The Experts below are selected from a list of 198 Experts worldwide ranked by ideXlab platform

Arjun K. Gupta - One of the best experts on this subject based on the ideXlab platform.

  • Adjusted empirical likelihood for long-memory time-series models
    Journal of Statistical Theory and Practice, 2017
    Co-Authors: Ramadha D. Piyadi Gamage, Wei Ning, Arjun K. Gupta
    Abstract:

    The empirical likelihood method has been applied to short-memory time-series models by Monti through the Whittle’s estimation method. Yau extended this idea to long-memory time series models. Nordman and Lahiri showed a new formulation of empirical likelihood for inference of dependent data. Asymptotic Distributions of the empirical likelihood ratio statistic for short and long-memory time series have been derived to construct confidence regions for the corresponding model parameters. However, computing profile empirical likelihood function involving constrained maximization does not always have a solution, which leads to several drawbacks. In this article, we propose an adjusted empirical likelihood procedure to modify the one proposed by Yau for the autoregressive fractionally integrated moving average (ARFIMA) model. It guarantees the existence of a solution to the required maximization problem and maintains an asymptotic Chi-Squared Distribution. Simulations have been carried out to illustrate that the adjusted empirical likelihood method for different long-time series models provides competitive confidence regions and coverage probabilities compared to the unadjusted ones, especially for small sample sizes.

Ramadha D. Piyadi Gamage - One of the best experts on this subject based on the ideXlab platform.

  • Adjusted empirical likelihood for long-memory time-series models
    Journal of Statistical Theory and Practice, 2017
    Co-Authors: Ramadha D. Piyadi Gamage, Wei Ning, Arjun K. Gupta
    Abstract:

    The empirical likelihood method has been applied to short-memory time-series models by Monti through the Whittle’s estimation method. Yau extended this idea to long-memory time series models. Nordman and Lahiri showed a new formulation of empirical likelihood for inference of dependent data. Asymptotic Distributions of the empirical likelihood ratio statistic for short and long-memory time series have been derived to construct confidence regions for the corresponding model parameters. However, computing profile empirical likelihood function involving constrained maximization does not always have a solution, which leads to several drawbacks. In this article, we propose an adjusted empirical likelihood procedure to modify the one proposed by Yau for the autoregressive fractionally integrated moving average (ARFIMA) model. It guarantees the existence of a solution to the required maximization problem and maintains an asymptotic Chi-Squared Distribution. Simulations have been carried out to illustrate that the adjusted empirical likelihood method for different long-time series models provides competitive confidence regions and coverage probabilities compared to the unadjusted ones, especially for small sample sizes.

Chintha Tellambura - One of the best experts on this subject based on the ideXlab platform.

  • New series representation for the trivariate non-central Chi-Squared Distribution
    IEEE Transactions on Communications, 2009
    Co-Authors: Prathapasinghe Dharmawansa, Nandana Rajatheva, Chintha Tellambura
    Abstract:

    This paper derives a new infinite series representation for the trivariate non-central Chi-Squared Distribution when the underlying correlated Gaussian variables have a tridiagonal form of an inverse covariance matrix. The joint probability density function is derived using Miller's approach and Dougall's identity. Moreover, the trivariate cumulative Distribution function (cdf) and characteristic function (chf) are also derived. Finally, the bivariate non-central Chi-Squared Distribution and some known forms are shown to be special cases of the more general Distribution. However, the derivation of non-central Chi-Squared Distribution for an arbitrary covariance matrix seems intractable via Miller's approach. Two applications of the newly derived results are provided for performance analysis of multiple input multiple output (MIMO) systems with transmit antenna selection over a correlated Rician fading environment. Some numerical results are also presented to verify the accuracy of the analytical expressions.

  • VTC Spring - On the Trivariate Non-Central Chi-Squared Distribution
    2007 IEEE 65th Vehicular Technology Conference - VTC2007-Spring, 2007
    Co-Authors: K. D. P. Dharmawansa, R.m.a.p. Rajatheva, Chintha Tellambura
    Abstract:

    In this paper, we derive a new infinite series representation for the trivariate non-central Chi-Squared Distribution when the underlying correlated Gaussian variables have tridiagonal form of inverse covariance matrix. We make use of the Miller's approach and the Dougall's identity to derive the joint density function. Moreover, the trivariate cumulative Distribution function (cdf) and characteristic function (chf) are also derived. Finally, bivariate noncentral Chi-Squared Distribution and some known forms are shown to be special cases of the more general Distribution. However, non-central Chi-Squared Distribution for an arbitrary covariance matrix seems intractable with the Miller's approach.

Wei Ning - One of the best experts on this subject based on the ideXlab platform.

