메뉴 건너뛰기




Volumn 16, Issue , 1998, Pages 463-484

17 Approximations to distributions of sample quantiles

(2)  Ma, Chunsheng a   Robinson, John a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 52649133142     PISSN: 01697161     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-7161(98)16019-4     Document Type: Review
Times cited : (5)

References (64)
  • 3
    • 0010817311 scopus 로고
    • Asymptotic representations related to jack knifing and bootstrapping L-statistics
    • Babu G.J., and Singh K. Asymptotic representations related to jack knifing and bootstrapping L-statistics. Sankhyā Ser. A. 46 (1984) 195-206
    • (1984) Sankhyā Ser. A. , vol.46 , pp. 195-206
    • Babu, G.J.1    Singh, K.2
  • 4
    • 0000177625 scopus 로고
    • A note on quantiles in large samples
    • Bahadur R.R. A note on quantiles in large samples. Ann. Math. Statist. 37 (1966) 577-580
    • (1966) Ann. Math. Statist. , vol.37 , pp. 577-580
    • Bahadur, R.R.1
  • 5
    • 0010880736 scopus 로고
    • Limit distributions for order statistics I, II
    • Balkema A.A., and de Haan L. Limit distributions for order statistics I, II. Theory Probab. Appl. 23 (1978) 77-92
    • (1978) Theory Probab. Appl. , vol.23 , pp. 77-92
    • Balkema, A.A.1    de Haan, L.2
  • 6
    • 0010883030 scopus 로고
    • Limit distributions for order statistics I, II
    • Balkema A.A., and de Haan L. Limit distributions for order statistics I, II. Theory Probab. Appl. 23 (1978) 341-358
    • (1978) Theory Probab. Appl. , vol.23 , pp. 341-358
    • Balkema, A.A.1    de Haan, L.2
  • 7
    • 0000596503 scopus 로고
    • Modified signed log likelihood ratio
    • Barndorff-Nielsen O.E. Modified signed log likelihood ratio. Biometrika 78 (1991) 557-563
    • (1991) Biometrika , vol.78 , pp. 557-563
    • Barndorff-Nielsen, O.E.1
  • 8
    • 0001453273 scopus 로고
    • Edgeworth and saddlepoint approximations with statistical applications (with discussion)
    • Barndorff-Nielsen O.E., and Cox D.R. Edgeworth and saddlepoint approximations with statistical applications (with discussion). J. Roy. Statist. Soc. Ser. B. 41 (1979) 279-312
    • (1979) J. Roy. Statist. Soc. Ser. B. , vol.41 , pp. 279-312
    • Barndorff-Nielsen, O.E.1    Cox, D.R.2
  • 11
    • 0001367156 scopus 로고
    • Saddlepoint approximations in statistics
    • Daniels H.E. Saddlepoint approximations in statistics. Ann. Math. Statist. 25 (1954) 631-650
    • (1954) Ann. Math. Statist. , vol.25 , pp. 631-650
    • Daniels, H.E.1
  • 12
    • 0002600304 scopus 로고
    • Saddlepoint approximations for estimating equations
    • Daniels H.E. Saddlepoint approximations for estimating equations. Biometrika 70 (1983) 89-96
    • (1983) Biometrika , vol.70 , pp. 89-96
    • Daniels, H.E.1
  • 13
    • 0003175161 scopus 로고
    • Tail probability approximations
    • Daniels H.E. Tail probability approximations. Inter. Statist. Rev. 55 (1987) 37-48
    • (1987) Inter. Statist. Rev. , vol.55 , pp. 37-48
    • Daniels, H.E.1
  • 14
    • 0002344794 scopus 로고
    • Bootstrap methods: Another look at the jacknife
    • Efron B. Bootstrap methods: Another look at the jacknife. Ann. Statist. 7 (1979) 1-26
    • (1979) Ann. Statist. , vol.7 , pp. 1-26
    • Efron, B.1
  • 16
    • 0000818352 scopus 로고
    • Relative deficiency of kernel type estimators of quantiles
    • Falk M. Relative deficiency of kernel type estimators of quantiles. Ann. Statist. 12 (1984) 261-268
