메뉴 건너뛰기




Volumn 83, Issue 404, 1988, Pages 941-953

Philatelic mixtures and multimodal densities

Author keywords

Bootstrap; Likelihood ratio test; Maximum likelihood; Mixtures of distributions; Modes; Nonparametric density estimation; Postage stamps; Quality control; Tests for multimodality

Indexed keywords


EID: 0006380024     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1988.10478683     Document Type: Article
Times cited : (108)

References (64)
  • 1
    • 0001665174 scopus 로고
    • Statistical Modelling of Data on Teaching Styles
    • (with discussion), Ser. A
    • Aitkin, M., Anderson, D., and Hinde, J. (1981), “Statistical Modelling of Data on Teaching Styles” (with discussion), Journal of the Royal Statistical Society, Ser. A, 144, 419–461.
    • (1981) Journal of the Royal Statistical Society , vol.144 , pp. 419-461
    • Aitkin, M.1    Erson, D.2    Hinde, J.3
  • 2
    • 0002582140 scopus 로고
    • Estimation and Hypothesis Testing in Finite Mixture Models
    • Ser. B
    • Aitkin, M., and Rubin, D. B. (1985), “Estimation and Hypothesis Testing in Finite Mixture Models,” Journal of the Royal Statistical Society, Ser. B, 47, 67–75.
    • (1985) Journal of the Royal Statistical Society , vol.47 , pp. 67-75
    • Aitkin, M.1    Rubin, D.B.2
  • 3
    • 0000417176 scopus 로고
    • Mixture Models, Outliers, and the EM Algorithm
    • Aitkin, M., and Wilson, G. T. (1980), “Mixture Models, Outliers, and the EM Algorithm,” Technometrics, 22, 325–331.
    • (1980) Technometrics , vol.22 , pp. 325-331
    • Aitkin, M.1    Wilson, G.T.2
  • 5
    • 84950473384 scopus 로고
    • Mexico: The 1872 Issue
    • Barron, J. H. (1915), “Mexico: The 1872 Issue,” Philatelic Journal of Great Britain, 25, 75–76, 98–100, 110–111, 124–125, 138–139, 152–154.
    • (1915) Philatelic Journal of Great Britain , vol.25
    • Barron, J.H.1
  • 7
    • 0014061349 scopus 로고
    • A Simple Method for Resolution of a Distribution Into Its Gaussian Components
    • Bhattacharya, C. G. (1967), “A Simple Method for Resolution of a Distribution Into Its Gaussian Components,” Biometrics, 23, 115–135.
    • (1967) Biometrics , vol.23 , pp. 115-135
    • Bhattacharya, C.G.1
  • 8
    • 0003064476 scopus 로고
    • Spline Transformations: Three New Diagnostic Aids for the Statistical Data-Analyst
    • (with discussion), Ser. B
    • Boneva, L. I., Kendall, D., and Stefanov, I. (1971), “Spline Transformations: Three New Diagnostic Aids for the Statistical Data-Analyst” (with discussion), Journal of the Royal Statistical Society, Ser. B, 33, 1–71.
    • (1971) Journal of the Royal Statistical Society , vol.33 , pp. 1-71
    • Boneva, L.I.1    Kendall, D.2    Stefanov, I.3
  • 9
    • 0001688136 scopus 로고
    • A Comparative Study of Some Kernel-Based Nonparametric Density Estimates
    • Bowman, A. W. (1985), “A Comparative Study of Some Kernel-Based Nonparametric Density Estimates,” Journal of Statistical Computation and Simulation, 21, 313–327.
    • (1985) Journal of Statistical Computation and Simulation , vol.21 , pp. 313-327
    • Bowman, A.W.1
  • 10
    • 84898431324 scopus 로고
    • Variable Kernel Estimates of Multivariate Densities
    • Breiman, L., Meisel, W., and Purcell, E. (1977), “Variable Kernel Estimates of Multivariate Densities,” Technometrics, 19, 135–144.
