BibTex RIS Kaynak Göster

A k-sample homogeneity test: the Harmonic Weighted Mass index

Yıl 2012, Cilt: 4 Sayı: 1, 17 - 39, 01.04.2012

Öz

We propose a quantification of the p-p plot that assigns equal weight to all distances between the respective distributions: the surface between the p-p plot and the diagonal. This surface is labelled the Harmonic Weighted Mass (HWM) index. We introduce the diagonal-deviation (d-d) plot that allows the index to be computed exactly under all circumstances. This two-dimensional d-d plot accommodates a straightforward extension to the k-sample HWM index, with k > 2. A Monte Carlo simulation based on an example involving long-term sovereign credit ratings illustrates the power of the HWM test.

Kaynakça

  • Anderson, T.W. and D.A. Darling (1952). Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193-212.
  • Cramér, H. (1928). On the composition of elementary errors II: statistical applications. Skandinavisk Aktuarietidskrift, 11, 141-180.
  • Dufour, J.M. (1995). Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics in econometrics. Technical report C.R.D.E., Université de Montreal.
  • Dufour, J.M. and J.F. Kiviet (1998). Exact inference methods for first-order autoregressive distributed lags models. Econometrica, 66, 79-104.
  • Fisz, M. (1960). On a result by M. Rosenblatt concerning the von Mises-Smirnov test. Annals of Mathematical Statistics, 31, 427-429.
  • Girling, A.J. (2000). Rank statistics expressible as integrals under PP- plots and receiver operating characteristics curves. Journal of the Royal Statistical Society B, 62, 367-382.
  • Hinloopen, J. (1997). Research and development, product differentiation, and robust estimation. Ph.D.-thesis, European University Institute.
  • Hinloopen, J. and R.J.L.M. Wagenvoort (2010). Identifying All Distinct Sample P-P Plots, with an Application to the exact Finite Sample Distribution of the L–FCvM Test Statistic. Tinbergen Institute Discussion Paper, TI 2010-083/1.
  • Holmgren, E.B. (1995). The p-p plot as a method of comparing treatment effects. Journal of the American Statistical Society, 90, 360-365.
  • IMF (2011). International Financial Statistics. http://www.imf.org (accessed March 31, 2012).
  • Johnson, B.McK. and T. Killeen (1983). An explicit formula for the C.D.F. of the L1 norm of the Brownian bridge. The Annals of Probability, 11, 807-808.
  • Kiefer, J. (1959). K-sample analogues of the Kolmogorov-Smirnov and Cramer-v.Mises tests. Annals of Mathematical Statistics, 30, 420-447.
  • Kolmogorov, A.N. (1933). Sulla determinizazione empirica delle leggi di probabilita. Giornale dell ’Istituto Italiano Attuari, 4, 1-11.
  • Kuiper, N.H. (1960). Tests concerning random points on a circle. Koninklijke Nederlandse Akademie van Wetenschappen, The Netherlands.
  • Rosenblatt, M. (1952). Limit theorems associated with variants of the von Mises statistic. Annals of Mathematical Statistics, 23, 617-623.
  • Scholz, F.W. and M.A. Stephens (1987). K-sample Anderson-Darling tests. Journal of the American Statistical Association, 82, 918-924.
  • Schmidt, F. and M. Trede (1995). A distribution free test for the two sample problem for general alternatives. Computational Statistics & Data Analysis, 20, 409-419.
  • Smirnov, N.V. (1939). On the deviation of the empirical distribution function. Mathematicheskii Sbornik, 6, 3-26.
  • Von Mises, R. (1931). Wahrscheinlichkeitsrechnung. Vienna: Deuticke.
  • Wilk, M.B. and R. Gnanadesikan (1968). Probability plotting methods for the analysis of data. Biometrika, 55, 1-17.
Yıl 2012, Cilt: 4 Sayı: 1, 17 - 39, 01.04.2012

