Large deviations and asymptotic efficiency of integral statistics for testing independence

1987 ◽  
Vol 38 (6) ◽  
pp. 2382-2390 ◽  
Author(s):  
Ya. Yu. Nikitin
Keyword(s):  
Large Deviations ◽  
Asymptotic Efficiency ◽  
Testing Independence

Asymptotic efficiency of exponentiality tests based on order statistics characterization

2010 ◽  
Vol 17 (4) ◽  
pp. 749-763
Author(s):  
Ya. Yu. Nikitin ◽  
Ksenia Yu. Volkova
Keyword(s):  
Large Deviations ◽  
Order Statistics ◽  
Asymptotic Efficiency ◽  
Bahadur Efficiency ◽  
Limiting Distributions ◽  
Scale Invariant ◽  
New Statistics

Abstract We propose new scale-invariant tests for exponentiality based on the characterization in terms of order statistics. Limiting distributions and large deviations of new statistics are described and their local Bahadur efficiency for common alternatives is calculated.

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

Sign in / Sign up

Export Citation Format

Share Document