A general method of minimum cross-entropy spectral estimation

Tzannes, M.A.; Politis, Dimitris N.; Tzannes, Nicolaos S.

doi:10.1109/tassp.1985.1164605

Cited by 25 publications

(10 citation statements)

References 8 publications

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“…Since a power spectral density actually is a probability density function of a random variable 2Trf, where f makes sense in terms of the instantaneous frequency of the associated random (not necessarily Gaussian) process [14], we can also use the relative entropy measure between S(w) and S 0 (w) [7], namely…”

Section: Signal Processingmentioning

confidence: 99%

A flatness-based generalized optimization approach to spectral estimation

Nadeu

Bertran

1990

Signal Processing

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Abstract. In the optimization formulation, once the known autocorrelations are fixed as constraints, the objective functional completely characterizes the corresponding method of spectral estimation. After observing that this functional involves a sort of spectral flatness maximization, the relationship between the form of its integrand and the salient trends of the various methods is pointed out. This serves as a basis to propose a generalized optimization approach that encompasses some classical estimators and originates new ones.Zusammenfassung. In der Optimierungs-Beschreibung charakterisiert das Funktional die jeweilige Methode zur Spektralschalzung vollstandig, wenn von festen Autokorrelationswerten ausgegangen wird. Nach dem Aufzeigen der Tatsache, daB dieses Funktional eine Art von Maximierung der Flachheit des Spektrums beinhaltet, wird die Beziehung zwischen der Form des Integranden und den herausragenden Richtungen der verschiedenen Methdden herausgestellt. Auf dieser Grundlage wird ein verallgemeinerter Optimierungs-Ansatz vorgeschlagen, der einige klassische Schatzer einschlieBt und neue hervorbringt. SchlieBlich wird die Brauchbarkeit der Vorstellung der spektralen Flachheit fiir die Spektralschatzung diskutiert.Resume. Dans un contexte d'optimisation,la fonction objectif caracterise completement la methode correspondante d'estimation spectrale des que les valeurs d'autocorrelation connues sent fixees comme contraintes. Observant que cette fonction objectif implique une certaine maximisation du caractere plat du spectre (en anglais spectral flatness), la relation entre la forme de !'integration et les traits saillants de differentes methodes est mise en evidence. Ceci sert de base a une approche generalisee de l'optimisation qui recouvre certains estimateurs classiques et permet d'en creer de nouveaux.

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Section: Signal Processingmentioning

confidence: 99%

A flatness-based generalized optimization approach to spectral estimation

Nadeu

Bertran

1990

Signal Processing

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“…Cui and Singh (2016a) applied MRE to monthly streamflow forecasting and showed its advantage over traditional autoregressive (AR) method or Burg entropy (BE) spectral analysis for both peak and low flow values with longer lead times. However, there is a minor drawback in the MRE theory that it suffers from restrictions on the nature of the process and dependence on the form of the assumed prior probability density function (Shore 1981;Tzannes et al 1985). The selected exponential distribution as prior was tested by Cui and Singh (2016a) using 50-100 years of historical data, which may not always be available.…”

Section: Introductionmentioning

confidence: 99%

“…The selected exponential distribution as prior was tested by Cui and Singh (2016a) using 50-100 years of historical data, which may not always be available. To overcome the restriction on the prior, Tzannes et al (1985) developed a general method of minimum relative entropy, where frequency was considered as a random variable. When a uniform prior is assumed, MRE reduces to the configurational entropy (CE) theory (Frieden 1972;Gull and Daniell 1978).…”

Section: Introductionmentioning

confidence: 99%

Minimum relative entropy theory for streamflow forecasting with frequency as a random variable

Cui

Singh

2016

Stoch Environ Res Risk Assess

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This paper develops a minimum relative entropy theory with frequency as a random variable, called MREF henceforth, for streamflow forecasting. The MREF theory consists of three main components: (1) determination of spectral density (2) determination of parameters by cepstrum analysis, and (3) extension of autocorrelation function. MREF is robust at determining the main periodicity, and provides higher resolution spectral density. The theory is evaluated using monthly streamflow observed at 20 stations in the Mississippi River basin, where forecasted monthly streamflows show the coefficient of determination (r 2 ) of 0.876, which is slightly higher in the Upper Mississippi (r 2 = 0.932) than in the Lower Mississippi (r 2 = 0.806).Comparison of different priors shows that the prior with the background spectral density with a peak at 1/12 frequency provides satisfactory accuracy, and can be used to forecast monthly streamflow with limited information. Four different entropy theories are compared, and it is found that the minimum relative entropy theory has an advantage over maximum entropy (ME) for both spectral estimation and streamflow forecasting, if additional information as a prior is given. Besides, MREF is found to be more convenient to estimate parameters with cepstrum analysis than minimum relative entropy with spectral power as random variable (MRES), and less information is needed to assume the prior. In general, the reliability of monthly streamflow forecasting from the highest to the lowest is for MREF, MRES, configuration entropy (CE), Burg entropy (BE), and then autoregressive method (AR), respectively.

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“…The configurational entropy spectral analysis (CESA) was introduced by Frieden (1972) and Gull and Daniell (1978), which is sometimes also referred to as maximum entropy method 2 (MEM2) or spectral MESA (SMESA) (Katsakos-Mavromichalis et al 1985;Tzannes et al 1985;Tzannes and Avgeris 1981). Superior to BESA, CESA has been shown to be not restricted to the AR process (Liefhebber and Boekee 1987;Ortigueira et al 1981).…”

Section: Introductionmentioning

confidence: 99%

“…RESA can be used for streamflow forecasting as well. Later, another version of RESA was developed by Tzannes et al (1985), considering frequency as a random variable. The RESA spectra are reported to have higher resolution and are more accurate in detecting peak location than other methods for spectral computation (Papademetriou 1998).…”

Section: Introductionmentioning

confidence: 99%

Entropy Theory for Streamflow Forecasting

Singh

Cui

2015

Environ. Process.

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Streamflow forecasting is used in river training and management, river restoration, reservoir operation, power generation, irrigation, and navigation. In hydrology, streamflow forecasting is often done using time series analysis. Although monthly streamflow time series are stochastic, they exhibit seasonal and periodic patterns. Therefore, streamflow forecasting entails modeling two main aspects: seasonality and correlation structure. Spectral analysis can be employed to characterize patterns of streamflow variation and identify the periodicity of streamflow. That is, it permits to extract significant information for understanding the streamflow process and prediction thereof. For forecasting streamflow, spectral analysis has, however, not yet been widely applied. Streamflow spectra can be determined using entropy theory. There are three ways to employ entropy theory: (1) Burg entropy, (2) configurational entropy, and (3) relative entropy. In either way, the methodology involves determination of spectral density, determination of parameters, and extension of autocorrelation function. This paper reviews the methods of spectral analysis using the entropy theory and tests them using streamflow data.

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A general method of minimum cross-entropy spectral estimation

Cited by 25 publications

References 8 publications

A flatness-based generalized optimization approach to spectral estimation

A flatness-based generalized optimization approach to spectral estimation

Minimum relative entropy theory for streamflow forecasting with frequency as a random variable

Entropy Theory for Streamflow Forecasting

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