New algorithms for computing the least trimmed squares regression estimator

Asymptotics of Least Trimmed Squares Regression

“…Thus, for any ε > 0 we find (1). Furthermore, denoting the cumulative distribution function of Z n by F z,n , the expectation…”

“…They form three groups: distributional Assumptions D for random variables in model (1), Assumptions H concerning properties of the regression function h(x, β), and finally, the identification Assumptions I.…”

General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

“…As h n /n determines the fraction of sample included in the GTE objective function, and consequently, the robustness properties of GTE, we want to asymptotically fix this fraction at λ, 1 2 ≤ λ ≤ 1. The trimming constant for a given sample size n can be then defined by h n = [λn], where [x] represents the integer part of x; in general, one can also consider any sequence {h n } n∈N such that h n /n → λ.…”

“…The LTS estimator belongs to the class of affine-equivariant estimators that achieve asymptotically the highest breakpoint 1/2 and it is generally preferred to the similar, but slowly converging least median of squares (LMS; Rousseeuw, 1984). 1 Thus, LTS has been receiving a lot of attention from the theoretical, computational, and application points of view. There are extensions involving nonlinear regression (Stromberg, 1993), weighted LTS (Víšek, 2002), and adaptive smooth trimming (Čížek, 2002), and in most of these cases, the asymptotic and breakdown behavior is known in the standard regression with i.i.d.…”

“…Simultaneously, there has been a significant development in computational methods (Agulló, 2001; Gilloni and Padberg, 2002;Rousseeuw and van Driessen, 1999). Last, but not least, there are also first applications of LTS in economics (Beňáček, Jarolím, and Víšek, 1998;Temple, 1998;Zaman, Rousseeuw, and Orhan, 2001) and finance (Knez and Ready, 1997; Kelly, 1997).…”