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Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estima...
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimat...
How many Laplace transforms of probability measures are there?
Laplace Transform bracketing metric entropy completely monotone func-tions smooth Gaussian process small deviation probability
2010/3/9
A bracketing metric entropy bound for the class of Laplace transforms of probability
measures on [0,1) is obtained through its connection with the small deviation
probability of a smooth Gaussian pr...
Almost sure properties of weighted vectorial martingales transforms with applications to prediction for linear regression models
least squares estimators cumulative prediction and estimation Linear regression models
2009/9/21
We establish new almost sure properties for powers of
weighted martingale transbrms. It allows us to deduce usefuI asymptotic
results for cumulative prediction and estimation errors associated
with...
Generalized t-transforms of probability measures and deformed convolutions
ConvoIution conditionally free moment-cumulant formula
2009/9/21
In this paper, the generalized (two-parameterized)
t-transformations on probability measures are introduced, in which the
t-transformation of Boiejko and Wysonariski can be obtained as the
special ...
CAUCHY TRANSFORMS OF MEASURES VIEWED AS SOME FUNCTIONALS OF FOURIER TRANSFORMS
Cauchy transform Fourier transform Laplace transform compound Poisson distribution
2009/9/18
The Cauchy transform of a positive measure plays an
important role in complex analysis and more recently in so-called free
probability. We show here that the Cauchy transform restricted to the
imag...