Functionals of Gasser--Muller estimators

Susan Gasser

submersible's spotlights as a slow-motion blizzard of mucus. Indeed, the biologists on this trip say they probably identified a dozen new species. (They need to double-check with their Russian colleagues, who have been at this business a lot longer and who have a literature that's both rich and hard to access). They're on the frontier of marine biology. The US Coast Guard provided the icebreake...

Efficient estimators for functionals of Markov chains with parametric marginals

Suppose we observe a geometrically ergodic Markov chain with a parametric model for the marginal, but no (further) information about the transition distribution. Then the empirical estimator for a linear functional of the joint law of two successive observations is no longer efficient. We construct an improved estimator and show that it is efficient. The construction is similar to a recent one ...

Kernel Type Plug-in Estimators of Functions of Multidimensional Density Functionals and Their Derivatives1

We consider a unified approach to investigation of plug-in pointwise estimators of the functions of the multidimensional density functionals and the derivatives of the functionals, including the functions of the conditional functionals and their derivatives, based on kernel estimators of the substitution elements. Let (Xt)t≥0 be a sequence of random variables satisfying the strong mixing (s.m.)...

Review of Georg Gasser, ed., How Successful Is Naturalism?

Convergence of the Gasser-mmller Estimator under -mixing Condition

This paper is devoted to convergence problems of the Gasser-MMller estima-tor for the regression function in a xed-design regression model. We prove the asymptotic normality and rates of uniform strong convergence for this type of estimators under the-mixing condition on the residuals. The proof of strong convergence is based on a Bernstein-type inequality which is very similar to that derived ...