Monthly Archives: January 2016

LAN for Linear Processes

Consider a m-vector linear process where are i.i.d. m-vector random variables with p.d.f. on , are matrices depending on a parameter vector . Set Assume the following conditions are satisfied A1 i) For some where denotes the sum of the … Continue reading

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Local Asymptotic Normality

The concept of Local Asymptotic Normality (LAN) – introduced by Lucien LeCam – is one of the most important and fundamental ideas of the general asymptotic statistical theory. The LAN property is of particular importance in the asymptotic theory of … Continue reading

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Whittle’s Approximate Likelihood

The Whittle Likelihood is a frequency-based approximation to the Gaussian Likelihood which is up to a constant asymptotically efficient. The Whittle estimate is asymptotically efficient and can be interpreted as minimum distance estimate of the distance between the parametric spectral … Continue reading

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Kullback-Leibler information and the consistency of the Hellinger metric.

Suppose is the true density of a random sample while is the assumed model. The Kullback-Leibler distance is defined as As we will show below the Kullback-Leibler information has a very useful property. We know that ,  . Hence so … Continue reading

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Akaike Information Criterion Statistics

Consider a distribution with and . Suppose independent drawings are made from the distribution and the resulting frequencies are given by , where . Then the probability of getting the same frequencies by sampling from is given by and thus … Continue reading

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