Asymptotic properties of least squares estimation with fuzzy observations

This paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input-output and random error terms. The asymptotic normality and strong consistency of the fuzzy least squares estimator (FLSE) are investigated; a confidence region based on a class of FLSEs is proposed; the asymptotic relative efficiency of FLSEs with respect to the crisp least squares estimators is also provided and a numerical example is given. Some simulation results are also presented to illustrate the behavior of FLSEs.

[1]  Hilmar Drygas,et al.  Weak and strong consistency of the least squares estimators in regression models , 1976 .

[2]  Dug Hun Hong,et al.  Extended fuzzy regression models using regularization method , 2004, Inf. Sci..

[3]  Hsien-Chung Wu,et al.  Statistical hypotheses testing for fuzzy data , 2005, Inf. Sci..

[4]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[5]  Ekrem Savaş,et al.  On -Statistically Convergent Double Sequences of Fuzzy Numbers , 2008 .

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

[7]  Abbas Parchami,et al.  Fuzzy estimation for process capability indices , 2007, Inf. Sci..

[8]  Chiang Kao,et al.  A fuzzy linear regression model with better explanatory power , 2002, Fuzzy Sets Syst..

[9]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[10]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[11]  Pierpaolo D'Urso,et al.  A least-squares approach to fuzzy linear regression analysis , 2000 .

[12]  Ping-Teng Chang,et al.  Fuzzy linear regression with spreads unrestricted in sign , 1994 .

[13]  Salih Aytar.  Statistical limit points of sequences of fuzzy numbers , 2004, Inf. Sci..

[14]  Przemyslaw Grzegorzewski,et al.  Testing statistical hypotheses with vague data , 2000, Fuzzy Sets Syst..

[15]  Wolfgang Näther,et al.  Least-squares fuzzy regression with fuzzy random variables , 2002, Fuzzy Sets Syst..

[16]  H. Tanka.  Fuzzy data analysis by possibilistic linear models , 1987 .

[17]  H. Robbins,et al.  Strong consistency of least squares estimates in multiple regression. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Miin-Shen Yang,et al.  Fuzzy least-squares linear regression analysis for fuzzy input-output data , 2002, Fuzzy Sets Syst..

[19]  Abraham Kandel,et al.  General fuzzy least squares , 1997, Fuzzy Sets Syst..

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

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

[22]  Miin-Shen Yang,et al.  Fuzzy least-squares algorithms for interactive fuzzy linear regression models , 2003, Fuzzy Sets Syst..

[23]  A. Celmins.  Least squares model fitting to fuzzy vector data , 1987 .

[24]  Bernhard F. Arnold.  Statistical tests optimally meeting certain fuzzy requirements on the power function and on the sample size , 1995, Fuzzy Sets Syst..

[25]  Pedro Gil,et al.  The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information , 1986 .

[26]  F. J. Hickernell,et al.  A New Class of Consistent Estimators for Stochastic Linear Regressive Models , 1997 .