    • (1977) Technometrics , vol.19 , pp. 135-144
    • Breiman, L.1    Meisel, W.2    Purcell, E.3
  • 12
    • 0040235492 scopus 로고
    • Consistent Cross-Validated Density Estimation
    • Chow, Y.-S., Geman, S., and Wu, L.-D. (1983), “Consistent Cross-Validated Density Estimation,” The Annals of Statistics, 11, 25–38.
    • (1983) The Annals of Statistics , vol.11 , pp. 25-38
    • Chow, Y.-S.1    Geman, S.2    Wu, L.-D.3
  • 13
    • 84946642214 scopus 로고
    • Estimation in Mixtures of Two Normal Distributions
    • Cohen, A. C. (1967), “Estimation in Mixtures of Two Normal Distributions,” Technometrics, 9, 15–28.
    • (1967) Technometrics , vol.9 , pp. 15-28
    • Cohen, A.C.1
  • 14
    • 0001381164 scopus 로고
    • Estimating the Components of a Mixture of Normal Distributions
    • Day, N. E. (1969), “Estimating the Components of a Mixture of Normal Distributions,” Biometrika, 56, 463–474.
    • (1969) Biometrika , vol.56 , pp. 463-474
    • Day, N.E.1
  • 17
    • 28244458389 scopus 로고
    • Pulmonary Mast Cells in Infants and Their Relation to Unexpected Deaths in Infancy
    • R. R. Robinson, Toronto: Canadian Foundation for the Study of Infant Deaths
    • Emery, J. L., and Carpenter, R. G. (1974), “Pulmonary Mast Cells in Infants and Their Relation to Unexpected Deaths in Infancy,” in Proceedings of the Francis E. Camps International Symposium On Sudden and Unexpected Deaths in Infancy, ed. R. R. Robinson, Toronto: Canadian Foundation for the Study of Infant Deaths, pp. 7–19.
    • (1974) Proceedings of the Francis E. Camps International Symposium on Sudden and Unexpected Deaths in Infancy , pp. 7-19
    • Emery, J.L.1    Carpenter, R.G.2
  • 19
    • 0001982339 scopus 로고
    • Stable Distributions and the Mixtures of Distributions Hypotheses for Common Stock Returns
    • Fielitz, B. D., and Rozelie, J. P. (1983), “Stable Distributions and the Mixtures of Distributions Hypotheses for Common Stock Returns,” Journal of the American Statistical Association, 78, 28–36.
    • (1983) Journal of the American Statistical Association , vol.78 , pp. 28-36
    • Fielitz, B.D.1    Rozelie, J.P.2
  • 20
    • 0000182679 scopus 로고
    • Some Methods for Studying the Mixture of Two Normal (Lognormal) Distributions
    • Fowlkes, E. B. (1979), “Some Methods for Studying the Mixture of Two Normal (Lognormal) Distributions,” Journal of the American Statistical Association, 74, 561–575.
    • (1979) Journal of the American Statistical Association , vol.74 , pp. 561-575
    • Fowlkes, E.B.1
  • 21
    • 0037847280 scopus 로고
    • A Comparison of Some Methods for Estimating Mixed Normal Distributions
    • Fryer, J. G., and Robertson, C. A. (1972), “A Comparison of Some Methods for Estimating Mixed Normal Distributions,” Biometrika, 59, 639–648.
    • (1972) Biometrika , vol.59 , pp. 639-648
    • Fryer, J.G.1    Robertson, C.A.2
  • 22
    • 0000311058 scopus 로고
    • On the Asymptotic Performance of the Log Likelihood Ratio Statistic for the Mixture Model and Related Results
    • L. M. LeCam and R. A. Olshen, Monterey, CA: Wadsworth
    • Ghosh, J. K., and Sen, P. K. (1985), “On the Asymptotic Performance of the Log Likelihood Ratio Statistic for the Mixture Model and Related Results,” in Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (Vol. 2), eds. L. M. LeCam and R. A. Olshen, Monterey, CA: Wadsworth, pp. 789–806.
