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In statistics, Whittle likelihood is an approximation to the likelihood function of a stationary Gaussian time series. It is named after the mathematician and statistician Peter Whittle, who introduced it in his PhD thesis in 1951. [1] It is commonly used in time series analysis and signal processing for parameter estimation and signal detection.
However, the estimate produced is biased, and although corrections can be made to the estimate, they may not always be satisfactory. [ 10 ] A method better suited for multidimensional probability density functions (pdf) is to first make a pdf estimate with some method, and then, from the pdf estimate, compute the entropy.
A Newey–West estimator is used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model where the standard assumptions of regression analysis do not apply. [1] It was devised by Whitney K. Newey and Kenneth D. West in 1987, although there are a number of later variants.
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The generic version is called the optimal Bayesian estimator, [1] which is the theoretical underpinning for every sequential estimator (but cannot be instantiated directly). It includes a Markov process for the state propagation and measurement process for each state, which yields some typical statistical independence relations.
In other words, the variance of its spectral estimate at a given frequency does not decrease as the number of samples used in the computation increases. This can be mitigated by averaging over time (Welch's method [2]) or over frequency . Welch's method is widely used for spectral density estimation (SDE).
Time variance (TVAR), symbolised as (), is the time stability of phase versus observation interval tau. It is a scaled variant of modified Allan variance . TDEV is a metric often used to determine an aspect of the quality of timing signals in telecommunication applications and is a statistical analysis of the phase stability of a signal over a ...
Sieve estimators have been used extensively for estimating density functions in high-dimensional spaces such as in Positron emission tomography (PET). The first exploitation of Sieves in PET for solving the maximum-likelihood image reconstruction problem was by Donald Snyder and Michael Miller, [1] where they stabilized the time-of-flight PET problem originally solved by Shepp and Vardi. [2]