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The Russian option: Reduced regret
 Ann. Appl. Probab
, 1993
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Cited by 61 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Representations of Gaussian processes equivalent to Wiener process
 Osaka J. Math
, 1968
"... The purpose of this paper is to get a canonical representation of Gaussian processes which are equivalent (or mutually absolutely continuous) to Wiener process. The main result is this. Suppose we are given a Gaussian process Yt on a probability space (Ω, 33, P), which is equivalent to Wiener proces ..."
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Cited by 14 (0 self)
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The purpose of this paper is to get a canonical representation of Gaussian processes which are equivalent (or mutually absolutely continuous) to Wiener process. The main result is this. Suppose we are given a Gaussian process Yt on a probability space (Ω, 33, P), which is equivalent to Wiener process. Then
A smoothing spline based test of model adequacy in polynomial regression
 Annals of Ins. of Stat. Math
"... Abstract. For the regression model yi =f(ti) + el (e's lid N(0,a2)), it is proposed to test the null hypothesis thatf is a polynomial of degree less than some given value m. The alternative is that f is such a polynomial plus a scale factor b ~/2 times an (m l)fold integrated Wiener process. ..."
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Cited by 13 (0 self)
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Abstract. For the regression model yi =f(ti) + el (e's lid N(0,a2)), it is proposed to test the null hypothesis thatf is a polynomial of degree less than some given value m. The alternative is that f is such a polynomial plus a scale factor b ~/2 times an (m l)fold integrated Wiener process. For this problem, it is shown that no uniformly (in b) most powerful test exists, but a locally (at b = 0) most powerful test does exist. Derivation and calculation of the test statistic is based on smoothing spline theory. Some approximations of the null distribution of the test statistic for the locally most powerful test are described. An example using real data is shown along with a computing algorithm. Key words and phrases: Regression, model adequacy, smoothing splines. 1.
On the shape of the ground state eigenvalue density of a random Hill’s equation
 Comm. Pure Appl. Math
, 2006
"... Consider the Hill’s operator Q = −d 2 /dx 2 +q(x) in which q(x), 0 ≤ x ≤ 1, is a White Noise. Denote by f(µ) the probability density function of −λ0(q), the negative of the ground state eigenvalue, at µ. We prove the detailed asymptotics: f(µ) = 4 µ exp ..."
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Cited by 5 (3 self)
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Consider the Hill’s operator Q = −d 2 /dx 2 +q(x) in which q(x), 0 ≤ x ≤ 1, is a White Noise. Denote by f(µ) the probability density function of −λ0(q), the negative of the ground state eigenvalue, at µ. We prove the detailed asymptotics: f(µ) = 4 µ exp
Threshold effects in parameter estimation as phase transitions in statistical mechanics
 IEEE Trans. Inf. Theory
"... Threshold effects in the estimation of parameters of non–linearly modulated, continuous– time, wideband waveforms, are examined from a statistical physics perspective. These threshold effects are shown to be analogous to phase transitions of certain disordered physical systems in thermal equilibriu ..."
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Cited by 3 (2 self)
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Threshold effects in the estimation of parameters of non–linearly modulated, continuous– time, wideband waveforms, are examined from a statistical physics perspective. These threshold effects are shown to be analogous to phase transitions of certain disordered physical systems in thermal equilibrium. The main message, in this work, is in demonstrating that this physical point of view may be insightful for understanding the interactions between two or more parameters to be estimated, from the aspects of the threshold effect. Index Terms: Non–linear modulation, parameter estimation, threshold effect, additive white Gaussian noise channel, bandwidth, statistical physics, disordered systems, random energy
Representation of Gaussian measures that are equivalent to Wiener measure
 Seminar de Probabilities XXXVII, 81–89. Springer Lecture Notes in Mathematics 1832
, 2003
"... Summary. We summarize results on the representation of Gaussian measures that are equivalent to Wiener measure and discuss consequences for the law of the sum of a Brownian motion and an independent fractional Brownian motion. ..."
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Summary. We summarize results on the representation of Gaussian measures that are equivalent to Wiener measure and discuss consequences for the law of the sum of a Brownian motion and an independent fractional Brownian motion.
ON EQUIVALENCE OF PROBABILITY MEASURES
, 1970
"... Let H be a real and separable Hilbert space, f the Borel afield of H sets, and III and ll2 two probability measures on (H,r). III and 1J2 are equivalent (mutually absolutely continuous) 1f, for Aef, 1J 1(A) = = 0 <=> 1J2 (A) = = o. Several sufficient conditions for equivalence are obtained in ..."
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Let H be a real and separable Hilbert space, f the Borel afield of H sets, and III and ll2 two probability measures on (H,r). III and 1J2 are equivalent (mutually absolutely continuous) 1f, for Aef, 1J 1(A) = = 0 <=> 1J2 (A) = = o. Several sufficient conditions for equivalence are obtained in this paper. Some of these results do not require that III and 112 be Gaussian. The conditions obtained are applied to show equivalence for some spec1fic measures when H is L
2005): On the equivalence of multiparameter Gaussian processes
 Journal of Theoretical Probability
"... Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a s ..."
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Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.
Absolute continuity between the Wiener and Stationary Gaussian Measures. preprint
, 1998
"... Abstract. It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to t ..."
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Abstract. It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spectrum of an associated operator, is essentially extraneous, providing a simple criterion for finite entropy distance in this case. 1. introduction Let C[1 − τ,1+τ] (where 0 <τ<1) denote the space of continuous functions on [1 − τ,1+τ]. A standard Brownian motion observed between times 1 − τ and 1 + τ induces on C[1 − τ,1+τ] the Wiener measure W τ. As a Gaussian measure, it is characterized by its correlation R(t, s) =t ∧ s for t, s ∈ [1 − τ,1+τ], and by its vanishing mean. A Gaussian measure, Q τ,onC[1 − τ,1+τ]isstationary if its mean is constant and its correlation is a Töeplitz function. That is, with X ∈ C[1 − τ,1+τ] being the sample path, and µt
1 A Statistical Analysis of Fukunaga Koontz Transform
, 2003
"... The Fukunaga Koontz Transform (FKT) has been proposed as a feature selection methodology for nearly 32 years. There are a huge number of citations. We have not seen a direct analysis between FKT, and a well established statistical method: Fisher Quadratic Discriminant Analysis (QDA). In this paper, ..."
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The Fukunaga Koontz Transform (FKT) has been proposed as a feature selection methodology for nearly 32 years. There are a huge number of citations. We have not seen a direct analysis between FKT, and a well established statistical method: Fisher Quadratic Discriminant Analysis (QDA). In this paper, under certain assumptions, we establish such a connection. We speculate that a link in a more general situation is hard to find. I.