotically normal--and this is true whether normality is assumed or not. For a general (nonnormal) mixed model, we show estimates of the variance components parameters that maximize the (restricted) Gaussian likelihood over a sequence of approximating parameter spaces (i.e.,…

自动边界修正AI 解读

Many popular curve estimators based on smoothing have difficulties caused by boundary effects. These effects are visually disturbing in practice and can play a dominant role in theoretical analysis. Local polynomial regression smoothers are known to correct boundary effects automatically. Some analogs are implemented for density estimation and the resulting estimators also achieve automatic boundary corrections. In both settings of density and regression estimation, we…

平滑Cox回归AI 解读

Nonparametric regression was shown by Beran and McKeague and Utikal to provide a flexible method for analysis of censored failure times and more general counting processes models in the presence of covariates. We discuss application of kernel smoothing towards estimation in a generalized Cox regression model with baseline intensity dependent on a covariate. Under regularity conditions we show that estimates of the regression parameters are asymptotically normal at rate…

杂录：样条变换后的线性回归AI 解读

In a transformation model h(Y) = X'β + ε for some smooth and usually monotone function h, we are often interested in the direction of β without knowing the exact form of h. We consider a projection of h onto a linear space of B-spline functions which has the highest correlation with the design variable X. As with the Box-Cox transformation, the transformed response may then be analysed by standard linear regression software. The direction estimate from canonical correlation…

局部线性密度估计的带宽选择AI 解读

Local linear density estimators achieve automatic boundary corrections and enjoy some typical optimal properties. Proper choice of the smoothing parameters is crucial for their performance. A data-based bandwidth selector is developed in the spirit of plug-in rules. Consistency and asymptotic normality of the selected bandwidth are demonstrated. The bandwidth is very efficient regardless of whether there are non-smooth boundaries in the support of the density or not.

连续时间过程非参数估计量与预测量的参数收敛速度AI 解读

We show that local irregularity of observed sample paths provides additional information which allows nonparametric estimators and predictors for continuous time processes to reach parametric rates in mean square as well as in a.s. uniform convergence. For example, we prove that under suitable conditions the kernel density estimator $f_T$ associated with the observed sample path $(X_t, 0 \leq t \leq T)$ satisfies $$\sup_{x \epsilon \mathbb{R}}|f_T(x) - f(x)| = o(\ln_k T(\frac{\ln T}{T})^{1/2}) \quad \text{a.s.}, k \geq 1$$…

A new variable bandwidth selector for kernel estimation is proposed. The application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over Besov classes. This implies that the procedure adapts to spatially inhomogeneous smoothness. In particular, the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients.

利用动态时间规整对齐曲线AI 解读

When studying some process or development in different subjects or units--be it biological, chemical or physical--we usually see a typical pattern, common to all curves. Yet there is variation both in amplitude and dynamics between curves. Following some ideas of structural analysis introduced by Kneip and Gasser, we study a method--dynamic time warping with a proper cost function--for estimating the shift or warping function from one curve to another to align the two…