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sestimat
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There are 8 letters in SESTIMAT ( A1E1I1M3S1T1 )
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Sestimat might refer to |
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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 * ... |