E. Parzen, "Probability density functionals and reproducing kernel Hilbert spaces", in Time Series Analysis, John Wiley & Sons, Inc., New York, 1963, (M. Rosenblatt, Ed.), pp. 155--169. Home/Search Document Not in Database Summary Related Articles Check |
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Gaussian Regression and Optimal Finite Dimensional.. - Zhu, Williams, Rohwer, .. (1997) (5 citations) (Correct)
....the covariance kernel V is its Green s function. If V is proper kernel, i.e. if Dirac s measures belong to the dual space H 0 1 (i.e. they are bounded linear functionals) then the space H 1 is called the reproducing kernel Hilbert space (rkhs) with reproducing kernel V (Aronszajn 1950, Parzen 1963, Kailath 1971, Yosida 1965) For further references see Wegman (1988) The reason to single out rkhs from all function spaces is that they guarantee the regression based on a finite amount of data to be a proper function, as point values at finite many points form a multivariate Gaussian with ....
Parzen, E.: 1963, Probability density functionals and reproducing kernel Hilbert spaces, in M. Rosenblatt (ed.), Proc. Symp. on Time Series Analysis, J. Wiley, New York, pp. 155--169.
Optimal Detection Using Bilinear Time-Frequency And Time-Scale .. - Sayeed, Jones (1995) (11 citations) (Correct)
....that is, E[n(t 1 )n(t 2 ) E[s(t 1 )s(t 2 ) 0 for all t 1 ; t 2 2 T . 2 Although we consider only binary hypotheses, most of the results can be readily extended to multiple hypotheses. We consider three wellknown cases, and in all cases we assume that the likelihood ratio (LR) exists [24, 19], which, in particular, implies that detection with zero probability of error is not possible [24] 3 Case I. a = 1, and n is white with its real and imaginary parts independent and of equal power spectral densities so that Rn (t 1 ; t 2 ) N 0 ffi(t 1 Gamma t 2 ) where ffi(t) is the Dirac ....
....only binary hypotheses, most of the results can be readily extended to multiple hypotheses. We consider three wellknown cases, and in all cases we assume that the likelihood ratio (LR) exists [24, 19] which, in particular, implies that detection with zero probability of error is not possible [24]. 3 Case I. a = 1, and n is white with its real and imaginary parts independent and of equal power spectral densities so that Rn (t 1 ; t 2 ) N 0 ffi(t 1 Gamma t 2 ) where ffi(t) is the Dirac delta function. The optimum test statistic is given by [19] LO (x) 1 N 0 h(R s (R s N 0 I) ....
E. Parzen, "Probability density functionals and reproducing kernel Hilbert spaces", in Time Series Analysis, John Wiley & Sons, Inc., New York, 1963, (M. Rosenblatt, Ed.), pp. 155--169.
Gaussian Regression and Optimal Finite Dimensional Linear Models - al. (1997) (5 citations) (Correct)
....which the covariance kernel V is its Green s function. If V is proper kernel, i.e. if Dirac s measures belong to the dual space H 0 1 (i.e. they are bounded linear functionals) then the space H 1 is called the reproducing kernel Hilbert space (rkhs) with reproducing kernel V [Aronszajn 1950; Parzen 1963; Kailath 1971; Yosida 1965] For further references see [Wegman 1988] The reason to single out rkhs from all function spaces is that they guarantee the regression based on a finite amount of data to be a proper function, as point values at finite many points form a multivariate Gaussian with ....
Parzen, E. (1963). Probability density functionals and reproducing kernel Hilbert spaces. In M. Rosenblatt (Ed.), Proc. Symp. on TIme Series Analysis, New York, pp. 155--169. J. Wiley.
Optimal Quadratic Detection And Estimation Using Generalized.. - Sayeed, Jones (1996) (1 citation) (Correct)
....hypothesis generalizations of these scenarios are naturally suited to JSR based detectors. 18 Such processes exist [33] and are sometimes referred to as circular. We also assume that perfect detection is not possible which, in particular, implies that the test statistics (58) and (60) exist [34]. 19 See footnote 24. 20 For example, the ratio of the largest eigenvalue of aRs to that of Rn 21 Deflection is a measure of SNR, and hence a good indicator of detector performance [32, 25] where (ff; fi) are the nuisance signal parameters that may be random or unknown. Under our ....
E. Parzen, "Probability density functionals and reproducing kernel Hilbert spaces," in Time Series Analysis, (John Wiley & Sons, Inc., New York), pp. 155--169, (M. Rosenblatt, Ed.), 1963.
Optimal Detection Using Bilinear - Time-Frequency And Time-Scale (Correct)
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E. Parzen, "Probability density functionals and reproducing kernel Hilbert spaces", in Time Series Analysis, John Wiley & Sons, Inc., New York, 1963, (M. Rosenblatt, Ed.), pp. 155--169.
Hilbert Spaces Induced By Toeplitz Covariance Kernels - Matache, Matache (2002) (1 citation) (Correct)
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Parzen E., Probability Density Functionals and Reproducing Kernel Hilbert Spaces, Proceedings of the Symposium on Time Series Analysis (1962.
Aspects of Fortet's work on reproducing kernel Hilbert spaces - Beder (Correct)
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Emanuel Parzen. Probability density functionals and reproducing kernel Hilbert spaces. In Murray Rosenblatt, editor, Symposium on Time Series Analysis. John Wiley & Sons, Inc., New York, 1963.
Hilbert Spaces Induced By Toeplitz Covariance Kernels - Matache, Matache (2002) (1 citation) (Correct)
No context found.
Parzen E., Probability Density Functionals and Reproducing Kernel Hilbert Spaces, Proceedings of the Symposium on Time Series Analysis (1962.
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