Displacement Determination of the Guard Electrode for the New Calculable Capacitor at NIM
We present our continuing work on the displacement determination of the guard electrode for the new vertical calculable capacitor. We describe a method for determining the displacement by actively locking the Fabry-Perot interferometer to a stabilized laser at two cavity lengths of interest. In order to lock the interferometer tightly, the modulation width of the laser is optimized for the full-width at half-maximum at the two different cavity lengths. For each of the cavity lengths, the Fabry-Perot interferometer is maintained at its resonance, and the cavity length is quantized with a space of λ/2. Then, its corresponding ratio between the fixed standard capacitor and the calculable capacitor is accurately measured by a capacitance bridge. The two main parameters for determining the displacement between the two cavity lengths-i.e., the difference in order number (AN) of the interferometer and the laser wavelength (λ)-are obtained from the capacitance bridge measurement based on a 1-pF standard capacitor with a priori value and the accurate wavelength measurement of an iodine laser, respectively. Evaluation of the displacement sensing system confirms a relative uncertainty of 5.2 × 10-9 over a range of 205 mm.
Progress on a New Measurement of von Klitzing Constant at NIM
This paper describes the progress on a new measurement of von Klitzing constant $\pmb{(R_{\text{k}})}$ through an experiment linking the new calculable capacitor and the quantized Hall resistance by means of a quadrature transfer at NIM. The recent improvements of the new calculable capacitor, the optical interferometry, the impedance measurement chain are presented.
Speci fi cation Test for Panel Data Models with Interactive Fixed E ff ects ∗
In this paper, we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects. Both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model. We estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic. We show that after being appropriately centered and standardized, the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of Pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by Prakasa Rao (2009). To improve the finite sample performance, we propose a bootstrap procedure to obtain the bootstrap -value. A small set of Monte Carlo simulations illustrates that our test performs well in finite samples. An application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth, initial income level and capital accumulation.