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半变系数模型的有效估计AI 解读

Motivated by two practical problems, we propose a new procedure for estimating a semivarying‐coefficient model. Asymptotic properties are established which show that the bias of the parameter estimator is of order h3 when a symmetric kernel is used, where h is the bandwidth, and the variance is of order n−1 and efficient in the semiparametric sense. Undersmoothing is unnecessary for the root‐n consistency of the estimators. Therefore, commonly used bandwidth selection…

Contributions made by Biometrika authors over the past century are described by arranging them into fairly coherent groups, with brief introductions whenever deemed necessary. The paper is concluded with a look at challenges in the new century.

一致的非参数阶数确定与混沌AI 解读

SUMMARY We give a brief introduction to deterministic chaos and a link between chaotic deterministic models and stochastic time series models. We argue that it is often natural to determine the embedding dimension in a noisy environment first in any systematic study of chaos. Setting the stochastic models within the framework of non-linear autoregression, we introduce the notion of a generalized partial autocorrelation and an order. We approach the estimation of the…

门限自回归的似然比检验AI 解读

SUMMARY This paper addresses the null distribution of the likelihood ratio statistic for threshold autoregression with normally distributed noise. The problem is non-standard because the threshold parameter is a nuisance parameter which is absent under the null hypothesis. We reduce the problem to the first-passage probability associated with a Gaussian process which, in some special cases, turns out to be a Brownian bridge. It is also shown that, in some specific cases, the…

摘要暂缺

连续时间延迟自回归过程札记AI 解读

A delayed autoregressive model in continuous time is proposed and its covariance structure analysed. A nonidentifiability problem in parameter estimation is pointed out.

摘要暂缺

不连续决策过程与门限自回归时间序列建模AI 解读

Setting the problem of approximating an underlying nonlinear time series model within the framework of Bayesian decision theory, we demonstrate how the general analysis of discontinuous decision processes developed by Smith, Harrison & Zeeman (1981) leads naturally to a threshold autoregression.

不连续决策过程与门限自回归时间序列建模AI 解读

Setting the problem of approximating an underlying nonlinear time series model within the framework of Bayesian decision theory, we demonstrate how the general analysis of discontinuous decision processes developed by Smith, Harrison & Zeeman (1981) leads naturally to a threshold autoregression.

门限自回归、极限环与周期性数据AI 解读

Summary The notion of a limit cycle, which can only exist in a non-linear system, plays the key role in the modelling of cyclical data. We have shown that the class of threshold autoregressive models is general enough to capture this notion, a definition of which in discrete time is proposed. The threshold value has an interesting interpretation. Simulation results are presented which demonstrate that this new class of models exhibits some well-known features of non-linear…

摘要暂缺

双变量非平稳过程的分析AI 解读

Summary In this paper, we propose a general definition of the evolutionary (time-dependent) cross-spectrum between two non-stationary processes and describe its physical interpretation. We also study the estimation of the evolutionary cross-spectrum at each time instant t from a single realization of a bivariate process. Further, we propose a definition (and a method of estimation) for the coherency (spectrum) between the two components of the bivariate process and show that…

传递函数时间依赖性的若干检验AI 解读

In studies of linear open loop systems, the assumption of time invariance is often tacitly made. In this paper we exploit a convenient frequency-domain approach to furnish tests for the time dependence of a transfer function, which is the most crucial notion in the case of linear systems. An extension of Tukey's test for nonadditivity is given in § 4. The proposed tests are illustrated numerically with both simulated and real data.

线性开环系统时变性的检验AI 解读

Summary We consider the problem of testing a given open-loop system for time-dependence. The test is based on just a single realization of the input and a single realization of the output. It makes use of the concept of the “evolutionary cross-spectra” of a non-stationary vector process and rests essentially on testing the “uniformity” of a set of vectors, whose components consist of the “evolutionary gain-spectra” and “evolutionary phase-spectra”. Using a logarithmic…