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一种快速有效的频率估计技术AI 解读

A technique is presented for the estimation of the frequency of a sinusoid in the presence of noise. The technique is based on fitting ARMA (2, 2) models iteratively, in a special way. The estimator is shown to be strongly consistent and as efficient as the least squares estimator of the frequency, or the periodogram maximizer. A simple accelerated version of the technique is shown to converge in a small number of iterations, the number depending on the accuracy of the…

周期函数频率的估计AI 解读

The problem of estimating the frequency and other parameters of a cyclical oscillation is considered, where the data consists of a periodic function observed subject to stationary additive noise. An estimation procedure is proposed and the asymptotic properties of the estimators established. Tests for unknown frequencies to be harmonics of a fundamental frequency are also developed and their asymptotic properties investigated. The procedures are applied to observations on…

频率估计的一种快速高效方法AI 解读

A technique is presented for the estimation of the frequency of a sinusoid in the presence of noise. The technique is based on fitting ARMA (2, 2) models iteratively, in a special way. The estimator is shown to be strongly consistent and as efficient as the least squares estimator of the frequency, or the periodogram maximizer. A simple accelerated version of the technique is shown to converge in a small number of iterations, the number depending on the accuracy of the…

周期函数的频率估计AI 解读

The problem of estimating the frequency and other parameters of a cyclical oscillation is considered, where the data consists of a periodic function observed subject to stationary additive noise. An estimation procedure is proposed and the asymptotic properties of the estimators established. Tests for unknown frequencies to be harmonics of a fundamental frequency are also developed and their asymptotic properties investigated. The procedures are applied to observations on…

关于混合模型假设检验中 Aitkin–Rubin 方法的札记AI 解读

SUMMARY In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.

随机系数自回归模型导论AI 解读

1 Introduction.- 1.1 Introduction.- Appendix 1.1.- Appendix 1.2.- 2 Stationarity and Stability.- 2.1 Introduction.- 2.2 Singly-Infinite Stationarity.- 2.3 Doubly-Infinite Stationarity.- 2.4 The Case of a Unit Eigenvalue.- 2.5 Stability of RCA Models.- 2.6 Strict Stationarity 37 Appendix 2.1.- 3 Least Squares Estimation of Scalar Models.- 3.1 Introduction.- 3.2 The Estimation Procedure.- 3.3 Strong Consistency and the Central Limit Theorem.- 3.4 The Consistent Estimation of…

多元自回归模型的阶数确定AI 解读

Summary The procedure proposed by Hannan and Quinn (1979) for determining the order of univariate autoregressions is extended to multivariate autoregressions. The procedure is shown to be strongly consistent, while other similar procedures may be shown to be strongly consistent by comparison.

自回归模型阶数的确定AI 解读

Summary It is shown that a strongly consistent estimation procedure for the order of an autoregression can be based on the law of the iterated logarithm for the partial autocorrelations. As compared to other strongly consistent procedures this procedure will underestimate the order to a lesser degree.