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Volumn 22, Issue 4, 2012, Pages 867-881

Nonparametric statistical analysis for multiple comparison of machine learning regression algorithms

Author keywords

Machine learning; Multiple comparison tests; Neural networks; Nonparametric statistical tests; Statistical regression

Indexed keywords

MULTIPLE COMPARISON; MULTIPLE COMPARISON TEST; NON-PARAMETRIC STATISTICAL ANALYSIS; NON-PARAMETRIC STATISTICAL TESTS; REGRESSION ALGORITHMS; REGRESSION PROBLEM; STATISTICAL REGRESSION; WILCOXON TEST;

EID: 84874613361     PISSN: None     EISSN: 1641876X     Source Type: Journal    
DOI: 10.2478/v10006-012-0064-z     Document Type: Article
Times cited : (146)

References (65)
  • 4
    • 0000196110 scopus 로고
    • Distribution of the kurtosis statistic b2 for normal samples
    • Anscombe, F. and Glynn, W. (1983). Distribution of the kurtosis statistic b2 for normal samples, Biometrika 70(1): 227-234.
    • (1983) Biometrika , vol.70 , Issue.1 , pp. 227-234
    • Anscombe, F.1    Glynn, W.2
  • 5
    • 80053917912 scopus 로고    scopus 로고
    • Hybrid classification ensemble using topology-preserving clustering
    • Baruque, B., Porras, S. and Corchado, E. (2011). Hybrid classification ensemble using topology-preserving clustering, New Generation Computing 29(3): 329-344.
    • (2011) New Generation Computing , vol.29 , Issue.3 , pp. 329-344
    • Baruque, B.1    Porras, S.2    Corchado, E.3
  • 6
    • 0009038905 scopus 로고
    • Improvements of general multiple test procedures for redundant systems of hypotheses
    • in P. Bauer, G. Hommel and E. Sonnemann (Eds.), Springer-Verlag, Berlin
    • Bergmann, G. and Hommel, G. (1988). Improvements of general multiple test procedures for redundant systems of hypotheses, in P. Bauer, G. Hommel and E. Sonnemann (Eds.), Multiple Hypotheses Testing, Springer-Verlag, Berlin, pp. 100-115.
    • (1988) Multiple Hypotheses Testing , pp. 100-115
    • Bergmann, G.1    Hommel, G.2
  • 7
    • 0000621802 scopus 로고    scopus 로고
    • Multivariable functional interpolation and adaptive networks
    • Broomhead, D. and Lowe, D. (1998). Multivariable functional interpolation and adaptive networks, Complex Systems 11: 321-355.
    • (1998) Complex Systems , vol.11 , pp. 321-355
    • Broomhead, D.1    Lowe, D.2
  • 8
    • 79953202198 scopus 로고    scopus 로고
    • Application of agent-based simulated annealing and tabu search procedures to solving the data reduction problem
    • DOI 102478/v10006-011-0004-0013
    • Czarnowski, I. and Jedrzejowicz, P. (2011). Application of agent-based simulated annealing and tabu search procedures to solving the data reduction problem, International Journal of Applied Mathematics and Computer Science 21(1): 57-68, DOI: 10.2478/v10006-011-0004-3.
    • (2011) International Journal of Applied Mathematics and Computer Science , vol.21 , Issue.1 , pp. 57-68
    • Czarnowski, I.1    Jedrzejowicz, P.2
  • 9
    • 0000103806 scopus 로고
    • Transformation to normality of the null distribution of g1
    • D'Agostino, R. (1970). Transformation to normality of the null distribution of g1, Biometrika 57(3): 679-681.
    • (1970) Biometrika , vol.57 , Issue.3 , pp. 679-681
    • D'Agostino, R.1
  • 10
    • 84952503973 scopus 로고
    • A suggestion for using powerful and informative tests of normality
    • D'Agostino, R., Belanger, A. and D'Agostino Jr., R. (1990). A suggestion for using powerful and informative tests of normality, The American Statistician 44(4): 316-321.
    • (1990) The American Statistician , vol.44 , Issue.4 , pp. 316-321
    • D'Agostino, R.1    Belanger, A.2    D'Agostino Jr., R.3
  • 11
    • 29644438050 scopus 로고    scopus 로고
    • Statistical comparisons of classifiers over multiple data sets
    • Demšar, J. (2006). Statistical comparisons of classifiers over multiple data sets, Journal of Machine Learning Research 7: 1-30.
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 1-30
    • Demšar, J.1
  • 12
    • 79960535211 scopus 로고    scopus 로고
    • A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms
    • Derrac, J., García, S., Molina, D. and Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms, Swarm and Evolutionary Computation 1: 3-18.
    • (2011) Swarm and Evolutionary Computation , vol.1 , pp. 3-18
    • Derrac, J.1    García, S.2    Molina, D.3    Herrera, F.4
  • 14
    • 21144459575 scopus 로고
    • On a monotonicity problem in step-down multiple test procedures
    • Finner, H. (1993). On a monotonicity problem in step-down multiple test procedures, Journal of the American Statistical Association 88(423): 920-923.
    • (1993) Journal of the American Statistical Association , vol.88 , Issue.423 , pp. 920-923
    • Finner, H.1
  • 15
    • 84944811700 scopus 로고
    • The use of ranks to avoid the assumption of normality implicit in the analysis of variance
    • Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance, Journal of the American Statistical Association 32(200): 675-701.
    • (1937) Journal of the American Statistical Association , vol.32 , Issue.200 , pp. 675-701
    • Friedman, M.1
  • 16
    • 64549120231 scopus 로고    scopus 로고
    • A study of statistical techniques and performance measures for genetics-based machine learning: Accuracy and interpretability
    • García, S., Fernández, A., Luengo, J. and Herrera, F. (2009). A study of statistical techniques and performance measures for genetics-based machine learning: Accuracy and interpretability, Soft Computing 10(13): 959-977.
    • (2009) Soft Computing , vol.10 , Issue.13 , pp. 959-977
    • García, S.1    Fernández, A.2    Luengo, J.3    Herrera, F.4
  • 17
    • 77549084648 scopus 로고    scopus 로고
    • Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power
    • García, S., Fernández, A. and Luengo, J.and Herrera, F. (2010). Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power, Information Sciences 180: 2044-2064.
    • (2010) Information Sciences , vol.180 , pp. 2044-2064
    • García, S.1    Fernández, A.2    Luengo, J.3    Herrera, F.4
  • 18
    • 58149287952 scopus 로고    scopus 로고
    • An extension on "Statistical comparisons of classifiers over multiple data sets" for all pairwise comparisons
    • García, S. and Herrera, F. (2008). An extension on "Statistical comparisons of classifiers over multiple data sets" for all pairwise comparisons, Journal of Machine Learning Research 9: 2677-2694.
    • (2008) Journal of Machine Learning Research , vol.9 , pp. 2677-2694
    • García, S.1    Herrera, F.2
  • 19
    • 78449246613 scopus 로고    scopus 로고
    • Nonparametric statistical analysis of machine learning algorithms for regression problems
    • in R. Setchi, I. Jordanov, R.J. Howlett and L.C. Jain (Eds.), Lecture Notes in Artificial Intelligence, Springer, Heidelberg
    • Graczyk, M., Lasota, T., Telec, Z. and Trawi'nski, B. (2010). Nonparametric statistical analysis of machine learning algorithms for regression problems, in R. Setchi, I. Jordanov, R.J. Howlett and L.C. Jain (Eds.), KES 2010, Lecture Notes in Artificial Intelligence, Vol. 6276, Springer, Heidelberg, pp. 111-120.
    • (2010) KES 2010 , vol.6276 , pp. 111-120
    • Graczyk, M.1    Lasota, T.2    Telec, Z.3    Trawi'nski, B.4
  • 20
    • 70450213781 scopus 로고    scopus 로고
    • Comparative analysis of premises valuation models using KEEL, RapidMiner, and WEKA
    • in N.T. Nguyen, R. Kowalczyk and S.-M. Chen (Eds.), Lecture Notes in Artificial Intelligence, Springer, Heidelberg
    • Graczyk, M., Lasota, T. and Trawi'nski, B. (2009). Comparative analysis of premises valuation models using KEEL, RapidMiner, and WEKA, in N.T. Nguyen, R. Kowalczyk and S.-M. Chen (Eds.), ICCCI 2009, Lecture Notes in Artificial Intelligence, Vol. 5796, Springer, Heidelberg, pp. 800-812.
    • (2009) ICCCI 2009 , vol.5796 , pp. 800-812
    • Graczyk, M.1    Lasota, T.2    Trawi'nski, B.3
  • 22
    • 33645762226 scopus 로고
    • A Sharper Bonferroni procedure for multiple tests of significance
    • Hochberg, Y. (1988). A Sharper Bonferroni procedure for multiple tests of significance, Biometrika 75(4): 800-802.
