3,187 research outputs found
Transfer maps and nonexistence of joint determinant
Transfer Maps, sometimes called norm maps, for Milnor's -theory were first
defined by Bass and Tate (1972) for simple extensions of fields via tame symbol
and Weil's reciprocity law, but their functoriality had not been settled until
Kato (1980). On the other hand, functorial transfer maps for the Goodwillie
group are easily defined. We show that these natural transfer maps actually
agree with the classical but difficult transfer maps by Bass and Tate. With
this result, we build an isomorphism from the Goodwillie groups to Milnor's
-groups of fields, which in turn provides a description of joint
determinants for the commuting invertible matrices. In particular, we
explicitly determine certain joint determinants for the commuting invertible
matrices over a finite field, the field of rational numbers, real numbers and
complex numbers into the respective group of units of given field.Comment: Some minor revisions have been made after the 1st versio
Maximum Score Estimation of Preference Parameters for a Binary Choice Model under Uncertainty
This paper develops maximum score estimation of preference parameters in the
binary choice model under uncertainty in which the decision rule is affected by
conditional expectations. The preference parameters are estimated in two
stages: we estimate conditional expectations nonparametrically in the first
stage and then the preference parameters in the second stage based on Manski
(1975, 1985)'s maximum score estimator using the choice data and first stage
estimates. The paper establishes consistency and derives rate of convergence of
the two-stage maximum score estimator. Moreover, the paper also provides
sufficient conditions under which the two-stage estimator is asymptotically
equivalent in distribution to the corresponding single-stage estimator that
assumes the first stage input is known. These results are of independent
interest for maximum score estimation with nonparametrically generated
regressors. The paper also presents some Monte Carlo simulation results for
finite-sample behavior of the two-stage estimator
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