114 research outputs found
Asymptotic inference in some heteroscedastic regression models with long memory design and errors
This paper discusses asymptotic distributions of various estimators of the
underlying parameters in some regression models with long memory (LM) Gaussian
design and nonparametric heteroscedastic LM moving average errors. In the
simple linear regression model, the first-order asymptotic distribution of the
least square estimator of the slope parameter is observed to be degenerate.
However, in the second order, this estimator is -consistent and
asymptotically normal for ; nonnormal otherwise, where and are
LM parameters of design and error processes, respectively. The
finite-dimensional asymptotic distributions of a class of kernel type
estimators of the conditional variance function in a more general
heteroscedastic regression model are found to be normal whenever ,
and non-normal otherwise. In addition, in this general model,
-consistency of the local Whittle estimator of based on pseudo
residuals and consistency of a cross validation type estimator of
are established. All of these findings are then used to propose a lack-of-fit
test of a parametric regression model, with an application to some currency
exchange rate data which exhibit LM.Comment: Published in at http://dx.doi.org/10.1214/009053607000000686 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Back-action Induced Non-equilibrium Effect in Electron Charge Counting Statistics
We report our study of the real-time charge counting statistics measured by a
quantum point contact (QPC) coupled to a single quantum dot (QD) under
different back-action strength. By tuning the QD-QPC coupling or QPC bias, we
controlled the QPC back-action which drives the QD electrons out of thermal
equilibrium. The random telegraph signal (RTS) statistics showed strong and
tunable non-thermal-equilibrium saturation effect, which can be quantitatively
characterized as a back-action induced tunneling out rate. We found that the
QD-QPC coupling and QPC bias voltage played different roles on the back-action
strength and cut-off energy.Comment: 4 pages, 4 figures, 1 tabl
Local Whittle estimator for anisotropic random fields
AbstractA local Whittle estimator is developed to simultaneously estimate the long memory parameters for stationary anisotropic scalar random fields. It is shown that these estimators are consistent and asymptotically normal, under some weak technical conditions. A brief simulation study illustrates a practical application of the estimator
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