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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.

Ayrıntılar

Konular Sosyal, İşletme
Diğer ID JA37MA46HA
Bölüm Makaleler
Yazarlar

Jeroen HİNLOOPEN Bu kişi benim


Rien J.lm. WAGENVOORT Bu kişi benim


Charles Van MARREWİJK Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2012
Yayınlandığı Sayı Yıl 2012, Cilt 4, Sayı 1

Kaynak Göster

Bibtex @ { ier278018, journal = {International Econometric Review}, issn = {1308-8793}, eissn = {1308-8815}, address = {Şairler Sokak, No:32/C, Gaziosmanpaşa, Ankara}, publisher = {Ekonometrik Araştırmalar Derneği}, year = {2012}, volume = {4}, pages = {17 - 39}, doi = {}, title = {A k-sample homogeneity test: the Harmonic Weighted Mass index}, key = {cite}, author = {Hinloopen, Jeroen and Wagenvoort, Rien J.lm. and Marrewijk, Charles Van} }
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 . Retrieved from https://dergipark.org.tr/tr/pub/ier/issue/26392/278018
MLA Hinloopen, J. , Wagenvoort, R. J. , Marrewijk, C. V. "A k-sample homogeneity test: the Harmonic Weighted Mass index" . International Econometric Review 4 (2012 ): 17-39 <https://dergipark.org.tr/tr/pub/ier/issue/26392/278018>
Chicago Hinloopen, J. , Wagenvoort, R. J. , Marrewijk, C. V. "A k-sample homogeneity test: the Harmonic Weighted Mass index". International Econometric Review 4 (2012 ): 17-39
RIS TY - JOUR T1 - A k-sample homogeneity test: the Harmonic Weighted Mass index AU - Jeroen Hinloopen , Rien J.lm. Wagenvoort , Charles Van Marrewijk Y1 - 2012 PY - 2012 N1 - DO - T2 - International Econometric Review JF - Journal JO - JOR SP - 17 EP - 39 VL - 4 IS - 1 SN - 1308-8793-1308-8815 M3 - UR - Y2 - 2021 ER -
EndNote %0 International Econometric Review A k-sample homogeneity test: the Harmonic Weighted Mass index %A Jeroen Hinloopen , Rien J.lm. Wagenvoort , Charles Van Marrewijk %T A k-sample homogeneity test: the Harmonic Weighted Mass index %D 2012 %J International Econometric Review %P 1308-8793-1308-8815 %V 4 %N 1 %R %U
ISNAD Hinloopen, Jeroen , Wagenvoort, Rien J.lm. , Marrewijk, Charles Van . "A k-sample homogeneity test: the Harmonic Weighted Mass index". International Econometric Review 4 / 1 (Nisan 2012): 17-39 .
AMA Hinloopen J. , Wagenvoort R. J. , Marrewijk C. V. A k-sample homogeneity test: the Harmonic Weighted Mass index. IER. 2012; 4(1): 17-39.
Vancouver Hinloopen J. , Wagenvoort R. J. , Marrewijk C. V. A k-sample homogeneity test: the Harmonic Weighted Mass index. International Econometric Review. 2012; 4(1): 17-39.
IEEE J. Hinloopen , R. J. Wagenvoort ve C. V. Marrewijk , "A k-sample homogeneity test: the Harmonic Weighted Mass index", International Econometric Review, c. 4, sayı. 1, ss. 17-39, Nis. 2012