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sestima

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There are 7 letters in SESTIMA ( A1E1I1M3S1T1 )

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Sestima might refer to
The goal of S-estimators is to have a simple high-breakdown regression estimator, which share the flexibility and nice asymptotic properties of M-estimators. The name "S-estimators" was chosen as they are based on estimators of scale.
* We will consider estimators of scale defined by a function
*
*
*
* ρ
*
*
* {\displaystyle \rho }
* , which satisfy
* R1 -
*
*
*
* ρ
*
*
* {\displaystyle \rho }
* is symmetric, continuously differentiable and
*
*
*
* ρ
* (
* 0
* )
* =
* 0
*
*
* {\displaystyle \rho (0)=0}
* .
* R2 - there exists
*
*
*
* c
* >
* 0
*
*
* {\displaystyle c>0}
* such that
*
*
*
* ρ
*
*
* {\displaystyle \rho }
* is strictly increasing on
*
*
*
* [
* c
* ,
* ∞
* [
*
*
* {\displaystyle [c,\infty [}
*
* For any sample
*
*
*
* {
*
* r
*
* 1
*
*
* ,
* .
* .
* .
* ,
*
* r
*
* n
*
*
* }
*
*
* {\displaystyle \{r_{1},...,r_{n}\}}
* of real numbers, we define the scale estimate
*
*
*
* s
* (
*
* r
*
* 1
*
*
* ,
* .
* .
* .
* ,
*
* r
*
* n
*
*
* )
*
*
* {\displaystyle s(r_{1},...,r_{n})}
* as the solution of*
*
*
*
*
* 1
* n
*
*
*
* ∑
*
* i
* =
* 1
*
*
* n
*
*
* ρ
* (
*
* r
*
* i
*
*
*
* /
*
* s
* )
* =
* K
*
*
* {\textstyle {\frac {1}{n}}\sum _{i=1}^{n}\rho (r_{i}/s)=K}
* ,
* where
*
*
*
* K
*
*
* {\displaystyle K}
* is the expectation value of
*
*
*
* ρ
*
*
* {\displaystyle \rho }
* for a standard normal distribution. (If there are more solutions to the above equation, then we take the one with the smallest solution for s; if there is no solution, then we put
*
*
*
* s
* (
*
* r
*
* 1
*
*
* ,
* .
* .
* .
* ,
*
* r
*
* n
*
*
* )
* =
* 0
*
*
* {\displaystyle s(r_{1},...,r_{n})=0}
* .)
* Definition:
* Let
*
*
*
* (
*
* x
*
* 1
*
*
* ,
*
* y
*
* 1
*
*
* )
* ,
* .
* .
* .
* ,
* (
*
* x
*
* n
* ...
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