Bias of the Quasi Score Estimator of a Measurement Error Model Under Misspecification of the Regressor Distribution

In a structural error model the structural quasi score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification the true model consists of a mixture of normal distributions which cluster round a single normal distribution, in the second type the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero very fast so that small deviations from the true model lead only to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model

The impact of bank and non-bank financial institutions on local economic growth in China.

Impact; Growth;

Note on Two Estimators for the Polynomial Regression with Errors in the Variables

This Note generalizes two estimators of the quadratic regression with measurement errors by Fuller and Wolter and Fuller to the polynomial case

On the bias of structural estimation methods in a polynomial regression with measurement error when the distribution of the latent covariate is a mixture of normals

The structural variant of a regression model with measurement error is characterized by the assumption of an underlying known distribution of the latent covariate. Several estimation methods, like regression calibration or structural quasi score estimation, take this distribution into account. In the case of a polynomial regression, which is studied here, structural quasi score takes the form of structural least squares (SLS). Usually the underlying latent distribution is assumed to be the normal distribution because then the estimation methods take a particularly simple form. SLS is consistent as long as this assumption is true. The purpose of the paper is to investigate the amount of bias that results from violations of the normality assumption for the covariate distribution. Deviations from normality are introduced by switching to a mixture of normal distributions. It turns out that the bias reacts only mildly to slight deviations from normality

Vibrational exciton nanoimaging of phases and domains in porphyrin nanocrystals.

Much of the electronic transport, photophysical, or biological functions of molecular materials emerge from intermolecular interactions and associated nanoscale structure and morphology. However, competing phases, defects, and disorder give rise to confinement and many-body localization of the associated wavefunction, disturbing the performance of the material. Here, we employ vibrational excitons as a sensitive local probe of intermolecular coupling in hyperspectral infrared scattering scanning near-field optical microscopy (IR s-SNOM) with complementary small-angle X-ray scattering to map multiscale structure from molecular coupling to long-range order. In the model organic electronic material octaethyl porphyrin ruthenium(II) carbonyl (RuOEP), we observe the evolution of competing ordered and disordered phases, in nucleation, growth, and ripening of porphyrin nanocrystals. From measurement of vibrational exciton delocalization, we identify coexistence of ordered and disordered phases in RuOEP that extend down to the molecular scale. Even when reaching a high degree of macroscopic crystallinity, identify significant local disorder with correlation lengths of only a few nanometers. This minimally invasive approach of vibrational exciton nanospectroscopy and -imaging is generally applicable to provide the molecular-level insight into photoresponse and energy transport in organic photovoltaics, electronics, or proteins

A Small Sample Estimator for a Polynomial Regression with Errors in the Variables

An adjusted least squares estimator, introduced by Cheng and Schneeweiss (1998) for consistently estimating a polynomial regression of any degree with errors in the variables, is modified such that it shows good results in small samples without losing its asymptotic properties for large samples. Simulation studies corroborate the theoretical findings. The new method is applied to analyse a geophysical law relating the depth of earthquakes to their distance from a trench where one of the earth's plates is submerged beneath another one