The Experts below are selected from a list of 9111 Experts worldwide ranked by ideXlab platform

Yasutada Oohama - One of the best experts on this subject based on the ideXlab platform.

  • secret key agreement from vector Gaussian sources by rate limited public communication
    IEEE Transactions on Information Forensics and Security, 2011
    Co-Authors: Shun Watanabe, Yasutada Oohama
    Abstract:

    We investigate the secret key agreement from correlated vector Gaussian sources in which legitimate parties can use public communication with limited rate. For the class of protocols with one-way public communication, we show that the optimal trade-off between the rate of key generation and the rate of the public communication is characterized as an optimization problem of a Gaussian Random Variable. The characterization is derived by using the enhancement technique introduced by Weingarten for multiple-input-multiple-output (MIMO) Gaussian broadcast channel.

  • secret key agreement from vector Gaussian sources by rate limited public communication
    International Symposium on Information Theory, 2010
    Co-Authors: Shun Watanabe, Yasutada Oohama
    Abstract:

    We investigate the secret key agreement from correlated vector Gaussian sources in which the legitimate parties can use the public communication with limited rate. For the class of protocols with the one-way public communication, we show that the optimal trade-off between the rate of key generation and the rate of the public communication is characterized as an optimization problem of a Gaussian Random Variable. The characterization is derived by using the enhancement technique introduced by Weingarten et. al. for MIMO Gaussian broadcast channel.

Anna Lytova - One of the best experts on this subject based on the ideXlab platform.

  • central limit theorem for linear eigenvalue statistics for a tensor product version of sample covariance matrices
    Journal of Theoretical Probability, 2018
    Co-Authors: Anna Lytova
    Abstract:

    For $$k,m,n\in {\mathbb {N}}$$ , we consider $$n^k\times n^k$$ Random matrices of the form $$\begin{aligned} {\mathcal {M}}_{n,m,k}({\mathbf {y}})=\sum _{\alpha =1}^m\tau _\alpha {Y_\alpha }Y_\alpha ^T,\quad {Y}_\alpha ={\mathbf {y}}_\alpha ^{(1)}\otimes \cdots \otimes {\mathbf {y}}_\alpha ^{(k)}, \end{aligned}$$ where $$\tau _{\alpha }$$ , $$\alpha \in [m]$$ , are real numbers and $${\mathbf {y}}_\alpha ^{(j)}$$ , $$\alpha \in [m]$$ , $$j\in [k]$$ , are i.i.d. copies of a normalized isotropic Random vector $${\mathbf {y}}\in {\mathbb {R}}^n$$ . For every fixed $$k\ge 1$$ , if the Normalized Counting Measures of $$\{\tau _{\alpha }\}_{\alpha }$$ converge weakly as $$m,n\rightarrow \infty $$ , $$m/n^k\rightarrow c\in [0,\infty )$$ and $${\mathbf {y}}$$ is a good vector in the sense of Definition 1.1, then the Normalized Counting Measures of eigenvalues of $${\mathcal {M}}_{n,m,k}({\mathbf {y}})$$ converge weakly in probability to a nonRandom limit found in Marchenko and Pastur (Math USSR Sb 1:457–483, 1967). For $$k=2$$ , we define a subclass of good vectors $${\mathbf {y}}$$ for which the centered linear eigenvalue statistics $$n^{-1/2}{{\mathrm{Tr}}}\varphi ({\mathcal {M}}_{n,m,2}({\mathbf {y}}))^\circ $$ converge in distribution to a Gaussian Random Variable, i.e., the Central Limit Theorem is valid.

Ivan Nourdin - One of the best experts on this subject based on the ideXlab platform.

