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New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Adapting to unknown smoothness via wavelet shrinkage
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1995
"... We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level by the princip ..."
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Cited by 1006 (18 self)
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also; if the unknown function has a smooth piece, the reconstruction is (essentially) as smooth as the mother wavelet will allow. The procedure is in a sense optimally smoothnessadaptive: it is nearminimax simultaneously over a whole interval of the Besov scale; the size of this interval depends
A Practical Guide to Wavelet Analysis
, 1998
"... A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength t ..."
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Cited by 869 (3 self)
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intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmller, cross
Least squares quantization in pcm.
 Bell Telephone Laboratories Paper
, 1982
"... AbstractIt has long been realized that in pulsecode modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as t ..."
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Cited by 1362 (0 self)
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as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the onethird power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary
When An InfinitelyRenormalizable Endomorphism Of The Interval Can Be Smoothed
"... Let K be a closed subset of a smooth manifold M , and let f : K ! K be a continuous selfmap of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism of the ambient space M . We give a necessary condition for the smoothability of the faithfully infini ..."
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infinitely intervalrenormalizable homeomorphisms of Cantor sets in the unit interval. This class contains, in particular, all minimal homeomorphisms of Cantor sets in the line which extend to continuous maps of an interval with zero topological entropy. I. Introduction We consider the faithfully infinitely
Sample Splitting and Threshold Estimation
 Econometrica
, 2000
"... Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuouslydistributed variable such as firm size. In addition, thr ..."
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Cited by 252 (3 self)
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models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number
A Smooth Converse Lyapunov Theorem for Robust Stability
 SIAM Journal on Control and Optimization
, 1996
"... . This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of wellknown classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded timevarying parameters in the sys ..."
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Cited by 196 (42 self)
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in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets. 1. Introduction. This work is motivated by problems of robust nonlinear stabilization
AND SMOOTHING
"... Optimal estimation problems arise in various different settings where indirect noisy observations are used to determine the underlying state of a timevarying system. For systems with nonlinear dynamics there exist various methods that extend linear filtering and smoothing methods to handle nonl ..."
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Optimal estimation problems arise in various different settings where indirect noisy observations are used to determine the underlying state of a timevarying system. For systems with nonlinear dynamics there exist various methods that extend linear filtering and smoothing methods to handle non
Results 1  10
of
339,212