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Sequential Specification Tests to Choose a Model: A Change-Point Approach
Researchers faced with a sequence of candidate model specifications must
often choose the best specification that does not violate a testable
identification assumption. One option in this scenario is sequential
specification tests: hypothesis tests of the identification assumption over the
sequence. Borrowing an idea from the change-point literature, this paper shows
how to use the distribution of p-values from sequential specification tests to
estimate the point in the sequence where the identification assumption ceases
to hold. Unlike current approaches, this method is robust to individual errant
p-values and does not require choosing a test level or tuning parameter. This
paper demonstrates the method's properties with a simulation study, and
illustrates it by application to the problems of choosing a bandwidth in a
regression discontinuity design while maintaining covariate balance and of
choosing a lag order for a time series model
Anomalous Hall Effect in three ferromagnets: EuFe4Sb12, Yb14MnSb11, and Eu8Ga16Ge30
The Hall resistivity (Rho_xy), resistivity (Rho_xx), and magnetization of
three metallic ferromagnets are investigated as a function of magnetic field
and temperature. The three ferromagnets, EuFe4Sb12 (Tc = 84 K), Yb14MnSb11 (Tc
= 53 K), and Eu8Ga16Ge30 (Tc = 36 K) are Zintl compounds with carrier
concentrations between 1 x 10^21 cm^-3 and 3.5 x 10^21 cm^-3. The relative
decrease in Rho_xx below Tc [Rho_xx(Tc)/Rho_xx(2 K)] is 28, 6.5, and 1.3 for
EuFe4Sb12, Yb14MnSb11, and Eu8Ga16Ge30 respectively. The low carrier
concentrations coupled with low magnetic anisotropies allow a relatively clean
separation between the anomalous (Rho_'xy), and normal contributions to the
measured Hall resistivity. For each compound the anomalous contribution in the
zero field limit is fit to alpha Rho_xx + sigma_xy rho_xx^2 for temperatures T
< Tc. The anomalous Hall conductivity, sigma_xy, is -220 +- 5 (Ohm^-1 cm^-1),
-14.7 +- 1 (Ohm^-1 cm^-1), and 28 +- 3 (Ohm^-1 cm^-1) for EuFe4Sb12,
Yb14MnSb11, and Eu8Ga16Ge30 respectively and is independent of temperature for
T < Tc if the change in spontaneous magnetization (order parameter) with
temperature is taken into account. These data are consistent with recent
theories of the anomalous Hall effect that suggest that even for stochiometric
ferromagnetic crystals, such as those studied in this article, the intrinsic
Hall conductivity is finite at T = 0, and is a ground state property that can
be calculated from the electronic structure.Comment: 22 pages, 13 figures Submitted to PR
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