Öz

Kaynakça

  • Anderson, T.W. and D.A. Darling (1952). Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193-212.
  • Cramér, H. (1928). On the composition of elementary errors II: statistical applications. Skandinavisk Aktuarietidskrift, 11, 141-180.
  • Dufour, J.M. (1995). Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics in econometrics. Technical report C.R.D.E., Université de Montreal.
  • Dufour, J.M. and J.F. Kiviet (1998). Exact inference methods for first-order autoregressive distributed lags models. Econometrica, 66, 79-104.
  • Fisz, M. (1960). On a result by M. Rosenblatt concerning the von Mises-Smirnov test. Annals of Mathematical Statistics, 31, 427-429.
  • Girling, A.J. (2000). Rank statistics expressible as integrals under PP- plots and receiver operating characteristics curves. Journal of the Royal Statistical Society B, 62, 367-382.
  • Hinloopen, J. (1997). Research and development, product differentiation, and robust estimation. Ph.D.-thesis, European University Institute.
  • Hinloopen, J. and R.J.L.M. Wagenvoort (2010). Identifying All Distinct Sample P-P Plots, with an Application to the exact Finite Sample Distribution of the L–FCvM Test Statistic. Tinbergen Institute Discussion Paper, TI 2010-083/1.
  • Holmgren, E.B. (1995). The p-p plot as a method of comparing treatment effects. Journal of the American Statistical Society, 90, 360-365.
  • IMF (2011). International Financial Statistics. http://www.imf.org (accessed March 31, 2012).
  • Johnson, B.McK. and T. Killeen (1983). An explicit formula for the C.D.F. of the L1 norm of the Brownian bridge. The Annals of Probability, 11, 807-808.
  • Kiefer, J. (1959). K-sample analogues of the Kolmogorov-Smirnov and Cramer-v.Mises tests. Annals of Mathematical Statistics, 30, 420-447.
  • Kolmogorov, A.N. (1933). Sulla determinizazione empirica delle leggi di probabilita. Giornale dell ’Istituto Italiano Attuari, 4, 1-11.
  • Kuiper, N.H. (1960). Tests concerning random points on a circle. Koninklijke Nederlandse Akademie van Wetenschappen, The Netherlands.
  • Rosenblatt, M. (1952). Limit theorems associated with variants of the von Mises statistic. Annals of Mathematical Statistics, 23, 617-623.
  • Scholz, F.W. and M.A. Stephens (1987). K-sample Anderson-Darling tests. Journal of the American Statistical Association, 82, 918-924.
  • Schmidt, F. and M. Trede (1995). A distribution free test for the two sample problem for general alternatives. Computational Statistics & Data Analysis, 20, 409-419.
  • Smirnov, N.V. (1939). On the deviation of the empirical distribution function. Mathematicheskii Sbornik, 6, 3-26.
  • Von Mises, R. (1931). Wahrscheinlichkeitsrechnung. Vienna: Deuticke.
  • Wilk, M.B. and R. Gnanadesikan (1968). Probability plotting methods for the analysis of data. Biometrika, 55, 1-17.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Konular İşletme
Diğer ID JA37MA46HA
Bölüm Makaleler
Yazarlar

Jeroen Hinloopen Bu kişi benim

Rien J.lm. Wagenvoort Bu kişi benim

Charles Van Marrewijk Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2012
Gönderilme Tarihi 1 Nisan 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 4 Sayı: 1

Kaynak Göster

APA Hinloopen, J., Wagenvoort, R. J., & Marrewijk, C. V. (2012). A k-sample homogeneity test: the Harmonic Weighted Mass index. International Econometric Review, 4(1), 17-39.
AMA Hinloopen J, Wagenvoort RJ, Marrewijk CV. A k-sample homogeneity test: the Harmonic Weighted Mass index. IER. Haziran 2012;4(1):17-39.
Chicago Hinloopen, Jeroen, Rien J.lm. Wagenvoort, ve Charles Van Marrewijk. “A K-Sample Homogeneity Test: The Harmonic Weighted Mass Index”. International Econometric Review 4, sy. 1 (Haziran 2012): 17-39.
EndNote Hinloopen J, Wagenvoort RJ, Marrewijk CV (01 Haziran 2012) A k-sample homogeneity test: the Harmonic Weighted Mass index. International Econometric Review 4 1 17–39.
IEEE J. Hinloopen, R. J. Wagenvoort, ve C. V. Marrewijk, “A k-sample homogeneity test: the Harmonic Weighted Mass index”, IER, c. 4, sy. 1, ss. 17–39, 2012.
ISNAD Hinloopen, Jeroen vd. “A K-Sample Homogeneity Test: The Harmonic Weighted Mass Index”. International Econometric Review 4/1 (Haziran 2012), 17-39.
JAMA Hinloopen J, Wagenvoort RJ, Marrewijk CV. A k-sample homogeneity test: the Harmonic Weighted Mass index. IER. 2012;4:17–39.
MLA Hinloopen, Jeroen vd. “A K-Sample Homogeneity Test: The Harmonic Weighted Mass Index”. International Econometric Review, c. 4, sy. 1, 2012, ss. 17-39.
Vancouver Hinloopen J, Wagenvoort RJ, Marrewijk CV. A k-sample homogeneity test: the Harmonic Weighted Mass index. IER. 2012;4(1):17-39.