    • (1984) Ann. Statist. , vol.12 , pp. 261-268
    • Falk, M.1
  • 17
    • 0001263212 scopus 로고
    • Asymptotic normality of the kernel quantile estimator
    • Falk M. Asymptotic normality of the kernel quantile estimator. Ann. Statist. 13 (1985) 428-433
    • (1985) Ann. Statist. , vol.13 , pp. 428-433
    • Falk, M.1
  • 18
    • 52649097261 scopus 로고
    • On the accuracy of the bootstrap approximation of the joint distribution of sample quantiles
    • Falk M. On the accuracy of the bootstrap approximation of the joint distribution of sample quantiles. Commun. Statist.-Theory Meth. 15 (1986) 2867-2876
    • (1986) Commun. Statist.-Theory Meth. , vol.15 , pp. 2867-2876
    • Falk, M.1
  • 19
    • 0347616369 scopus 로고
    • Bootstrapping the sample quantiles: a survey
    • Bootstrapping and Related Techniques, proceedings,. Jochel K.-H., Rothe G., and Sendler W. (Eds). Trier, FRG, s1990, Springer-Verlag, New York
    • Falk M. Bootstrapping the sample quantiles: a survey. In: Jochel K.-H., Rothe G., and Sendler W. (Eds). Bootstrapping and Related Techniques, proceedings,. Trier, FRG, s1990. Lecture Notes in Economics and Mathematical Systems 376 (1992), Springer-Verlag, New York 165-172
    • (1992) Lecture Notes in Economics and Mathematical Systems , vol.376 , pp. 165-172
    • Falk, M.1
  • 20
    • 15844398058 scopus 로고
    • Edgeworth expansions for studentized and prepivoted sample quantiles
    • Falk M., and Janas D. Edgeworth expansions for studentized and prepivoted sample quantiles. Statist. Probab. Lett. 14 (1992) 13-24
    • (1992) Statist. Probab. Lett. , vol.14 , pp. 13-24
    • Falk, M.1    Janas, D.2
  • 21
    • 0001449653 scopus 로고
    • Weak convergence of smoothed and nonsmoothed bootstrap quantile estimates
    • Falk M., and Reiss R.-D. Weak convergence of smoothed and nonsmoothed bootstrap quantile estimates. Ann. Prob. (1989) 362-371
    • (1989) Ann. Prob. , pp. 362-371
    • Falk, M.1    Reiss, R.-D.2
  • 22
    • 0040136043 scopus 로고
    • Bootstrapping the distance between smooth bootstrap and sample quantile function
    • Falk M., and Reiss R.-D. Bootstrapping the distance between smooth bootstrap and sample quantile function. Probab. Th. Rel. Fields 82 (1989) 177-186
    • (1989) Probab. Th. Rel. Fields , vol.82 , pp. 177-186
    • Falk, M.1    Reiss, R.-D.2
  • 23
    • 70350303663 scopus 로고
    • Small-sample asymptotic distributions of M-estimators of location
    • Field C.A., and Hampel F.R. Small-sample asymptotic distributions of M-estimators of location. Biometrika 69 (1982) 29-46
    • (1982) Biometrika , vol.69 , pp. 29-46
    • Field, C.A.1    Hampel, F.R.2
  • 24
    • 0003306638 scopus 로고
    • Small Sample Asymptotics
    • Hayward, CA
    • Field C.A., and Ronchetti E. Small Sample Asymptotics. IMS Notes 13 (1990), Hayward, CA
    • (1990) IMS Notes , vol.13
    • Field, C.A.1    Ronchetti, E.2
  • 25
    • 0000538713 scopus 로고
    • A new proof of the Bahadur representation of quantiles and an application
    • Ghosh J.K. A new proof of the Bahadur representation of quantiles and an application. Ann. Math. Statist. 42 (1971) 1957-1961
    • (1971) Ann. Math. Statist. , vol.42 , pp. 1957-1961
    • Ghosh, J.K.1
  • 28
    • 0001667485 scopus 로고
    • On the distribution of a studentized quantile
    • Hall P., and Sheather S.J. On the distribution of a studentized quantile. J. Roy. Statist. Soc. Ser. B 50 (1988) 381-391