    • (1985) Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer , vol.2 , pp. 789-806
    • Ghosh, J.K.1    Sen, P.K.2
  • 23
    • 84950634092 scopus 로고    scopus 로고
    • A. (1980), “Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data
    • (with discussion)
    • Good, I. J., and Gaskins, R. A. (1980), “Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data” (with discussion), Journal of the American Statistical Association, 75, 42–73.
    • Journal of the American Statistical Association , vol.75 , pp. 42-73
    • Good, I.J.1    Gaskins, R.2
  • 24
    • 0000139737 scopus 로고
    • Cross-Validation in Density Estimation
    • Hall, P. (1982), “Cross-Validation in Density Estimation,” Biometrika, 69, 383–390.
    • (1982) Biometrika , vol.69 , pp. 383-390
    • Hall, P.1
  • 25
    • 0000881495 scopus 로고
    • A Failure of Likelihood Asymptotics for Normal Mixtures
    • L. M. LeCam and R. A. Olshen, Monterey, CA: Wadsworth
    • Hartigan, J. A. (1985), “A Failure of Likelihood Asymptotics for Normal Mixtures,” in Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (Vol. 2), eds. L. M. LeCam and R. A. Olshen, Monterey, CA: Wadsworth, pp. 807–810.
    • (1985) Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer , vol.2 , pp. 807-810
    • Hartigan, J.A.1
  • 27
    • 0001218902 scopus 로고
    • Computation of the DIP Statistic to Test for Unimodality (Algorithm AS217)
    • Hartigan, P. M. (1985), “Computation of the DIP Statistic to Test for Unimodality (Algorithm AS217),” Applied Statistics, 34, 320–325.
    • (1985) Applied Statistics , vol.34 , pp. 320-325
    • Hartigan, P.M.1
  • 28
    • 0000198785 scopus 로고
    • Estimation of Parameters for a Mixture of Normal Distributions
    • Hasselblad, V. (1966), “Estimation of Parameters for a Mixture of Normal Distributions,” Technometrics, 8, 431–446.
    • (1966) Technometrics , vol.8 , pp. 431-446
    • Hasselblad, V.1
  • 29
    • 84963176093 scopus 로고
    • On MLE of the Parameters of a Mixture of Two Normal Distributions When the Sample Size Is Small
    • Hosmer, D. W. (1973), “On MLE of the Parameters of a Mixture of Two Normal Distributions When the Sample Size Is Small,” Communications in Statistics, 1, 217–227.
    • (1973) Communications in Statistics , vol.1 , pp. 217-227
    • Hosmer, D.W.1
  • 31
    • 0023570352 scopus 로고
    • On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture
    • McLachlan, G. J. (1987), “On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture,” Applied Statistics, 36, 318–324.
    • (1987) Applied Statistics , vol.36 , pp. 318-324
    • McLachlan, G.J.1
  • 33
    • 34250115918 scopus 로고
    • An Examination of Procedures for Determining the Number of Clusters in a Data Set
    • Milligan, G. W., and Cooper, M. C. (1985), “An Examination of Procedures for Determining the Number of Clusters in a Data Set,” Psychometrika, 50, 159–179.
    • (1985) Psychometrika , vol.50 , pp. 159-179
    • Milligan, G.W.1    Cooper, M.C.2
  • 34
    • 0001473437 scopus 로고
    • On Estimation of a Probability Density Function and Mode
    • Parzen, E. (1962), “On Estimation of a Probability Density Function and Mode,” Annals of Mathematical Statistics, 33, 1065–1076.
