Regularity and Uniqueness for Constrained M-Estimates and Redescending M-Estimates

On the Maximum Bias Functions of Mm-estimates and Constrained M-estimates of Regression

We derive the maximum bias functions of the MM -estimates and the constrained M -estimates or CM -estimates of regression and compare them to the maximum bias functions of the S -estimates and the τ -estimates of regression. In these comparisons, the CM -estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a C...

Redescending M -estimators

In finite sample studies redescending M -estimators outperform bounded M -estimators (see for example, Andrews et al., 1972). Even though redescenders arise naturally out of the maximum likelihood approach if one uses very heavy-tailed models, the commonly used redescenders have been derived from purely heuristic considerations. Using a recent approach proposed by Shurygin, we studied the optim...

Coefficient Estimates for a New Subclasses of m-fold Symmetric Bi-Univalent Functions

The purpose of the present paper is to introduce two new subclasses of the function class ∑m  of bi-univalent functions which both f  and f-1  are m-fold symmetric analytic functions. Furthermore, we obtain estimates on the initial coefficients for functions in each of these new subclasses. Also we explain the relation between our results with earlier known results.

DEMAND ESTIMATES FOR AGRICULTURAL, MANUFACTURING AND SERVICE PRODUCTS

Uniqueness and a Priori Estimates

Under some conditions on f(u), we show that for small, the only solutions to the following elliptic equation u ? u + f(u) = 0 in ; u > 0 in ; @u @ = 0 on @ are constants, provided that R 3 is convex. The proof only uses integration by parts.