In this paper, we analyze the properties of nonparametric estimators of a regression function when some covariates are not directly observed, but have only been estimated by some nonparametric procedure. We provide general results that can be used to establish rates of consistency or asymptotic normality in numerous econometric applications, including nonparametric estimation of simultaneous eq...

The algebra of invariants of several 3×3 matrices under the action of the orthogonal group by simultaneous conjugation is considered over a field of characteristic different from two. The maximal degree of elements of minimal system of generators is described with deviation 3. 2000 Mathematics Subject Classification: 16R30; 13A50.

Utilizing early time response and low-frequency data, the complete electromagnetic response of a threedimensional conducting structure is generated. By using mutually complementary data, simultaneous extrapolation in time and frequency domains are carried out. This is performed through the use of the associated Hermite polynomials. The interesting property of the Hermite polynomials is that the...

A linear group G < GL(n) acts on d-tuples of n×n matrices by simultaneous conjugation. In [Adv. Math. 19 (1976), 306–381] Procesi established generators and relations between them for G-invariants, where G is GL(n), O(n), and Sp(n) and the characteristic of base field is zero. We continue generalization of the mentioned results to the case of positive characteristic originated by Donkin in [Inv...

Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.

This work describes an approach for smoothing noisy peak-shaped analytical data based on the identification of the structural form of the signal. The data series was described first as a succession of ‘peak structures’ and then as a succession of ‘meta-peak structures’. This description enabled convenient identification of the characteristic peaks arising from an analytical measurement and thei...

In this appendix we describe bidding strategies we have designed to study simultaneous ascending auction games [Reeves et al., 2003, MacKie-Mason et al., 2004, Reeves et al., 2005, Osepayshvili et al., 2005, Wellman et al., 2007]. Throughout this appendix we use the concept of an SAA environment, which comprises an SAA mechanism over M goods, a set of N agents, and a probability distribution D ...

This note revisits the identification theorems of B. Brown (1983) and Roehrig (1988). We describe an error in the proofs of the main identification theorems in these papers, and provide an important counterexample to the theorems on the identification of the reduced form. Specifically, the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions o...

Several research thrusts in the area of data management have focused on understanding how changes in the data affect the output of a view or standing query. Example applications are explaining query results, propagating updates through views, and anonymizing datasets. An important aspect of this analysis is the problem of deleting a minimum number of tuples from the input tables to make a given...

We give a non-technical introduction to convergence-divergence models, a new modeling approach for phylogenetic data that allows for the usual divergence of species post speciation but also allows for species to converge, i.e. become more similar over time. By examining the 3-taxon case in some detail we illustrate that phylogeneticists have been “spoiled” in the sense of not having to think ab...