Fuzzy Statistical Analysis of Multiple Regression with Crisp and Fuzzy Covariates and Applications in Analyzing Economic Data of China

This paper extends the simple fuzzy linear regression model to multiple fuzzy linear regression model in which response variable is fuzzy variable and part of the covariates are crisp variables. The least squares methods based on DK-metric and the idea of stepwise regression are applied in parameter estimation. The significance test of the regression coefficients is considered. The Bootstrap methods are used to compute the standard errors of the estimates and P-values of tests. Fuzzy diagnostics based on DK-metric are also developed to detect the outliers. Some simulations are performed to verify the obtained results, which are found to be satisfied. Finally, the early warning of macro-economic index data of China are illustrated our methodology.

[1]  Hongtu Zhu,et al.  Diagnostic measures for empirical likelihood of general estimating equations , 2008 .

[2]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[3]  Erling B. Andersen.  Diagnostics in categorical data analysis , 1992 .

[4]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

[5]  E. Lee,et al.  Nonparametric fuzzy regression—k-NN and kernel smoothing techniques , 1999 .

[6]  Phil Diamond,et al.  Fuzzy least squares , 1988, Inf. Sci..

[7]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[8]  Wolfgang Näther,et al.  Linear Regression with Random Fuzzy Variables: Extended Classical Estimates, Best Linear Estimates, Least Squares Estimates , 1998, Inf. Sci..

[9]  Ana Colubi,et al.  Estimation of a simple linear regression model for fuzzy random variables , 2009, Fuzzy Sets Syst..

[10]  Bo-Cheng Wei,et al.  Exponential Family Nonlinear Models , 1998 .

[11]  R. Cook.  Detection of influential observation in linear regression , 2000 .

[12]  R. Kruse,et al.  Statistics with vague data , 1987 .

[13]  P. Diamond,et al.  Extended fuzzy linear models and least squares estimates , 1997 .

[14]  Wolfgang Näther.  Linear Statistical Inference for Random Fuzzy Data , 1997 .

[15]  Bo-Cheng Wei,et al.  Case-deletion measures for models with incomplete data , 2001 .

[16]  Ana Colubi,et al.  Least squares estimation of linear regression models for convex compact random sets , 2007, Adv. Data Anal. Classif..

[17]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[18]  Edward W. Frees,et al.  Influence Diagnostics for Linear Longitudinal Models , 1997 .

[19]  Carlo Bertoluzza,et al.  On a new class of distances between fuzzy numbers , 1995 .

[20]  Wolfgang Näther,et al.  On the variance of random fuzzy variables , 2002 .