    • (1962) Annals of Mathematical Statistics , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 35
    • 84950321853 scopus 로고
    • Estimating Mixtures of Normal Distributions and Switching Regressions
    • Quandt, R. E., and Ramsey, J. B. (1978), “Estimating Mixtures of Normal Distributions and Switching Regressions,” Journal of the American Statistical Association, 73, 730–738.
    • (1978) Journal of the American Statistical Association , vol.73 , pp. 730-738
    • Quandt, R.E.1    Ramsey, J.B.2
  • 36
    • 0001642762 scopus 로고
    • A Note on the Aitkin-Rubin Approach to Hypothesis Testing in Mixture Models
    • Ser. B
    • Quinn, B. G., McLachlan, G. J., and Hjort, N. L. (1987), “A Note on the Aitkin-Rubin Approach to Hypothesis Testing in Mixture Models,” Journal of the Royal Statistical Society, Ser. B, 49, 311–314.
    • (1987) Journal of the Royal Statistical Society , vol.49 , pp. 311-314
    • Quinn, B.G.1    McLachlan, G.J.2    Hjort, N.L.3
  • 37
    • 0021404166 scopus 로고
    • Mixture Densities, Maximum Likelihood, and the EM Algorithm
    • Redner, R. A., and Walker, H. F. (1984), “Mixture Densities, Maximum Likelihood, and the EM Algorithm,” SIAM Review, 26, 195–239.
    • (1984) SIAM Review , vol.26 , pp. 195-239
    • Redner, R.A.1    Walker, H.F.2
  • 38
    • 0001529784 scopus 로고
    • Remarks on Some Nonparametric Estimates of a Density Function
    • Rosenblatt, M. (1956), “Remarks on Some Nonparametric Estimates of a Density Function,” Annals of Mathematical Statistics, 27, 832–837.
    • (1956) Annals of Mathematical Statistics , vol.27 , pp. 832-837
    • Rosenblatt, M.1
  • 39
    • 0004718732 scopus 로고
    • Monte Carlo Study of Three Data-Based Nonparametric Probability Density Estimators
    • Scott, D. W., and Factor, L. E. (1981), “Monte Carlo Study of Three Data-Based Nonparametric Probability Density Estimators,” Journal of the American Statistical Association, 76, 9–15.
    • (1981) Journal of the American Statistical Association , vol.76 , pp. 9-15
    • Scott, D.W.1    Factor, L.E.2
  • 42
    • 85042555524 scopus 로고
    • Choosing the Window Width When Estimating a Density
    • Silverman, B. W. (1978a), “Choosing the Window Width When Estimating a Density,” Biometrika, 65, 1–11.
    • (1978) Biometrika , vol.65 , pp. 1-11
    • Silverman, B.W.1
  • 43
    • 0012951472 scopus 로고
    • Density Ratios, Empirical Likelihood, and Cot Death
    • —— (1978b), “Density Ratios, Empirical Likelihood, and Cot Death,” Applied Statistics, 27, 26–33.
    • (1978) Applied Statistics , vol.27 , pp. 26-33
    • Silverman, B.W.1
  • 44
    • 0344763947 scopus 로고
    • Density Estimation for Univariate and Bivariate Data
    • V. Barnett, New York: John Wiley
    • —— (1981a), “Density Estimation for Univariate and Bivariate Data,” in Interpreting Multivariate Data, ed. V. Barnett, New York: John Wiley, pp. 37–53.
    • (1981) Interpreting Multivariate Data , pp. 37-53
    • Silverman, B.W.1
  • 45
    • 0002333325 scopus 로고
    • Using Kernel Density Estimates to Investigate Multimodality
    • Ser. B
    • —— (1981b), “Using Kernel Density Estimates to Investigate Multimodality,” Journal of the Royal Statistical Society, Ser. B, 43, 97–99.
