论文检索

片段式及相关类型函数型数据的协方差估计AI 解读

Aurore Delaiglea , Peter Halla, Wei Huanga* & Alois Kneipb a ACEMS and School of Mathematics and Statistics, University of Melbourne , Parkville , VIC , Australia;; b Department of Economics and Hausdorff Center for Mathematics, Universität Bonn , Bonn , Germany † This work was initiated with Peter Hall during a visit of Kneip to the University Melbourne. Peter died on January 9, 2016.Color versions of one or more of the figures in the article can be found online at…

利用投影对函数型数据进行分组聚类AI 解读

Summary We show that, in the functional data context, by appropriately exploiting the functional nature of the data, it is possible to cluster the observations asymptotically perfectly. We demonstrate that this level of performance can sometimes be achieved by the k-means algorithm as long as the data are projected on a carefully chosen finite dimensional space. In general, the notion of an ideal cluster is not clearly defined. We derive our results in the setting where the…

含噪高频数据中误差分布的频域分析AI 解读

Data observed at a high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or smooth random function, and measurement error. Supposing that the latent component is an Itô diffusion process, we propose to estimate the measurement error density function by applying a deconvolution technique with appropriate localization. Our estimator, which does not require equally-spaced…

非参数协变量调整回归AI 解读

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied…

函数型数据的截断线性模型AI 解读

Summary A conventional linear model for functional data involves expressing a response variable Y in terms of the explanatory function X (t), via the model Y=a+∫Ib(t)X(t)dt+error, where a is a scalar, b is an unknown function and I=[0,α] is a compact interval. However, in some problems the support of b or X, I1 say, is a proper and unknown subset of I, and is a quantity of particular practical interest. Motivated by a real data example involving particulate emissions, we…

通过数据扰动改善非参数密度估计的形态与精度AI 解读

Summary Motivated by both the shortcomings of high order density estimators, and the increasingly large data sets in many areas of modern science, we introduce new high order, non-parametric density estimators that are guaranteed to be positive and do not have highly oscillatory tails. Our approach is based on data perturbation, e.g. by tilting or data sharpening. It leads to new estimators that are more accurate than conventional kernel techniques that use positive kernels,…

误差分布未知时的非参数反卷积方法AI 解读

Summary In the non-parametric deconvolution problem, to estimate consistently a density or distribution from a sample of data contaminated by additive random noise, it is often assumed that the noise distribution is completely known or that an additional sample of replicated or validation data is available. Methods also have been suggested for estimating the scale of the error distribution, but they require somewhat restrictive smoothness assumptions on the signal…

通过倾斜重加权排序观测影响力AI 解读

Summary We suggest a new approach, which is applicable for general statistics computed from random samples of univariate or vector-valued or functional data, to assessing the influence that individual data have on the value of a statistic, and to ranking the data in terms of that influence. Our method is based on, first, perturbing the value of the statistic by ‘tilting’, or reweighting, each data value, where the total amount of tilt is constrained to be the least possible,…

非参数测量误差回归的置信带AI 解读

Summary Errors-in-variables regression is important in many areas of science and social science, e.g. in economics where it is often a feature of hedonic models, in environmental science where air quality indices are measured with error, in biology where the vegetative mass of plants is frequently obscured by mismeasurement and in nutrition where reported fat intake is typically subject to substantial error. To date, in non-parametric contexts, the great majority of work has…

构造二项与泊松参数置信区间的样本分割方法AI 解读

Summary We introduce a new method for improving the coverage accuracy of confidence intervals for means of lattice distributions. The technique can be applied very generally to enhance existing approaches, although we consider it in greatest detail in the context of estimating a binomial proportion or a Poisson mean, where it is particularly effective. The method is motivated by a simple theoretical result, which shows that, by splitting the original sample of size n into…

微分方程参数的快速简便一步估计AI 解读

Summary Differential equations are customarily used to describe dynamic systems. Existing methods for estimating unknown parameters in those systems include parameter cascade, which is a spline-based technique, and pseudo-least-squares, which is a local-polynomial-based two-step method. Parameter cascade is often referred to as a ‘one-step method’, although it in fact involves at least two stages: one to choose the tuning parameter and another to select model parameters. We…

反卷积密度估计中的参数辅助非参数方法AI 解读

Nonparametric estimation of a density from contaminated data is a difficult problem, for which convergence rates are notoriously slow. We introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density, without degrading much the quality of purely nonparametric estimators in other cases. We establish optimal convergence rates for our problem…

构造函数型数据分类器时离散数据平滑带宽的意外性质AI 解读

The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually smooth functions that were not actually observed. Existing literature shows that this approach is effective, and even optimal, when using functional data methods for prediction or hypothesis testing. However, in the present paper we show…

利用删失函数型数据进行分类AI 解读

We consider classification of functional data when the training curves are not observed on the same interval. Different types of classifier are suggested, one of which involves a new curve extension procedure. Our approach enables us to exploit the information contained in the endpoints of these intervals by incorporating it in an explicit but flexible way. We study asymptotic properties of our classifiers, and show that, in a variety of settings, they can even produce…

构造函数非参数置信带的简单 Bootstrap 方法AI 解读

Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on…

含变换噪声数据分类中的反卷积AI 解读

In the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We…

配对排名列表随机退化的中等偏差推断AI 解读

Consider a problem where N items (objects or individuals) are judged by assessors using their perceptions of a set of performance criteria, or alternatively by technical devices. In particular, two assessors might rank the items between 1 and N on the basis of relative performance, independently of each other. We can aggregate the rank lists by assigning one if the two assessors agree, and zero otherwise, and we can modify this approach to make it robust against…

实现函数型数据的近乎完美分类AI 解读

Summary We show that, in functional data classification problems, perfect asymptotic classification is often possible, making use of the intrinsic very high dimensional nature of functional data. This performance is often achieved by linear methods, which are optimal in important cases. These results point to a marked contrast between classification for functional data and its counterpart in conventional multivariate analysis, where the dimension is kept fixed as the sample…

函数型数据偏最小二乘的方法与理论AI 解读

The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often…

同质分组检测数据的非参数回归AI 解读

We introduce new nonparametric predictors for homogeneous pooled data in the context of group testing for rare abnormalities and show that they achieve optimal rates of convergence. In particular, when the level of pooling is moderate, then despite the cost savings, the method enjoys the same convergence rate as in the case of no pooling. In the setting of “over-pooling” the convergence rate differs from that of an optimal estimator by no more than a logarithmic factor. Our…

高斯变分近似的渐近正态性与有效推断AI 解读

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent…

基于Student t统计量的高维数据分析方法：稳健性与精度AI 解读

Summary Student’s t-statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, e.g. robustness against heavy-tailed sampling distributions, that were not explicitly considered until relatively recently. We explore these features of the t-statistic in the context of its application to very high dimensional problems, including feature selection and ranking, the simultaneous…

具有非参数连接函数的单指标与多指标函数型回归AI 解读

Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional functions. This difficulty has led to an emphasis on the so-called functional linear model, which is much more flexible than common linear models in finite dimension, but nevertheless imposes structural constraints on the relationship between…

体视学体积估计的分布估计量与置信区间AI 解读

Assessing the precision of volume estimates from systematic samples is a question of great practical importance, but statistically a challenging task due to the strong spatial dependence of the data and typically small sample sizes. The approach taken in this paper is more ambitious than earlier methodologies, the goal of which was estimation of the variance of a volume estimator v̂, rather than estimation of the distribution of v̂. We shall show that bootstrap methods yield…