  • Adjusted empirical likelihood for long-memory time-series models
    Journal of Statistical Theory and Practice, 2017
    Co-Authors: Ramadha D. Piyadi Gamage, Wei Ning, Arjun K. Gupta
    Abstract:

    The empirical likelihood method has been applied to short-memory time-series models by Monti through the Whittle’s estimation method. Yau extended this idea to long-memory time series models. Nordman and Lahiri showed a new formulation of empirical likelihood for inference of dependent data. Asymptotic Distributions of the empirical likelihood ratio statistic for short and long-memory time series have been derived to construct confidence regions for the corresponding model parameters. However, computing profile empirical likelihood function involving constrained maximization does not always have a solution, which leads to several drawbacks. In this article, we propose an adjusted empirical likelihood procedure to modify the one proposed by Yau for the autoregressive fractionally integrated moving average (ARFIMA) model. It guarantees the existence of a solution to the required maximization problem and maintains an asymptotic Chi-Squared Distribution. Simulations have been carried out to illustrate that the adjusted empirical likelihood method for different long-time series models provides competitive confidence regions and coverage probabilities compared to the unadjusted ones, especially for small sample sizes.

David Yoo - One of the best experts on this subject based on the ideXlab platform.

  • Probabilistic sensitivity analysis for novel second-order reliability method (SORM) using generalized Chi-Squared Distribution
    Structural and Multidisciplinary Optimization, 2014
    Co-Authors: David Yoo, Ikjin Lee, Hyunkyoo Cho
    Abstract:

    Reliability-based design optimization (RBDO) requires evaluation of sensitivities of probabilistic constraints. To develop RBDO utilizing the recently proposed novel second-order reliability method (SORM) that improves conventional SORM approaches in terms of accuracy, the sensitivities of the probabilistic constraints at the most probable point (MPP) are required. Thus, this study presents sensitivity analysis of the novel SORM at MPP for more accurate RBDO. During analytic derivation in this study, it is assumed that the Hessian matrix does not change due to the small change of design variables. The calculation of the sensitivity based on the analytic derivation requires evaluation of probability density function (PDF) of a linear combination of non-central chi-square variables, which is obtained by utilizing general Chi-Squared Distribution. In terms of accuracy, the proposed probabilistic sensitivity analysis is compared with the finite difference method (FDM) using the Monte Carlo simulation (MCS) through numerical examples. The numerical examples demonstrate that the analytic sensitivity of the novel SORM agrees very well with the sensitivity obtained by FDM using MCS when a performance function is quadratic in U-space and input variables are normally distributed. It is further shown that the proposed sensitivity is accurate enough compared with FDM results even for a higher order performance function.

  • A Novel Second-Order Reliability Method (SORM) Using Noncentral or Generalized Chi-Squared Distributions
    Journal of Mechanical Design, 2012
    Co-Authors: Ikjin Lee, Yoojeong Noh, David Yoo
    Abstract:

    This paper proposes a novel second-order reliability method (SORM) using noncentral or general Chi-Squared Distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point in standard normal U-space, (2) error due to approximating the quadratic function in U-space by a parabolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only, which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two types of errors by describing the quadratic failure surface with the linear combination of noncentral chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper. The first approach directly calculates the probability of failure using numerical integration of the joint probability density function over the linear failure surface, and the second approach uses the cumulative Distribution function of the linear failure surface for the calculation of the probability of failure. The proposed method is compared with first-order reliability method, conventional SORM, and Monte Carlo simulation results in terms of accuracy. Since it contains fewer approximations, the proposed method shows more accurate reliability analysis results than existing SORM without sacrificing efficiency.

  • A Novel Second-Order Reliability Method (SORM) Using Non-Central or Generalized Chi-Squared Distributions
    Volume 3: 38th Design Automation Conference Parts A and B, 2012
    Co-Authors: Ikjin Lee, David Yoo, Yoojeong Noh
    Abstract:

    This paper proposes a novel second-order reliability method (SORM) using non-central or general Chi-Squared Distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point (MPP) in the standard normal U-space, (2) error due to approximating the quadratic function in U-space by a hyperbolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two errors by describing the quadratic failure surface with the linear combination of non-central chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper. The first approach directly calculates the probability of failure using numerical integration of the joint probability density function (PDF) over the linear failure surface and the second approach uses the cumulative Distribution function (CDF) of the linear failure surface for the calculation of the probability of failure. The proposed method is compared with first-order reliability method (FORM), conventional SORM, and Monte Carlo simulation (MCS) results in terms of accuracy. Since it contains fewer approximations, the proposed method shows more accurate reliability analysis results than existing SORM without sacrificing efficiency.Copyright © 2012 by ASME