    • (1981) Journal of the Royal Statistical Society , vol.43 , pp. 97-99
    • Silverman, B.W.1
  • 46
    • 0002518214 scopus 로고
    • Some Properties of a Test for Multimodality Based on Kernel Density Estimates
    • J. F. C. Kingman and G. E. H. Reuter, Cambridge, U.K.: Cambridge University Press
    • —— (1983), “Some Properties of a Test for Multimodality Based on Kernel Density Estimates,” in Probability, Statistics, and Analysis, eds. J. F. C. Kingman and G. E. H. Reuter, Cambridge, U.K.: Cambridge University Press, pp. 248–259.
    • (1983) Probability, Statistics, and Analysis , pp. 248-259
    • Silverman, B.W.1
  • 47
    • 0000997747 scopus 로고
    • Spline Smoothing: The Equivalent Variable Method
    • —— (1984), “Spline Smoothing: The Equivalent Variable Method,” The Annals of Statistics, 12, 898–916.
    • (1984) The Annals of Statistics , vol.12 , pp. 898-916
    • Silverman, B.W.1
  • 50
    • 0001048793 scopus 로고
    • An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates
    • Stone, C. J. (1984), “An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates,” The Annals of Statistics, 12, 1285–1297.
    • (1984) The Annals of Statistics , vol.12 , pp. 1285-1297
    • Stone, C.J.1
  • 52
    • 0004677025 scopus 로고
    • The Estimation of Quality-Adjusted Rates of Return in Stamp Auctions
    • Taylor, W. M. (1983), “The Estimation of Quality-Adjusted Rates of Return in Stamp Auctions,” The Journal of Finance, 38, 1095–1110.
    • (1983) The Journal of Finance , vol.38 , pp. 1095-1110
    • Taylor, W.M.1
  • 54
    • 0015376605 scopus 로고
    • Nonparametric Probability Density Estimation (Part 1)
    • Wegman, E. J. (1972a), “Nonparametric Probability Density Estimation” (Part 1), Technometrics, 14, 533–546.
    • (1972) Technometrics , vol.14 , pp. 533-546
    • Wegman, E.J.1
  • 58
    • 0001690678 scopus 로고
    • Add a New Dimension to Your Philately
    • —— (1983b), “Add a New Dimension to Your Philately,” The American Philatelist, 97, 342–349.
    • (1983) The American Philatelist , vol.97 , pp. 342-349
    • Wilson, I.G.1
  • 59
    • 84950436400 scopus 로고
    • How Thick Is ‘Thick’? How Thin Is ‘Thin’?
    • —— (1984), “How Thick Is ‘Thick’? How Thin Is ‘Thin’?” The American Philatelist, 98, 442–452.
    • (1984) The American Philatelist , vol.98 , pp. 442-452
    • Wilson, I.G.1
  • 60
    • 0012393308 scopus 로고
    • Pattern Clustering by Multivariate Mixture Analysis
    • Wolfe, J. H. (1970), “Pattern Clustering by Multivariate Mixture Analysis,” Multivariate Behavioral Research, 5, 329–350.
    • (1970) Multivariate Behavioral Research , vol.5 , pp. 329-350
    • Wolfe, J.H.1
  • 61
    • 0004776832 scopus 로고
    • A Bootstrap Testing Procedure for Investigating the Number of Subpopulations
    • Wong, M. A. (1985), “A Bootstrap Testing Procedure for Investigating the Number of Subpopulations,” Journal of Statistical Computation and Simulation, 22, 99–112.
    • (1985) Journal of Statistical Computation and Simulation , vol.22 , pp. 99-112
    • Wong, M.A.1
  • 64
    • 0023524748 scopus 로고
    • Noise, Histogram and Cluster Validity for Gaussian-Mixture Data
    • Yarman-Vural, F., and Ataman, E. (1987), “Noise, Histogram and Cluster Validity for Gaussian-Mixture Data,” Pattern Recognition, 20, 385–401.
    • (1987) Pattern Recognition , vol.20 , pp. 385-401
    • Yarman-Vural, F.1    Ataman, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.