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重复半连续数据中长期趋势密度的非参数估计AI 解读

We consider nonparametric estimation of the density of the long-term trend of a semicontinuous variable observed repeatedly over time. These variables arise when measuring the intensity of an intermittent phenomenon, such as the intake of an episodically consumed nutrient or the concentration of an intermittent toxic substance: when the phenomenon is absent, the measurement is equal to zero; otherwise, it is positive. Semicontinuous data are usually represented by a two-part…

存在测量误差的间歇性食物摄入分布的半参数估计AI 解读

Dietary data collected from 24-hour dietary recalls are observed with significant measurement errors. In the nonparametric curve estimation literature, much of the effort has been devoted to designing methods that are consistent under contamination by noise, and which have been traditionally applied for analyzing those data. However, some foods such as alcohol or fruits are consumed only episodically, and may not be consumed during the day when the 24-hour recall is…

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…

协变量缺失时基于群组检测数据估计条件患病率AI 解读

We consider estimating the conditional prevalence of a disease from data pooled according to the group testing mechanism. Consistent estimators have been proposed in the literature, but they rely on the data being available for all individuals. In infectious disease studies where group testing is frequently applied, the covariate is often missing for some individuals. There, unless the missing mechanism occurs completely at random, applying the existing techniques to the…

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…

Peter Hall对反卷积研究的主要贡献AI 解读

Peter Hall died in Melbourne on January 9, 2016. He was an extremely prolific researcher and contributed to many different areas of statistics. In this paper, I talk about my experience with Peter and I summarise his main contributions to deconvolution, which include measurement error problems and problems in image analysis.

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…

GARCH 模型中具有根 T 收敛率的密度估计AI 解读

We consider a new nonparametric estimator of the stationary density of the logarithm of the volatility of the GARCH(1,1) model. This problem is particularly challenging since this density is still unknown, even in cases where the model parameters are given. Although the volatility variables are only observed with multiplicative independent innovation errors with unknown density, we manage to construct a nonparametric procedure which estimates the log volatility density…

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…

协变量聚合的群组检测数据中患病率的参数与非参数估计AI 解读

Group testing is a technique employed in large screening studies involving infectious disease, where individuals in the study are grouped before being observed. Parametric and nonparametric estimators of conditional prevalence have been developed in the group testing literature, in the case where the binary variable indicating the disease status is available only for the group, but the explanatory variable is observed for each individual. However, for reasons such as the…

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…

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…

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…

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…

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…

混样检测数据的非参数回归分析AI 解读

Group testing is a procedure used to reduce the cost and increase the speed of large screening studies in which infection or contamination of individuals is detected by a test carried out on a sample of, for example, blood, urine, or water. Instead of testing the sample of each individual, the method involves pooling samples of groups of several individuals and testing those pooled samples. We construct a nonparametric procedure for estimating the conditional probability of…

测量误差下形状约束非参数密度与回归的检验和估计AI 解读

In many applications we can expect that, or are interested to know if, a density function or a regression curve satisfies some specific shape constraints. For example, when the explanatory variable, X, represents the value taken by a treatment or dosage, the conditional mean of the response, Y , is often anticipated to be a monotone function of X. Indeed, if this regression mean is not monotone (in the appropriate direction) then the medical or commercial value of the…

一类 Lévy 过程的非参数估计AI 解读

We consider estimation for a class of Lévy processes, modelled as a sum of a drift, a symmetric stable process and a compound Poisson process. We propose a nonparametric approach to estimating unknown parameters of our model, including the drift, the scale and index parameters in the stable law, the mean of the Poisson process and the underlying jump size distribution. We show that regression and nonparametric deconvolution methods, based on the empirical characteristic…

为随机函数分布定义概率密度AI 解读

The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the notion of density when functional data are considered in the space determined by the eigenfunctions of principal component analysis. This leads to a transparent and meaningful surrogate for density defined in terms of the average value of…