  • optimal berry esseen rates on the wiener space the barrier of third and fourth cumulants
    arXiv: Probability, 2011
    Co-Authors: Hermine Bierme, Ivan Nourdin, Aline Bonami, Giovanni Peccati
    Abstract:

    Let {F_n} be a normalized sequence of Random Variables in some fixed Wiener chaos associated with a general Gaussian field, and assume that E[F_n^4] --> E[N^4]=3, where N is a standard Gaussian Random Variable. Our main result is the following general bound: there exist two finite constants c,C>0 such that, for n sufficiently large, c max(|E[F_n^3]|, E[F_n^4]-3) < d(F_n,N) < C max(|E[F_n^3]|, E[F_n^4]-3), where d(F_n,N) = sup |E[h(F_n)] - E[h(N)]|, and h runs over the class of all real functions with a second derivative bounded by 1. This shows that the deterministic sequence max(|E[F_n^3]|, E[F_n^4]-3) completely characterizes the rate of convergence (with respect to smooth distances) in CLTs involving chaotic Random Variables. These results are used to determine optimal rates of convergence in the Breuer-Major central limit theorem, with specific emphasis on fractional Gaussian noise.

  • central limit theorems for multiple skorokhod integrals
    Journal of Theoretical Probability, 2010
    Co-Authors: Ivan Nourdin, David Nualart
    Abstract:

    In this paper, we prove a central limit theorem for a sequence of multiple Skorokhod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian Random Variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted Hermite variations of the fractional Brownian motion are discussed.

  • exact rate of convergence of some approximation schemes associated to sdes driven by a fractional brownian motion
    Journal of Theoretical Probability, 2007
    Co-Authors: Andreas Neuenkirch, Ivan Nourdin
    Abstract:

    In this article, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H. We consider two cases. If H>1/2, the exact rate of convergence of the Euler scheme is determined. We show that the error of the Euler scheme converges almost surely to a Random Variable, which in particular depends on the Malliavin derivative of the solution. This result extends those contained in J. Complex. 22(4), 459–474, 2006 and C.R. Acad. Sci. Paris, Ser. I 340(8), 611–614, 2005. When 1/6Random Variable, which depends on the solution of the equation and an independent Gaussian Random Variable.

N C Beaulieu - One of the best experts on this subject based on the ideXlab platform.

  • a simple polynomial approximation to the Gaussian q function and its application
    IEEE Communications Letters, 2009
    Co-Authors: Yunfei Chen, N C Beaulieu
    Abstract:

    A simple polynomial approximation to the Gaussian Q-function is proposed, based on the observation that a Gaussian Random Variable can be well approximated by a sum of uniform Random Variables. The approximation can be used to obtain accurate explicit approximations to problems that otherwise do not have explicit solutions or approximate explicit solutions. As an example, an explicit expression for the average symbol error rate of M-ary pulse amplitude modulation in lognormal channels is derived using the new approximation, and the approximate symbol error rate is shown to be very close to the exact value.

  • Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels
    IEEE Transactions on Communications, 2008
    Co-Authors: Peng Tan, N C Beaulieu
    Abstract:

    A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian Random Variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.

  • bit error probability analysis of ofdm systems in the presence of channel estimation error over rayleigh and ricean fading channels
    International Conference on Communications, 2006
    Co-Authors: Peng Tan, N C Beaulieu
    Abstract:

    A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to sums of several conditional probability functions which can be calculated by using proper complex Gaussian Random Variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sinc interpolator with Hamming windowing and a Wiener interpolator, are compared.

Donald B Rubin - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic theory of reRandomization in treatment control experiments
    Proceedings of the National Academy of Sciences of the United States of America, 2018
    Co-Authors: Xinran Li, Peng Ding, Donald B Rubin
    Abstract:

    Although complete Randomization ensures covariate balance on average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. ReRandomization discards Randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for reRandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. We develop asymptotic theory for reRandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian Random Variable and truncated Gaussian Random Variables. This distribution follows because reRandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete Randomization, reRandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the average causal effect.

  • asymptotic theory of reRandomization in treatment control experiments
    arXiv: Statistics Theory, 2016
    Co-Authors: Xinran Li, Peng Ding, Donald B Rubin
    Abstract:

    Although complete Randomization ensures covariate balance on average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. ReRandomization discards Randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for reRandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. To supplement existing results, we develop asymptotic theory for reRandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian Random Variable and a truncated Gaussian Random Variable. This distribution follows because reRandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We also demonstrate that, compared to complete Randomization, reRandomization reduces the asymptotic sampling variances and quantile ranges of the difference-in-means estimator. Moreover, our work allows the construction of accurate large-sample confidence intervals for the average causal effect, thereby revealing further advantages of reRandomization over complete Randomization.