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Somnath Datta - One of the best experts on this subject based on the ideXlab platform.

  • first order random coefficient integer valued autoregressive processes
    Journal of Statistical Planning and Inference, 2007
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    A first-order random coefficient integer-valued autoregressive (RCINAR(1)) model is introduced. Ergodicity of the process is established. Moments and autocovariance functions are obtained. Conditional least squares and quasi-likelihood estimators of the model parameters are derived and their asymptotic properties are established. The performance of these estimators is compared with the maximum likelihood estimator via simulation.

  • inference for pth order random coefficient integer valued autoregressive processes
    Journal of Time Series Analysis, 2006
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    A pth-order random coefficient integer-valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.

  • inference for pth order random coefficient integer valued autoregressive processes
    Journal of Time Series Analysis, 2006
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    .  A pth-order random coefficient integer-valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets.

Emre Telatar - One of the best experts on this subject based on the ideXlab platform.

  • a new entropy power inequality for integer valued random variables
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Saeid Haghighatshoar, Emmanuel Abbe, Emre Telatar
    Abstract:

    The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function yields a sharp inequality $H(X+X^{\prime})-H(X)\geq{{1}\over{2}}-o(1)$ when $X$ , $X^{\prime}$ are independent identically distributed (i.i.d.) with high entropy. This paper provides the inequality $H(X+X^{\prime})-H(X)\geq g(H(X))$ , where $X$ , $X^{\prime}$ are arbitrary i.i.d. integer-valued random variables and where $g$ is a universal strictly positive function on $\BBR_{+}$ satisfying $g(0)=0$ . Extensions to nonidentically distributed random variables and to conditional entropies are also obtained.

  • A new entropy power inequality for integer-valued random variables
    2013 IEEE International Symposium on Information Theory, 2013
    Co-Authors: Saeid Haghighatshoar, Emmanuel Abbe, Emre Telatar
    Abstract:

    The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function yields a sharp inequality H(X + X') - H(X) ≥ 1/2 - o(l) when X,X' are i.i.d. with high entropy. This paper provides the inequality H(X + X') - H(X) ≥ g(H(X)), where X, X' are arbitrary i.i.d. integer-valued random variables and where g is a universal strictly positive function on R+ satisfying g(0) = 0. Extensions to non identically distributed random variables and to conditional entropies are also obtained.

  • a new entropy power inequality for integer valued random variables
    arXiv: Information Theory, 2013
    Co-Authors: Saeid Haghighatshoar, Emmanuel Abbe, Emre Telatar
    Abstract:

    The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function provides a sharp inequality $H(X+X')-H(X)\geq 1/2 -o(1)$ when $X,X'$ are i.i.d. with high entropy. This paper provides the inequality $H(X+X')-H(X) \geq g(H(X))$, where $X,X'$ are arbitrary i.i.d. integer-valued random variables and where $g$ is a universal strictly positive function on $\mR_+$ satisfying $g(0)=0$. Extensions to non identically distributed random variables and to conditional entropies are also obtained.

Haitao Zheng - One of the best experts on this subject based on the ideXlab platform.

  • first order random coefficient integer valued autoregressive processes
    Journal of Statistical Planning and Inference, 2007
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    A first-order random coefficient integer-valued autoregressive (RCINAR(1)) model is introduced. Ergodicity of the process is established. Moments and autocovariance functions are obtained. Conditional least squares and quasi-likelihood estimators of the model parameters are derived and their asymptotic properties are established. The performance of these estimators is compared with the maximum likelihood estimator via simulation.

  • inference for pth order random coefficient integer valued autoregressive processes
    Journal of Time Series Analysis, 2006
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    A pth-order random coefficient integer-valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.

  • inference for pth order random coefficient integer valued autoregressive processes
    Journal of Time Series Analysis, 2006
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    .  A pth-order random coefficient integer-valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets.

Saeid Haghighatshoar - One of the best experts on this subject based on the ideXlab platform.

  • a new entropy power inequality for integer valued random variables
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Saeid Haghighatshoar, Emmanuel Abbe, Emre Telatar
    Abstract:

    The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function yields a sharp inequality $H(X+X^{\prime})-H(X)\geq{{1}\over{2}}-o(1)$ when $X$ , $X^{\prime}$ are independent identically distributed (i.i.d.) with high entropy. This paper provides the inequality $H(X+X^{\prime})-H(X)\geq g(H(X))$ , where $X$ , $X^{\prime}$ are arbitrary i.i.d. integer-valued random variables and where $g$ is a universal strictly positive function on $\BBR_{+}$ satisfying $g(0)=0$ . Extensions to nonidentically distributed random variables and to conditional entropies are also obtained.

  • A new entropy power inequality for integer-valued random variables
    2013 IEEE International Symposium on Information Theory, 2013
    Co-Authors: Saeid Haghighatshoar, Emmanuel Abbe, Emre Telatar
    Abstract:

    The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function yields a sharp inequality H(X + X') - H(X) ≥ 1/2 - o(l) when X,X' are i.i.d. with high entropy. This paper provides the inequality H(X + X') - H(X) ≥ g(H(X)), where X, X' are arbitrary i.i.d. integer-valued random variables and where g is a universal strictly positive function on R+ satisfying g(0) = 0. Extensions to non identically distributed random variables and to conditional entropies are also obtained.

  • a new entropy power inequality for integer valued random variables
    arXiv: Information Theory, 2013
    Co-Authors: Saeid Haghighatshoar, Emmanuel Abbe, Emre Telatar
    Abstract:

    The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function provides a sharp inequality $H(X+X')-H(X)\geq 1/2 -o(1)$ when $X,X'$ are i.i.d. with high entropy. This paper provides the inequality $H(X+X')-H(X) \geq g(H(X))$, where $X,X'$ are arbitrary i.i.d. integer-valued random variables and where $g$ is a universal strictly positive function on $\mR_+$ satisfying $g(0)=0$. Extensions to non identically distributed random variables and to conditional entropies are also obtained.

I.v. Basawa - One of the best experts on this subject based on the ideXlab platform.

  • first order random coefficient integer valued autoregressive processes
    Journal of Statistical Planning and Inference, 2007
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    A first-order random coefficient integer-valued autoregressive (RCINAR(1)) model is introduced. Ergodicity of the process is established. Moments and autocovariance functions are obtained. Conditional least squares and quasi-likelihood estimators of the model parameters are derived and their asymptotic properties are established. The performance of these estimators is compared with the maximum likelihood estimator via simulation.

  • inference for pth order random coefficient integer valued autoregressive processes
    Journal of Time Series Analysis, 2006
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    A pth-order random coefficient integer-valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.

  • inference for pth order random coefficient integer valued autoregressive processes
    Journal of Time Series Analysis, 2006
    Co-Authors: Haitao Zheng, I.v. Basawa, Somnath Datta
    Abstract:

    .  A pth-order random coefficient integer-valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets.