This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators--intermediaries between sample mean and sample median--that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general …

Most algorithms for the least-squares estimation of non-linear parameters have centered about either of two approaches. On the one hand, the model may be expanded as a Taylor series and corrections to the several parameters calculated at each iteration on the assumption of local linearity. On the other hand, various modifications of the method of steepest-descent have been used. Both methods not …

Consider a situation in which it is desired to gain knowledge about the true value of some parameter (or about the true state of the world) by means of experimentation. Let Ω denote the set of all possible values of the parameter θ, and suppose that the experimenter's knowledge about the true value of θ can be expressed, at each stage of experimentation, in terms of a probability distribution ξ …

The Michigan Mathematical Journal