    • (1988) J. Roy. Statist. Soc. Ser. B , vol.50 , pp. 381-391
    • Hall, P.1    Sheather, S.J.2
  • 30
    • 0000184603 scopus 로고
    • The modified signed likelihood statistic and saddlepoint approximations
    • Jensen J.L. The modified signed likelihood statistic and saddlepoint approximations. Biometrika 79 (1992) 693-703
    • (1992) Biometrika , vol.79 , pp. 693-703
    • Jensen, J.L.1
  • 31
    • 70350346725 scopus 로고
    • O-statistics ans their applications
    • Kaigh W.D. O-statistics ans their applications. Commun. Statist.-Theory Meth. 11 (1988) 2217-2238
    • (1988) Commun. Statist.-Theory Meth. , vol.11 , pp. 2217-2238
    • Kaigh, W.D.1
  • 32
    • 0001152423 scopus 로고
    • On Bahadur's representation of sample quantiles
    • Kiefer J. On Bahadur's representation of sample quantiles. Ann. Math. Statist. 38 (1967) 1323-1342
    • (1967) Ann. Math. Statist. , vol.38 , pp. 1323-1342
    • Kiefer, J.1
  • 33
    • 0003438568 scopus 로고
    • Series Approximation Methods in Statistics
    • Springer-Verlag, Prague
    • Kolassa J.E. Series Approximation Methods in Statistics. Lecture Notes in Statistics 88 (1994), Springer-Verlag, Prague
    • (1994) Lecture Notes in Statistics , vol.88
    • Kolassa, J.E.1
  • 34
    • 38249007778 scopus 로고
    • On the Bahadur-Ghosh-Kiefer representation of sample quantiles
    • Lahiri S.N. On the Bahadur-Ghosh-Kiefer representation of sample quantiles. Statist. Prob. Lett. 15 (1992) 163-168
    • (1992) Statist. Prob. Lett. , vol.15 , pp. 163-168
    • Lahiri, S.N.1
  • 35
    • 0000660352 scopus 로고
    • Saddlepoint approximation for the distribution function of the sum of independent random variables
    • Lugannani R., and Rice S.O. Saddlepoint approximation for the distribution function of the sum of independent random variables. Adv. Appl. Prob. 12 (1980) 475-490
    • (1980) Adv. Appl. Prob. , vol.12 , pp. 475-490
    • Lugannani, R.1    Rice, S.O.2
  • 37
    • 0039840721 scopus 로고
    • Bahadur representation of sample quantiles based on smoothed estimates of a distribution function
    • Mack Y.DP. Bahadur representation of sample quantiles based on smoothed estimates of a distribution function. Probab. Math. Statist. 8 (1987) 183-189
    • (1987) Probab. Math. Statist. , vol.8 , pp. 183-189
    • Mack, Y.DP.1
  • 38
    • 0001102173 scopus 로고
    • Some new estimate for distribution functions
    • Nadaraya E.A. Some new estimate for distribution functions. Theory Prob. Appl. 9 (1964) 497-500
    • (1964) Theory Prob. Appl. , vol.9 , pp. 497-500
    • Nadaraya, E.A.1
  • 39
    • 0001473437 scopus 로고
    • On estimation of a probability density function and mode
    • Parzen E. On estimation of a probability density function and mode. Ann. Math. Statist. 33 (1962) 1065-1076
    • (1962) Ann. Math. Statist. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 40
    • 79951913194 scopus 로고
    • Nonparametric statistical data modeling
    • Parzen E. Nonparametric statistical data modeling. J. Amer. Statist. Assoc. 74 (1979) 105-131
    • (1979) J. Amer. Statist. Assoc. , vol.74 , pp. 105-131
    • Parzen, E.1
  • 41
    • 70350343001 scopus 로고
    • Limit theorems for random central order statistics
    • Adaptive Statistical Procedures and Related Topics. Ryzin J.V. (Ed)
    • Puri M.L., and Ralescu S.S. Limit theorems for random central order statistics. In: Ryzin J.V. (Ed). Adaptive Statistical Procedures and Related Topics. IMS Lecture Notes 8 (1986) 467-475
