On the performance of estimators of parameter in autoregressive model of order one and optimal prediction under asymmetric loss

Roychowdhury, Soma; Bhattacharya, Debasis

doi:10.3233/mas-2008-3306

Cited by 4 publications

(3 citation statements)

References 2 publications

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“…[2] Our primary concern in this section is to present a method to calculate the distribution of the posterior meanθ , given by Equation (3). [2] Our primary concern in this section is to present a method to calculate the distribution of the posterior meanθ , given by Equation (3).…”

Section: Posterior Mean Distributionmentioning

confidence: 99%

“…In this paper, using the posterior mean derived by Roychowdhury and Bhattacharya, [2] we present a procedure for the calculation of its conditional distribution. We have also furnished a practical procedure to calculate decision-making indices EVPI and EVSI, for the finite action space whenever the value function is linear, and for the infinite action space whenever the opportunity loss function is quadratic.…”

Section: Conclusion and Remarksmentioning

confidence: 99%

“…where v = σ 2 /θ , derived by Roychowdhury and Bhattacharya, [2] and we present a procedure for the calculation of its conditional distribution. The distribution of the statistic given by Equation (2), for v = 0, is discussed in [5].…”

Section: Introductionmentioning

confidence: 99%

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Typical decision problems in the first-order autoregressive time series

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Applied statistical decision theory has wide applications in decision-making fields of studies, such as economic, business management and industrial managements. In this work, following Pratt et al.'s [Introduction to statistical decision theory. 3rd ed. Cambridge, MA: The MIT Press; 2001] approach, we provide theoretical and practical formulations for the calculations of the key decision-making indices expected value of perfect information and expected value of sample information, whenever the unknown state appears to be the first-order autoregressive (AR) time series parameter that assumes a normal prior distribution. A practical procedure is furnished for calculating the decision-making indices. We treat the finite and infinite state spaces for the linear value functions and the quadratic opportunity losses. Interestingly our investigations on the distribution of the mean of the posterior distribution lead us to a general form for the corresponding statistic and its distribution, discussed by Reeves [The distribution of the maximum likelihood estimator of the parameter in the first-order AR series. Biometrika. 1972;59:387-394], Moschopoulos and Canada [The distribution function of a linear combination of chi-squares. Comput Math Appl. 1984;10:383-386], and Roychowdhury and Bhattacharya [On the performance of estimators of parameter in AR model of order one and optimal prediction under asymmetric loss. Model Assist Stat Appl. 2008;3:225-232].

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Section: Posterior Mean Distributionmentioning

confidence: 99%

Section: Conclusion and Remarksmentioning

confidence: 99%