Strong Consistency of M-Estimates for the Linear Model

摘要

Let (sub 1),...,(sub n),... be i.i.d. observations of a random vector (X,Y) were Y is one-dimensional and X may be multi-dimensional. Suppose that the regression of Y to X, in some sense, is a linear function alpha sub o + beta sub o. It is desired to estimate the unknown parameters alpha sub o, beta sub o, using the observations (sub 1),...(sub n,). A much discussed class of estimates is the so-called M-estimate, which takes the solution of a certain minimization problem as the estimator. Here rho is a properly selected function defined over R' = (infinity).