A Feasible Bayesian Estimator of Quantiles for Projectile Accuracy from Non-iid Data

References

• Atkinson , K. 1978 . An Introduction to Numerical Analysis , New York : John Wiley .
   Google Scholar
• Berger , J. O. 1985 . Statistical Decision Theory and Bayesian Analysis, , 2nd ed. , New York : Springer-Verlag .
   Google Scholar
• Blischke , W. R. and Halpin , A. H. 1966 . Asymptotic Properties of Some Estimators of Quantiles of Circular Error . Journal of the American Statistical Association , 61 : 618 – 632 .
   Web of Science ®Google Scholar
• Brown , R. H. 1986 . The Distribution of Quadratic Forms in Normal Random Variables . SIAM Journal of Scientific and Statistical Computing , 7 : 689 – 695 .
   Web of Science ®Google Scholar
• Cacoullos , T. and Koutras , M. 1984 . Quadratic Forms in Spherical Random Variables: Generalized Noncentral χ2 Distribution . Naval Research Logistics Quarterly , 31 : 447 – 461 .
   Google Scholar
• Chanda , K. C. 1979 . Asymptotic Expansion of Quantiles Computed From Mixed Samples . Calcutta Statistical Association Bulletin , 28 : 37 – 46 .
   Google Scholar
• Chin , D. C. Comparative Study of Several Multivariate Stochastic Approximation Algorithms . Proceedings of the American Statistical Association, Statistical Computing Section . pp. 223 – 228 .
   Google Scholar
• Eckler , A. R. 1988 . Target Coverage . Encyclopedia of Statistical Sciences , 9 : 180 – 182 .
   Google Scholar
• Evans , M. , Govindarajulu , Z. and Barteoulot , J. 1985 . Estimates of Circular Error Probabilities , Stanford University, Dept. of Statistics . Technical Report 367
   Google Scholar
• Gelfand , A. E. and Smith , A. F. M. 1990 . Sampling-Based Approaches to Calculating Marginal Densities . Journal of the American Statistical Association , 85 : 398 – 409 .
   Web of Science ®Google Scholar
• Gelfand , A. E. and Smith , A. F. M. 1991 . Gibbs Sampling for Marginal Posterior Expectations . Communication in Statistics–Part A, Theory and Methods , 20 : 1747 – 1766 .
   Web of Science ®Google Scholar
• Govindarajulu , Z. 1986 . A Note on Circular Error Probabilities . Naval Research Logistics Quarterly , 33 : 423 – 429 .
   Google Scholar
• Grubbs , F. E. 1964 . Approximate Circular and Noncircular Offset Probabilities of Hitting . Operations Research , 12 : 51 – 62 .
   Web of Science ®Google Scholar
• Hill , S. D. and Brokloff , N. A. Estimating Quantiles of Circular Error for Non-i.i.d. Observations . presented at the American Statistical Association Annual Meeting (General Methodology Section) . August 18–21 , San Francisco .
   Google Scholar
• Jensen , D. R. and Solomon , H. 1972 . A Gaussian Approximation to the Distribution of a Definite Quadratic Form . Journal of the American Statistical Association , 67 : 898 – 902 .
   Web of Science ®Google Scholar
• Kempthorne , O. and Folks , L. 1971 . Probability, Statistics, and Data Analysis , Ames , IA : Iowa State University Press .
   Google Scholar
• Lawless , J. E. 1982 . Statistical Models and Methods for Lifetime Data , New York : John Wiley .
   Google Scholar
• Maryak , J. L. and Spall , J. C. 1987a . Conditions for the Insensitivity of the Bayesian Posterior Distribution to the Choice of Prior Distribution . Statistics and Probability Letters , 5 : 401 – 407 .
   Web of Science ®Google Scholar
• Maryak , J. L. and Spall , J. C. Bayesian Estimation of Quantiles of Circular Error From Non-i.i.d. Data . Proceedings of the American Statistical Association, Business and Economics Statistics Section . pp. 427 – 430 .
   Google Scholar
• Prakasa Rao , B. L. S. 1987 . Asymptotic Theory of Statistical Inference , New York : John Wiley .
   Google Scholar
• Rai , K. and Van Ryzin , J. 1984 . Multihit Models for Bivariate Quantal Responses . Statistics and Decisions , 2 : 111 – 130 .
   Google Scholar
• Ralston , A. 1965 . A First Course in Numerical Analysis , New York : McGraw-Hill .
   Google Scholar
• Rubinstein , R. Y. 1986 . Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks , New York : John Wiley .
   Google Scholar
• Spall , J. C. 1992 . Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation . IEEE Transactions on Automatic Control , 37 : 332 – 341 .
   Web of Science ®Google Scholar
• Spall , J. C. and Hill , S. D. 1990 . Least-Informative Bayesian Prior Distributions for Finite Samples Based on Information Theory . IEEE Transactions on Automatic Control , 35 : 580 – 583 .
   Web of Science ®Google Scholar
• Taub , A. E. and Thomas , M. A. 1983 . Confidence Intervals for CEP When the Errors are Elliptical Normal Naval Surface Weapons Center Technical Report TR 83–205
   Google Scholar
• Thomas , M. A. and Crigler , J. R. 1974 . Tolerance Limits for the p-Dimensional Radial Error Distribution . Communications in Statistics , 3 : 477 – 483 .
   Google Scholar
• Tierney , L. and Kadane , J. B. 1986 . Accurate Approximations for Posterior Moments and Marginal Densities . Journal of the American Statistical Association , 81 : 82 – 86 .
   Web of Science ®Google Scholar
• Titterington , D. M. , Smith , A. F. M. and Makov , U. E. 1985 . Statistical Analysis of Finite Mixture Distributions , New York : John Wiley .
   Google Scholar
• Zacks , S. 1971 . Theory of Statistical Inference , New York : John Wiley .
   Google Scholar
• Zeger , S. L. and Karim , M. R. 1991 . Generalized Linear Models With Random Effects: A Gibbs Sampling Approach . Journal of the American Statistical Association , 86 : 79 – 86 .
   Web of Science ®Google Scholar
• Zellner , A. 1977 . “ Maximal Data Information Prior Distributions ” . In New Developments in the Applications of Bayesian Methods , Edited by: Aykac , A. and Brumat , C. 211 – 232 . Amsterdam : North-Holland .
   Google Scholar