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演化周期函数的统计推断AI 解读

Summary In the study of variable stars, where the light reaching an observer fluctuates over time, it can be difficult to explain the nature of the variation unless it follows a regular pattern. In this respect, so-called periodic variable stars are particularly amenable to analysis. There, radiation varies in a perfectly periodic fashion, and period length is a major focus of interest. We develop methods for conducting inference about features that might account for…

用周期图估计非参数回归中的周期AI 解读

Properties of the periodogram are seldom studied in the setting of nonparametric regression, although that is the context in which the periodogram is widely applied in astronomy. There it is a competitor with more recent least-squares methods. The periodogram has the advantage of providing significant graphical insight into statistical and numerical aspects of the problem. However, as we show in the present paper, it also has drawbacks. The estimator that it produces has…

利用降维近似条件分布函数AI 解读

Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of Y|X, but that of Y|θTX, where the unit vector θ is selected so that the approximation is optimal under a least-squares criterion. We show that θ may be estimated root-n consistently. Furthermore, estimation of the conditional distribution…

多周期函数解卷积的非参数方法AI 解读

Summary Multiperiodic functions, or functions that can be represented as finite additive mixtures of periodic functions, arise in problems related to stellar radiation. There they represent the overall variation in radiation intensity with time. The individual periodic components generally correspond to different sources of radiation and have intrinsic physical meaning provided that they can be ‘deconvolved’ from the mixture. We suggest a combination of kernel and orthogonal…

时间序列误差下非参数回归推断的差分方法AI 解读

Summary We show that difference-based methods can be used to construct simple and explicit estimators of error covariance and autoregressive parameters in nonparametric regression with time series errors. When the error process is Gaussian our estimators are efficient, but they are available well beyond the Gaussian case. As an illustration of their usefulness we show that difference-based estimators can be used to produce a simplified version of time series…

时间序列的数据倾斜方法AI 解读

Summary We develop a general methodology for tilting time series data. Attention is focused on a large class of regression problems, where errors are expressed through autoregressive processes. The class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression, robust statistical inference and estimation subject to constraints. The method can be viewed as ‘empirical…

含缺失值马尔可夫模型中变分似然下界的推断适用性AI 解读

Summary Variational methods have been proposed for obtaining deterministic lower bounds for log-likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for…

依赖性对密度估计随机精度度量的影响AI 解读

In kernel density estimation, those data values that make a nondegenerate contribution to the estimator (computed at a given point) tend to be spaced well apart. This property has the effect of suppressing many of the conventional consequences of long-range dependence, for example, slower rates of convergence, which might otherwise be revealed by a traditional loss-or risk-based assessment of performance. From that viewpoint, dependence has to be very long-range indeed…

基于任意阶自回归计算的 bootstrap 置信域AI 解读

Summary Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods…

条件分布函数的估计方法AI 解读

Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the…

依赖指数半参数估计量收敛速率的说明AI 解读

Considerable recent attention has been devoted to semiparametric estimation of the dependence index, or the Hurst constant, using methods based on information in either frequency or time domains. Convergence rates of estimators in the frequency domain have been derived, and in the present paper we obtain them for estimators in the time domain. It is shown that the latter can have superior performance for moderate-range time series, but are inferior in the context of…

依赖数据密度估计中的带宽选择AI 解读

We address the empirical bandwidth choice problem in cases where the range of dependence may be virtually arbitrarily long. Assuming that the observed data derive from an unknown function of a Gaussian process, it is argued that, unlike more traditional contexts of statistical inference, in density estimation there is no clear role for the classical distinction between short- and long-range dependence. Indeed, the "boundaries" that separate different modes of behaviour for…

短程与长程相关误差下非参数回归的带宽选择AI 解读

We analyse methods based on the block bootstrap and leave-out cross-validation, for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence. A novel analytical device for modelling the dependence structure of errors is introduced. This allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice. It is shown that, provided block length or leave-out number,…

基于周期图的分形性质估计量AI 解读

We suggest an estimator, based on the periodogram, of the fractal index and fractal dimension of a continuous, stationary Gaussian process. We argue that the cosine part of the periodogram is more appropriate than the full periodogram for this application. The term "semiperiodogram" is used to describe the cosine component, and our estimator is based on simple linear regression of the logarithm of the semiperiodogram on the algorithm of frequency. Theoretical properties of…

协方差函数的非参数估计AI 解读

We describe kernel methods for estimating the covariance function of a stationary stochastic process, and show how to ensure that the estimator has the positive semidefiniteness property. From a practical viewpoint, our method is significant because it does not demand a parametric model for covariance. From a technical angle, our results exhibit a striking departure from those in more familiar cases of kernel estimation. For example, in the context of covariance estimation,…