    • (1986) IMS Lecture Notes , vol.8 , pp. 467-475
    • Puri, M.L.1    Ralescu, S.S.2
  • 42
    • 38249011842 scopus 로고
    • A remainder estimate for the normal approximation of perturbed sample quantiles
    • Ralescu S.S. A remainder estimate for the normal approximation of perturbed sample quantiles. Statist. Probab. Lett. 14 (1992) 293-298
    • (1992) Statist. Probab. Lett. , vol.14 , pp. 293-298
    • Ralescu, S.S.1
  • 43
    • 38249008218 scopus 로고
    • Asymptotoic derivations between perturbed empirical and quantile processes
    • Ralescu S.S. Asymptotoic derivations between perturbed empirical and quantile processes. J. Statist. Plann. Infer. 32 (1992) 243-258
    • (1992) J. Statist. Plann. Infer. , vol.32 , pp. 243-258
    • Ralescu, S.S.1
  • 44
    • 0001849730 scopus 로고
    • Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles
    • Ralescu S.S., and Sun S. Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles. J. Statist. Plann. Infer. 35 (1993) 55-64
    • (1993) J. Statist. Plann. Infer. , vol.35 , pp. 55-64
    • Ralescu, S.S.1    Sun, S.2
  • 45
    • 84972528712 scopus 로고
    • Saddlepoint methods and statistical inference
    • Reid N. Saddlepoint methods and statistical inference. Statist. Sci. 3 (1988) 213-238
    • (1988) Statist. Sci. , vol.3 , pp. 213-238
    • Reid, N.1
  • 46
    • 0010868083 scopus 로고
    • On the accuracy of the normal approximation for quantiles
    • Reiss R.-D. On the accuracy of the normal approximation for quantiles. Ann. Prob. 2 (1974) 741-744
    • (1974) Ann. Prob. , vol.2 , pp. 741-744
    • Reiss, R.-D.1
  • 47
    • 0010804731 scopus 로고
    • Asymptotic expansions for sample quantiles
    • Reiss R.-D. Asymptotic expansions for sample quantiles. Ann. Prob. 4 (1976) 249-258
    • (1976) Ann. Prob. , vol.4 , pp. 249-258
    • Reiss, R.-D.1
  • 48
    • 84935168496 scopus 로고
    • One-sided test for quantiles in certain nonparametric models
    • Gnedenko B.V., Puri M.L., and Vincze I. (Eds), North-Holland Publishing Company, New York
    • Reiss R.-D. One-sided test for quantiles in certain nonparametric models. In: Gnedenko B.V., Puri M.L., and Vincze I. (Eds). Nonparametric Statistical Inference, Colloq Math. Soc. János Bolyai 32 (1982), North-Holland Publishing Company, New York 759-772
    • (1982) Nonparametric Statistical Inference, Colloq Math. Soc. János Bolyai 32 , pp. 759-772
    • Reiss, R.-D.1
  • 50
    • 0003006735 scopus 로고
    • Saddlepoint approximations for permutation tests and confidence intervals
    • Robinson J. Saddlepoint approximations for permutation tests and confidence intervals. J. Roy. Statist. Soc. Ser. B. 44 (1982) 91-101
    • (1982) J. Roy. Statist. Soc. Ser. B. , vol.44 , pp. 91-101
    • Robinson, J.1
  • 52
    • 0001529784 scopus 로고
    • Remarks on some nonparametric estimates of a density function
    • Rosenblatt M. Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27 (1956) 832-837
    • (1956) Ann. Math. Statist. , vol.27 , pp. 832-837
    • Rosenblatt, M.1
  • 53
    • 34249769644 scopus 로고
    • Berry-Esséen rate in asymptotic normality for perturbed sample quantiles
    • Seoh M., and Puri M.L. Berry-Esséen rate in asymptotic normality for perturbed sample quantiles. Metrika 41 (1994) 99-108
    • (1994) Metrika , vol.41 , pp. 99-108
    • Seoh, M.1    Puri, M.L.2
  • 57
    • 0000521133 scopus 로고
    • The bootstrap: to smooth or not to smooth?
