The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Augustine C. M. Wong - One of the best experts on this subject based on the ideXlab platform.
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A note on Bayesian and frequentist parametric inference for a Scalar Parameter of interest
Statistics & Probability Letters, 2013Co-Authors: Augustine C. M. WongAbstract:In this paper, a new approximation of the marginal posterior distribution function is obtained. Moreover, for the location-scale model, by applying the shrinkage argument, a new approximation of the conditional distribution function of the signed likelihood ratio statistic given an ancillary statistic is derived from the approximated marginal posterior distribution.
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On standardizing the signed root log likelihood ratio statistic
Statistics & Probability Letters, 2012Co-Authors: L. Jiang, Augustine C. M. WongAbstract:A simple connection between the Bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant of the p∗ formula–an approximate conditional density for the maximum likelihood estimate given an exact or an approximate ancillary statistic–was established in Barndorff-Nielsen and Cox (1984). In this paper, the explicit form of the normalizing constant of the p∗ formula for the Scalar Parameter model is derived. By change of variables, the mean and variance of the signed root log likelihood ratio statistic are obtained explicitly, and, hence, tail probabilities can be calculated from the standardized signed root log likelihood ratio statistic. Examples are used to illustrate the implementation and accuracy of the proposed method.
Graziano Chesi - One of the best experts on this subject based on the ideXlab platform.
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lmi based computation of the instability measure of continuous time linear systems with a Scalar Parameter
Canadian Conference on Electrical and Computer Engineering, 2014Co-Authors: Graziano ChesiAbstract:Measuring the instability is a fundamental issue in control systems. This paper investigates the instability measure defined as the sum of the real parts of the unstable eigenvalues, which has important applications such as stabilization with information constraint. We consider continuous-time linear systems whose coefficients are linear functions of a Scalar Parameter constrained into an interval. The problem is to determine the largest instability measure for all admissible values of the Parameter. Two sufficient and necessary conditions for establishing upper bounds on the sought instability measure are proposed in terms of linear matrix inequality (LMI) feasibility tests. The first condition exploits Lyapunov functions, while the second condition is based on the determinants of some specific matrices. Some numerical examples are used to compare the proposed conditions.
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technical communique exact robust stability analysis of uncertain systems with a Scalar Parameter via lmis
Automatica, 2013Co-Authors: Graziano ChesiAbstract:This paper provides an exact linear matrix inequality (LMI) condition for robust asymptotic stability of uncertain systems depending polynomially on a Scalar Parameter in both continuous-time and discrete-time cases. Specifically, this condition exploits sum of squares (SOS) techniques and is based on the construction of polynomials of known degree that detect the presence of eigenvalues on the boundary of the stability region. It is shown that this condition requires a much smaller computational burden than existing exact LMI conditions which might be prohibitive even for small scale systems.
Ulrich K Muller - One of the best experts on this subject based on the ideXlab platform.
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t statistic based correlation and heterogeneity robust inference
Journal of Business & Economic Statistics, 2010Co-Authors: Rustam Ibragimov, Ulrich K MullerAbstract:We develop a general approach to robust inference about a Scalar Parameter of interest when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Szekely (2005) concerning the small sample properties of the standard t-test: For a significance level of 5% or lower, the t-test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q≥2 groups, estimate the model for each group, and conduct a standard t-test with the resulting q Parameter estimators of interest. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the Parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlat...
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t statistic based correlation and heterogeneity robust inference
2007Co-Authors: Rustam Ibragimov, Ulrich K MullerAbstract:We develop a general approach to robust inference about a Scalar Parameter when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Sz´ekely (2005) concerning the small sample properties of the standard t-test: For a significance level of 5% or lower, the t-test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q ≥ 2 groups, estimate the model for each group and conduct a standard t-test with the resulting q Parameter estimators. This results in valid inference as long as the groups are chosen in a way that ensures the Parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.
Egi Satoshi - One of the best experts on this subject based on the ideXlab platform.
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Symbolical Index Reduction and Completion Rules for Importing Tensor Index Notation into Programming Languages
2021Co-Authors: Egi SatoshiAbstract:In mathematics, many notations have been invented for the concise representation of mathematical formulae. Tensor index notation is one of such notations and has been playing a crucial role in describing formulae in mathematical physics. This paper shows a programming language that can deal with symbolical tensor indices by introducing a set of tensor index rules that is compatible with two types of Parameters, i.e., Scalar and tensor Parameters. When a tensor Parameter obtains a tensor as an argument, the function treats the tensor argument as a whole. In contrast, when a Scalar Parameter obtains a tensor as an argument, the function is applied to each component of the tensor. On a language with Scalar and tensor Parameters, we can design a set of index reduction rules that allows users to use tensor index notation for arbitrary user-defined functions without requiring additional description. Furthermore, we can also design index completion rules that allow users to define the operators concisely for differential forms such as the wedge product, exterior derivative, and Hodge star operator. In our proposal, all these tensor operators are user-defined functions and can be passed as arguments of high-order functions.Comment: 13 pages. arXiv admin note: substantial text overlap with arXiv:1702.0634
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Scalar and Tensor Parameters for Importing the Notation in Differential Geometry into Programming
2018Co-Authors: Egi SatoshiAbstract:This paper proposes a method for importing tensor index notation, including Einstein summation notation, into programming. This method involves introducing two types of Parameters, i.e, Scalar and tensor Parameters. As an ordinary function, when a tensor Parameter obtains a tensor as an argument, the function treats the tensor argument as a whole. In contrast, when a Scalar Parameter obtains a tensor as an argument, the function is applied to each component of the tensor. This paper shows that introducing these two types of Parameters enables us to apply arbitrary functions to tensor arguments using index notation without requiring an additional description to enable each function to handle tensors. Furthermore, we show this method can be easily extended to define concisely the operators for differential forms such as the wedge product, exterior derivative, and Hodge star operator. It is achieved by providing users the method for controlling the completion of omitted indices.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1702.0634
L. Jiang - One of the best experts on this subject based on the ideXlab platform.
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On standardizing the signed root log likelihood ratio statistic
Statistics & Probability Letters, 2012Co-Authors: L. Jiang, Augustine C. M. WongAbstract:A simple connection between the Bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant of the p∗ formula–an approximate conditional density for the maximum likelihood estimate given an exact or an approximate ancillary statistic–was established in Barndorff-Nielsen and Cox (1984). In this paper, the explicit form of the normalizing constant of the p∗ formula for the Scalar Parameter model is derived. By change of variables, the mean and variance of the signed root log likelihood ratio statistic are obtained explicitly, and, hence, tail probabilities can be calculated from the standardized signed root log likelihood ratio statistic. Examples are used to illustrate the implementation and accuracy of the proposed method.
