Research Article

A Criterion for the Fuzzy Set Estimation of the Regression Function

Table 1

IMSE* values of the estimations for the fuzzy set estimator and the kernel estimators.

𝑣 𝑛 I M S E [ ̂ 𝑟 𝑛 ] I M S E [ ̂ 𝑟 N W 𝐾 𝐸 ] I M S E [ ̂ 𝑟 N W 𝐾 𝐺 ]

1 0 0 0 . 0 0 9 3 0 . 0 1 1 1 0 . 0 1 1 5
0 . 2 2 5 0 0 . 0 0 4 5 0 . 0 0 5 3 0 . 0 0 5 5
5 0 0 0 . 0 0 2 6 0 . 0 0 3 1 0 . 0 0 3 2

1 0 0 0 . 0 0 8 3 0 . 0 1 1 1 0 . 0 1 1 5
0 . 1 5 2 5 0 0 . 0 0 4 0 0 . 0 0 5 3 0 . 0 0 5 5
5 0 0 0 . 0 0 2 3 0 . 0 0 3 1 0 . 0 0 3 2

1 0 0 0 . 0 0 7 0 0 . 0 1 1 1 0 . 0 1 1 5
0 . 1 0 2 5 0 0 . 0 0 3 4 0 . 0 0 5 3 0 . 0 0 5 5
5 0 0 0 . 0 0 1 9 0 . 0 0 3 1 0 . 0 0 3 2

*Minimum IMSE* in each row.