    • (1988) Biometrika , vol.75 , Issue.4 , pp. 800-802
    • Hochberg, Y.1
  • 23
    • 0001589146 scopus 로고
    • Ranks methods for combination of independent experiments in analysis of variance
    • Hodges, J. and Lehmann, E. (1962). Ranks methods for combination of independent experiments in analysis of variance, Annals of Mathematical Statistics 33: 482-497.
    • (1962) Annals of Mathematical Statistics , vol.33 , pp. 482-497
    • Hodges, J.1    Lehmann, E.2
  • 24
    • 0022965475 scopus 로고
    • An improved sequentially rejective Bonferroni test procedure
    • Holland, B. and Copenhaver, M. (1987). An improved sequentially rejective Bonferroni test procedure, Biometrics 43(2): 417-423.
    • (1987) Biometrics , vol.43 , Issue.2 , pp. 417-423
    • Holland, B.1    Copenhaver, M.2
  • 25
    • 0002294347 scopus 로고
    • A simple sequentially rejective multiple test procedure
    • Holm, S. (1979). A simple sequentially rejective multiple test procedure, Scandinavian Journal of Statistics 6: 65-70.
    • (1979) Scandinavian Journal of Statistics , vol.6 , pp. 65-70
    • Holm, S.1
  • 26
    • 0001669952 scopus 로고
    • A stagewise rejective multiple test procedure based on a modified Bonferroni test
    • Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test, Biometrika 75(2): 383-386.
    • (1988) Biometrika , vol.75 , Issue.2 , pp. 383-386
    • Hommel, G.1
  • 27
    • 0028449404 scopus 로고
    • A rapid algorithm and a computer program for multiple test procedures using procedures using logical structures of hypotheses
    • Hommel, G.and Bernhard, G. (1994). A rapid algorithm and a computer program for multiple test procedures using procedures using logical structures of hypotheses, Computer Methods and Programs in Biomedicine 43: 213-216.
    • (1994) Computer Methods and Programs in Biomedicine , vol.43 , pp. 213-216
    • Hommel, G.1    Bernhard, G.2
  • 28
    • 0037238922 scopus 로고    scopus 로고
    • Empirical evaluation of the improved RPROP learning algorithm
    • Igel, C. and Hüsken, M. (2003). Empirical evaluation of the improved RPROP learning algorithm, Neurocomputing 50: 105-123.
    • (2003) Neurocomputing , vol.50 , pp. 105-123
    • Igel, C.1    Hüsken, M.2
  • 29
    • 0001750957 scopus 로고
    • Approximations of the critical region of the Friedman statistic
    • Iman, R. and Davenport, J. (1980). Approximations of the critical region of the Friedman statistic, Communications in Statistics 18: 571-595.
    • (1980) Communications in Statistics , vol.18 , pp. 571-595
    • Iman, R.1    Davenport, J.2
  • 30
    • 77951774214 scopus 로고    scopus 로고
    • Method of classifier selection using the genetic approach
    • Jackowski, K. and Wózniak, M. (2010). Method of classifier selection using the genetic approach, Expert Systems 27(2): 114-128.
    • (2010) Expert Systems , vol.27 , Issue.2 , pp. 114-128
    • Jackowski, K.1    Wózniak, M.2
  • 31
    • 0002437730 scopus 로고
    • A test for normality of observations and regression residuals
    • Jarque, C. and Bera, A. (1987). A test for normality of observations and regression residuals, International Statistical Review 55(2): 163-172.
    • (1987) International Statistical Review , vol.55 , Issue.2 , pp. 163-172
    • Jarque, C.1    Bera, A.2
  • 32
    • 80053921821 scopus 로고    scopus 로고
    • Boosting-based sequential output prediction
    • Kajdanowicz, T. and Kazienko, P. (2011). Boosting-based sequential output prediction, New Generation Computing 29(3): 293-307.
    • (2011) New Generation Computing , vol.29 , Issue.3 , pp. 293-307
    • Kajdanowicz, T.1    Kazienko, P.2
  • 33
    • 80052133092 scopus 로고    scopus 로고
    • Comparison of several univariate normality tests regarding type I error rate and power of the test in simulation based small samples
    • Keskin, S. (2006). Comparison of several univariate normality tests regarding type I error rate and power of the test in simulation based small samples, Journal of Applied Science Research 2(5): 296-300.
