Sentence examples for moderate deviations from inspiring English sources

Hu et al. [23] achieved cramér type moderate deviations for the maximum of self-normalized sums.

Fan [16] investigated moderate deviations for M-estimators in linear models with ϕ-mixing errors.

random fields and Gut [3] also showed convergence rates for probabilities of moderate deviations for independent random fields.

Fan [19] considered the model (1.1) with φ-mixing errors, and the moderate deviations for the M-estimators.

The most problematic combination of 5 items and 100 observations revealed moderate deviations from the limiting distribution.

Liu [5] studied the sufficient and necessary conditions of moderate deviations for dependent random variables with heavy tails.

Wang and Zhang [13] established the moderate deviation principle for stochastic reaction-diffusion equations.

Like the large deviations, the moderate deviation problems arise in the theory of statistical inference quite naturally.

Computational simulation using GRI-MECH 3.0 showed satisfactory agreement with the experimental data up to 20 atm, and moderate deviation for pressure above 40 atm.

Lastly, robustness of AFSMC is verified against relatively large structural uncertainties as well as with respect to a moderate deviation in the uniform inlet flow velocity.

A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gaussian process are shown.