
Recent Posts
Recent Comments
LAN for Linear Proce… on Local Asymptotic Normality Akaike Information C… on KullbackLeibler information a… Archives
Categories
Meta
Monthly Archives: January 2016
LAN for Linear Processes
Consider a mvector linear process where are i.i.d. mvector 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
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
Whittle’s Approximate Likelihood
The Whittle Likelihood is a frequencybased 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
KullbackLeibler information and the consistency of the Hellinger metric.
Suppose is the true density of a random sample while is the assumed model. The KullbackLeibler distance is defined as As we will show below the KullbackLeibler information has a very useful property. We know that , . Hence so … Continue reading
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