Linear estimators and predictors based on generalized order statistics from generalized pareto distributions

Communications in Statistics - Theory and Methods

Volumn 39, Issue 2, 2010, Pages 311-326

  Burkschat, M ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Best linear invariant estimator; Best linear invariant predictor; Best linear unbiased estimator; Best linear unbiased predictor; BLEE; BLIE; BLUE; BLUP; Exponential distribution; Location and scale parameters; Non Negativity of BLUE; Pareto distribution

Indexed keywords

BEST LINEAR UNBIASED ESTIMATOR; BEST LINEAR UNBIASED PREDICTOR; EXPONENTIAL DISTRIBUTIONS; LOCATION AND SCALE PARAMETERS; NON-NEGATIVITY; PARETO DISTRIBUTIONS;

PARETO PRINCIPLE; PHASE MATCHING;

ESTIMATION;

EID: 77951191088     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920902746630     Document Type: Article

References (39)

1. Ahsanullah, M. (1980). Linear prediction of record values for the two parameter exponential distribution. Ann. Inst. Statist. Math. 32:363-368.
2. Ahsanullah, M. (1992). Record values of independent and identically distributed continous random variables. Pakistan J. Stat. 8:9-34.
3. Ahsanullah, M. (1996). Generalized order statistics from two parameter uniform distribution. Commun. Statist. Theor. Meth. 25:2311-2318.
4. Ahsanullah, M. (1997). Generalized order statistics from power function. J. Appl. Stat. Sci. 5:283-290.
5. Ahsanullah, M. (2000). Generalized order statistics from exponential distribution. J. Statist. Plann. Infer. 85:85-91.
6. Ahsanullah, M., Habibullah, M. (2000). Estimation of parameters of a Pareto distribution by generalized order statistics. Commun. Statist. Theor. Meth. 29:1597-1609.
7. Arnold, B. C., Balakrishnan, N., Nagaraja, H. N. (1992). A First Course in Order Statistics. New York: Wiley.
8. Arnold, B. C., Balakrishnan, N., Nagaraja, H. N. (1998). Records. New York: Wiley.
9. Bai, Z., Sarkar, S. K., Wang, W. (1997). Positivity of the best unbiased L-estimator of the scale parameter with complete or selected order statistics from location-scale distribution. Statist. Probab. Lett. 32:181-188.
10. Balakrishnan, N., Cohen, A. C. (1991). Order Statistics and Inference. Boston: Academic Press.
11. Balakrishnan, N., Sandhu, R. A. (1996). Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type II censored samples. Sankhya Ser. B 58:1-9.
12. Balakrishnan, N., Rao, C. R. (1997). A note on best linear unbiased estimation based on order statistics. Amer. Statist. 51:181-185.
13. Balakrishnan, N., Rao, C. R. eds. (1998). Handbook of Statistics. Vol.17. Elsevier: Amsterdam.
14. Balakrishnan, N., Aggarwala, R. (2000). Progressive Censoring. Boston: Birkhäuser.
15. Balakrishnan, N., Cramer, E., Kamps, U., Schenk, N. (2001). Progressive Type II censored order statistics from exponential distributions. Statistics 35:537-556. (Pubitemid 33683309)
16. Balakrishnan, N., Papadatos, N. (2002). The use of spacings in the estimation of a scale parameter. Statist. Probab. Lett. 57:193-204.
17. Belzunce, F., Mercader, J.-A., Ruiz, J.-M. (2005). Stochastic comparisons of generalized order statistics. Probab. Eng. Inform. Sci. 19:99-120.
18. Bondesson, L. (1979). On best equivariant and best unbiased equivariant estimators in the extended Gauss-Markov model. Scand. J. Statist. 6:22-28.
19. Burkschat, M., Cramer, E., Kamps, U. (2007). Linear estimation of location and scale parameters based on generalized order statistics from generalized Pareto distributions. In: Ahsanullah, M., Raqab, M. Z., eds. Recent Developments in Ordered Random Variables. Hauppauge: Nova Science, pp. 253-261.
20. Christensen, R. (2002). Plane Answers to Complex Questions - The Theory of Linear Models. 3rd ed. New York: Springer.
21. Cramer, E., Kamps, U. (2001a). Estimation with sequential order statistics from exponential distributions. Ann. Inst. Statist. Math. 53:307-324. (Pubitemid 33617338)
22. Cramer, E., Kamps, U. (2001b). Sequential k-out-of-n systems. In: Balakrishnan, N., Rao, C. R. eds., Handbook of Statistics - Advances in Reliability. Vol.20. Amsterdam: Elsevier, pp. 301-372.
23. David, H. A., Nagaraja, H. N. (2003). Order Statistics. 3rd ed. Hoboken: Wiley.
24. Doganaksoy, N., Balakrishnan, N. (1997). A useful property of best linear unbiased predictors with applications to life testing. Amer. Statist. 51:22-28.
25. Embrechts, P., Klüppelberg, C., Mikosch, T. (1997). Modelling Extremal Events. Berlin: Springer.
26. Goldberger, A. S. (1962). Best linear unbiased prediction in the generalized linear regression model. J. Amer. Statist. Assoc. 57:369-375.
27. Kaminsky, K. S., Nelson, P. I. (1975). Best linear unbiased prediction of order statistics in location and scale families. J. Amer. Statist. Assoc. 70:145-150.
28. Kaminsky, K. S., Nelson, P. I. (1998). Prediction of order statistics. In: Balakrishnan, N., Rao, C. R. eds. Handbook of Statistics. vol.17. Amsterdam: Elsevier.
29. Kamps, U. (1995a). A Concept of Generalized Order Statistics. Stuttgart: Teubner.
30. Kamps, U. (1995b). A concept of generalized order statistics. J. Statist. Plann. Infer. 48:1-23.
31. Lehmann, E. L., Casella, G. (1998). Theory of Point Estimation. 2nd ed. New York: Springer.
32. Llyod, E. H. (1952). Least squares estimation of location and scale parameters using order statistics. Biometrika 39:88-95.
33. Magnus, J. R., Neudecker, H. (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics. 2nd ed. New York: Wiley.
34. Malinowska, I., Pawlas, P., Szynal, D. (2006). Estimation of location and scale parameters for the Burr XII distribution using generalized order statistics. Lin. Algebra Appl. 417:150-162.
35. Mann, N. (1969). Optimum estimators for linear functions of location and scale parameters. Ann. Math. Statist. 40:2149-2155.
36. Nagaraja, H. N. (1984). Asymptotic linear prediction of extreme order statistics. Ann. Inst. Statist. Math. 36:289-299.
37. Nelson, W. B. (2004). Applied Life Data Analysis. Hoboken, NJ: Wiley.
38. Pickands, J. (1975). Statistical inference using extreme order statistics. Ann. Statist. 3:119-131.
39. Reiss, R.-D. (1989). Approximate Distributions of Order Statistics. New York: Springer.