A general lemma on probabilities of large deviations

Rudzkis, Rimantas; Saulis, L.; Statulevičius, V.

doi:10.1007/bf00972235

Cited by 57 publications

(54 citation statements)

References 3 publications

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“…For example Rudzkis et al [41] develop the following result. Consider a variate Y with mean 0 and variance 1.…”

Section: Cumulantsmentioning

confidence: 94%

<title>Uses of cumulants in wavelet analysis</title>

Brillinger

1994

Advanced Signal Processing: Algorithms, Architectures, and Implementations V

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Cumulants are useful in studying nonlinear phenomena and in developing (approximate) statistical properties of quantities computed from random process data. Wavelet analysis is a powerful tool for the approximation and estimation of curves and surfaces. This work considers both wavelets and cumulants, developing some sampling properties of linear wavelet fits to a signal in the presence of additive stationary noise via the calculus of cumulants. Of some concern is the construction of approximate confidence bounds around a fit. Some extensions to spatial processes, irregularly observed processes and long memory processes are indicated.

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“…For example Rudzkis et al [41] develop the following result. Consider a variate Y with mean 0 and variance 1.…”

Section: Cumulantsmentioning

confidence: 94%

<title>Uses of cumulants in wavelet analysis</title>

Brillinger

1994

Advanced Signal Processing: Algorithms, Architectures, and Implementations V

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show abstract

“…Condition (S) and its generalizations (see [34]) appeared to be very useful for the normal approximation, because it reduced the problem of large deviations to the problem of estimating such "nice" quantities as cumulants (a comprehensive review of the results under condition (S) can be found in the book by Saulis and Statulevieius [35]). As proyed by Alelkevieien6 and Statulevi~ius [7], analogues of condition (S) can also be formulated for other infinitely divisible approximations.…”

Section: Integral and Local Estimatesmentioning

confidence: 98%