    • (2006) Journal of Applied Science Research , vol.2 , Issue.5 , pp. 296-300
    • Keskin, S.1
  • 35
    • 70450212253 scopus 로고    scopus 로고
    • Comparative analysis of evolutionary fuzzy models for premises valuation using KEEL
    • in N.T. Nguyen, R. Kowalczyk and S.-M. Chen (Eds.), Lecture Notes in Artificial Intelligence, Springer, Heidelberg
    • Krzystanek, M., Lasota, T. and Trawi'nski, B. (2009). Comparative analysis of evolutionary fuzzy models for premises valuation using KEEL, in N.T. Nguyen, R. Kowalczyk and S.-M. Chen (Eds.), ICCCI 2009, Lecture Notes in Artificial Intelligence, Vol. 5796, Springer, Heidelberg, pp. 838-849.
    • (2009) ICCCI 2009 , vol.5796 , pp. 838-849
    • Krzystanek, M.1    Lasota, T.2    Trawi'nski, B.3
  • 38
    • 39449085826 scopus 로고    scopus 로고
    • A two-step rejection procedure for testing multiple hypotheses
    • Li, J. (2008). A two-step rejection procedure for testing multiple hypotheses, Journal of Statistical Planning and Inference 138(6): 1521-1527.
    • (2008) Journal of Statistical Planning and Inference , vol.138 , Issue.6 , pp. 1521-1527
    • Li, J.1
  • 39
    • 34247990255 scopus 로고
    • On the Kolmogorov-Smirnov test for normality with mean and variance unknown
    • Lilliefors, H. (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown, Journal of the American Statistical Association 62(318): 399-402.
    • (1967) Journal of the American Statistical Association , vol.62 , Issue.318 , pp. 399-402
    • Lilliefors, H.1
  • 40
    • 60249094201 scopus 로고    scopus 로고
    • A study on the use of statistical tests for experimentation with neural networks: Analysis of parametric test conditions and non-parametric tests
    • Luengo, J., García, S. and Herrera, F. (2009). A study on the use of statistical tests for experimentation with neural networks: Analysis of parametric test conditions and non-parametric tests, Expert Systems with Applications 36: 7798-7808.
    • (2009) Expert Systems with Applications , vol.36 , pp. 7798-7808
    • Luengo, J.1    García, S.2    Herrera, F.3
  • 41
    • 80052930921 scopus 로고    scopus 로고
    • On employing fuzzy modeling algorithms for the valuation of residential premises
    • Lughofer, E., Trawínski, B., Trawínski, K., Kempa, O. and Lasota, T. (2011). On employing fuzzy modeling algorithms for the valuation of residential premises, Information Sciences 181: 5123-5142.
    • (2011) Information Sciences , vol.181 , pp. 5123-5142
    • Lughofer, E.1    Trawínski, B.2    Trawínski, K.3    Kempa, O.4    Lasota, T.5
  • 42
    • 0027205884 scopus 로고
    • A scaled conjugate gradient algorithm for fast supervised learning
    • Moller, F. (1990). A scaled conjugate gradient algorithm for fast supervised learning, Neural Networks 6: 525-533.
    • (1990) Neural Networks , vol.6 , pp. 525-533
    • Moller, F.1
  • 45
    • 0006354851 scopus 로고
    • Karl Pearson and the chi-squared test
    • Plackett, R. (1983). Karl Pearson and the chi-squared test, International Statistical Review 51(1): 59-72.
    • (1983) International Statistical Review , vol.51 , Issue.1 , pp. 59-72
    • Plackett, R.1
  • 46
    • 0001071040 scopus 로고
    • A resource allocating network for function interpolation
    • Plat, J. (1991). A resource allocating network for function interpolation, Neural Computation 3(2): 213-225.
    • (1991) Neural Computation , vol.3 , Issue.2 , pp. 213-225
    • Plat, J.1
  • 47
    • 0001308639 scopus 로고
    • Using weighted rankings in the analysis of complete blocks with additive block effects
    • Quade, D. (1979). Using weighted rankings in the analysis of complete blocks with additive block effects, Journal of the American Statistical Association 74: 680-683.
    • (1979) Journal of the American Statistical Association , vol.74 , pp. 680-683
    • Quade, D.1
  • 48
    • 77951180564 scopus 로고    scopus 로고
    • An empirical power comparison of univariate goodness-of-fit tests for normality
    • Romão, X., Delgado, R. and Costa, A. (2010). An empirical power comparison of univariate goodness-of-fit tests for normality, Journal of Statistical Computation and Simulation 80(5): 545-591.
    • (2010) Journal of Statistical Computation and Simulation , vol.80 , Issue.5 , pp. 545-591
    • Romão, X.1    Delgado, R.2    Costa, A.3
  • 49
    • 0001618721 scopus 로고
    • A sequentially rejective test procedure based on a modified Bonferroni inequality
    • Rom, D. (1990). A sequentially rejective test procedure based on a modified Bonferroni inequality, Biometrika 77(3): 663-665.
