Description Usage Arguments Details Value Note Author(s) See Also Examples

This function calculates the M-estimator of scale with loss function given in `M`

for a matrix of trapezoidal fuzzy numbers `F`

. For computing the M-estimator, a method called “iterative reweighting” is used. The employed metric in the M-equation can be the 1-norm distance, the mid/spr distance or the *(\varphi,θ)*-wabl/ldev/rdev distance. The function first checks if the input matrix `F`

is given in the correct form (tested by `checkingTra`

).

1 | ```
M.estimate(F, M, est_initial, delta, epsilon, type, a = 1, b = 1, theta = 1/3)
``` |

`F` |
matrix of dimension |

`M` |
name of the loss function. It can be “Huber”, “Tukey” or “Cauchy”. |

`est_initial` |
initial scale estimate. |

`delta` |
number in (0,1). It is present in the M-equation. |

`epsilon` |
number >0. It is the tolerance allowed in the algorithm. |

`type` |
number 1, 2 or 3: if |

`a` |
number >0, by default |

`b` |
number >0, by default |

`theta` |
number >0, by default |

See examples

The function returns the value of the M-estimator of scale, which is a real number.

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

`checkingTra`

, `Rho1Tra`

, `DthetaphiTra`

, `DwablphiTra`

1 2 3 4 5 6 7 | ```
# Example 1:
F=SimulCASE1(100)
U=Median1norm(F)
est_initial=MDD(F,U,1)
delta=0.5
epsilon=10^(-5)
M.estimate(F,"Huber",est_initial,delta,epsilon,1)
``` |

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