The increment ratio statistic

Local estimation of the Hurst index of multifractional Brownian motion by Increment Ratio Statistic method

We investigate here the Central Limit Theorem of the Increment Ratio Statistic of a multifractional Brownian motion, leading to a CLT for the time varying Hurst index. The proofs are quite simple relying on Breuer-Major theorems and an original freezing of time strategy. A simulation study shows the goodness of fit of this estimator.

An adaptive estimator of the memory parameter and the goodness-of-fit test using a multidimensional increment ratio statistic

The increment ratio (IR) statistic was first defined and studied in Surgailis et al. (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. Firstly, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Secondly, a good...

Ratio model for suprathreshold hue-increment detection.

We use psychophysical techniques to investigate the neural mechanisms subserving suprathreshold chromatic discrimination in human vision. We address two questions: (1) How are the postreceptoral detection mechanism responses combined to form suprathreshold chromatic discriminators? and (2) How do these discriminators contribute to color perception? We use a pedestal paradigm in which the subjec...

Asymptotic Expansions of Thelikelihood Ratio Test Statistic

SUMMARY. Likelihood ratio tests are used to test ordered hypotheses involving the parameters of k independent samples from an exponential family. For the test of constancy of the parameters versus an ordered alternative, the likelihood ratio test statistic is asymptotically distributed as a mixture of k chi-squared distributions under the null hypothesis. This paper derives an asymptotic expans...

An Optimal Property of the Likelihood Ratio Statistic