    • Silverman B.W., and Young G.A. The bootstrap: to smooth or not to smooth?. Biometrika 74 (1987) 469-479
    • (1987) Biometrika , vol.74 , pp. 469-479
    • Silverman, B.W.1    Young, G.A.2
  • 58
    • 0000824767 scopus 로고
    • On the asymptotic accuracy of Efrons bootstrap
    • Singh K. On the asymptotic accuracy of Efrons bootstrap. Ann. Statist. 9 (1981) 1187-1195
    • (1981) Ann. Statist. , vol.9 , pp. 1187-1195
    • Singh, K.1
  • 59
    • 0010879851 scopus 로고
    • Limit distributions for the terms of a variational series
    • In Russia. (English translation in
    • In Russia. (English translation in. Smirnov N.V. Limit distributions for the terms of a variational series. Trudy Mat. Inst. Steklov. 25 (1949)
    • (1949) Trudy Mat. Inst. Steklov. , vol.25
    • Smirnov, N.V.1
  • 60
    • 0002865363 scopus 로고
    • Limit distributions for the terms of a variational series
    • In Russia. (English translation in
    • In Russia. (English translation in. Smirnov N.V. Limit distributions for the terms of a variational series. Amer. Math. Soc. Transl. Ser. 1 11 (1962) 82-143
    • (1962) Amer. Math. Soc. Transl. Ser. , vol.1 , Issue.11 , pp. 82-143
    • Smirnov, N.V.1
  • 61
    • 84950625757 scopus 로고
    • Simon Newcomb, Percy Daniell, and the history of robust estimation 1885-1920
    • Stigler S.M. Simon Newcomb, Percy Daniell, and the history of robust estimation 1885-1920. J. Amer. Statist. Assoc. 68 (1973) 872-879
    • (1973) J. Amer. Statist. Assoc. , vol.68 , pp. 872-879
    • Stigler, S.M.1
  • 62
    • 53149084709 scopus 로고
    • Bahadur representation of kernel quantile estimators
    • Xiang X.J. Bahadur representation of kernel quantile estimators. Scand. J. Statist. 21 (1994) 169-178
    • (1994) Scand. J. Statist. , vol.21 , pp. 169-178
    • Xiang, X.J.1
  • 63
    • 0001297102 scopus 로고
    • A smooth nonparametric estimator of a quantile function
    • Yang S.S. A smooth nonparametric estimator of a quantile function. J. Amer. Statist. Assoc. 80 (1985) 1004-1011
    • (1985) J. Amer. Statist. Assoc. , vol.80 , pp. 1004-1011
    • Yang, S.S.1
  • 64
    • 38249017368 scopus 로고
    • Smooth nonparametric estimation of the quantile function
    • Zelterman D. Smooth nonparametric estimation of the quantile function. J. Statist. Plann. Infer. 26 (1990) 339-352
    • (1990) J. Statist. Plann. Infer. , vol.26 , pp. 339-352
    • Zelterman, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.