    • (1990) Biometrika , vol.77 , Issue.3 , pp. 663-665
    • Rom, D.1
  • 50
    • 0027412562 scopus 로고
    • A pocket-calculator algorithm for the Shapiro-Francia test for non-normality: An application to medicine
    • Royston, P. (1993). A pocket-calculator algorithm for the Shapiro-Francia test for non-normality: An application to medicine, Statistics in Medicine 12(2): 181-184.
    • (1993) Statistics in Medicine , vol.12 , Issue.2 , pp. 181-184
    • Royston, P.1
  • 51
    • 27144463192 scopus 로고    scopus 로고
    • On comparing classifiers: Pitfalls to avoid and a recommended approach
    • Salzberg, S. (1997). On comparing classifiers: Pitfalls to avoid and a recommended approach, Data Mining and Knowledge Discovery 1: 317-327.
    • (1997) Data Mining and Knowledge Discovery , vol.1 , pp. 317-327
    • Salzberg, S.1
  • 52
    • 84890829458 scopus 로고
    • Modified sequentially rejective multiple test procedures
    • Shaffer, J. (1986). Modified sequentially rejective multiple test procedures, Journal of the American Statistical Association 81(395): 826-831.
    • (1986) Journal of the American Statistical Association , vol.81 , Issue.395 , pp. 826-831
    • Shaffer, J.1
  • 53
    • 0000898845 scopus 로고
    • An analysis of variance test for normality (complete samples)
    • Shapiro, S. and Wilk, M. (1965). An analysis of variance test for normality (complete samples), Biometrika 52(3/4): 591-611.
    • (1965) Biometrika , vol.52 , Issue.3-4 , pp. 591-611
    • Shapiro, S.1    Wilk, M.2
  • 55
    • 79957885701 scopus 로고    scopus 로고
    • Investigation of genetic algorithms with self-adaptive crossover mutation and selection
    • In E. Corchado M. Kurzy'nski And M. Wo'zniak (Eds.), Lecture Notes in Artificial Intelligence, Springer, Heidelberg
    • Smetek, M. and Trawi'nski, B. (2011). Investigation of genetic algorithms with self-adaptive crossover, mutation, and selection, in E. Corchado, M. Kurzy'nski and M. Wo'zniak (Eds.), HAIS 2011, Lecture Notes in Artificial Intelligence, Vol. 6678, Springer, Heidelberg, pp. 116-123.
    • (2011) HAIS 2011 , vol.6678 , pp. 116-123
    • Smetek, M.1    Trawi'nski, B.2
  • 60
    • 77950190340 scopus 로고    scopus 로고
    • Self-adaptation of parameters in a learning classifier system ensemble machine
    • DOI 102478/v10006-010-0012-0018
    • Tróc, M. and Unold, O. (2010). Self-adaptation of parameters in a learning classifier system ensemble machine, International Journal of Applied Mathematics and Computer Science 20(1): 157-174, DOI: 10.2478/v10006-010-0012-8.
    • (2010) International Journal of Applied Mathematics and Computer Science , vol.20 , Issue.1 , pp. 157-174
    • Tróc, M.1    Unold, O.2
  • 61
    • 0001884644 scopus 로고
    • Individual comparisons by ranking methods
    • Wilcoxon, F. (1945). Individual comparisons by ranking methods, Biometrics 1: 80-83.
    • (1945) Biometrics , vol.1 , pp. 80-83
    • Wilcoxon, F.1
  • 62
    • 0027057407 scopus 로고
    • Adjusted p-values for simultaneous inference
    • Wright, S. (1992). Adjusted p-values for simultaneous inference, Biometrics 48: 1005-1013.
    • (1992) Biometrics , vol.48 , pp. 1005-1013
    • Wright, S.1
  • 64
    • 80053918498 scopus 로고    scopus 로고
    • Classification performance of bagging and boosting type ensemble methods with small training sets
    • Zaman, M. and Hirose, H. (2011). Classification performance of bagging and boosting type ensemble methods with small training sets, New Generation Computing 29(3): 277-292.
    • (2011) New Generation Computing , vol.29 , Issue.3 , pp. 277-292
    • Zaman, M.1    Hirose, H.2
  • 65
    • 0004232308 scopus 로고    scopus 로고
    • 5th Edn., Prentice Hall, Upper Saddle River, NJ
    • Zar, J. (2009). Biostatistical Analysis, 5th Edn., Prentice Hall, Upper Saddle River, NJ.
    • (2009) Biostatistical Analysis
    • Zar, J.1


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