Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model <Emphasis Type="Bold">AX=B</Emphasis>

A multivariate measurement error model AXB is considered. The errors in [A,B] are rowwise independent, but within each row the errors may be correlated. Some of the columns are observed without errors, and in addition the error covariance matrices may differ from row to row. The total covariance structure of the errors is supposed to be known up to a scalar factor. The fully weighted total least squares estimator of X is studied, which in the case of normal errors coincides with the maximum likelihood estimator. We give mild conditions for weak and strong consistency of the estimator, when the number of rows in A increases. The results generalize the conditions of Gallo given for a univariate homoscedastic model (where B is a vector), and extend the conditions of Gleser given for the multivariate homoscedastic model. We derive the objective function for the estimator and propose an iteratively reweighted numerical procedure.Acknowledgements.A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe. S. Van Huffel is a full professor with the Katholieke Universiteit Leuven. This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP Phase V-22), initiated by the Belgian State, Prime Ministers Office-Federal Office for Scientific, Technical and Cultural Affairs, of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) Predictive computer models for medical classification problems using patient data and expert knowledge, of the FWO projects G.0200.00, G.0078.01 and G.0270.02. The scientific responsibility is assumed by its authors. The authors would like to thank Maria Luisa Rastello and Amedeo Premoli for bringing the EW-TLS problem to their attention. The authors are grateful to two anonymous referees for the valuable comments.     

Results on the bias and inconsistency of ordinary least squares for the linear probability model

This note formalizes bias and inconsistency results for ordinary least squares (OLS) on the linear probability model and provides sufficient conditions for unbiasedness and consistency to hold. The conditions suggest that a “trimming estimator” may reduce OLS bias.     

Another Approach to Data Envelopment Analysis in Noisy Environments: DEA+

In this paper a DEA+ labeled approach for efficiency measurement in the stochastic case is presented along with a consistency proof and some preliminary evidence illustrating the small sample performance. DEA+ can basically handle multi-output technologies like standard DEA but allows to filter noise, that might have disturbed production and unlike a related approach does not require panel data. Consistency of DEA+ relies on the assumption of i.i.d. distributed and bounded noise and requires radial efficiency measurement. First Monte Carlo experiments show that a DEA+ based average inefficiency estimator performs well for samples of size n=100 in one-output, two-input settings compared to the corresponding Stochastic Frontier Estimator. Sensitivity of DEA+ performance with respect to parametrization of noise is weak, but higher noise contribution requires much larger sample size for satisfactory results.     

Spatial local M-estimation under association

We investigate the asymptotic behavior of a robust version of local linear regression estimators with variable bandwidth for spatial associated processes. The weak consistency of the proposed estimators is given under appropriate conditions. Furthermore, we establish the asymptotic normality of the estimators, from which expressions for the asymptotic bias and variance can be derived.     

中国经济增长的特征、可持续性与潜在增长率估算:一个综述

在本文通过对中国经济增长的表现特征、可持续性和潜在增长率估算三方面的理论综述,进一步论述了中国经济增长的发展脉络,并在此基础上提出研究中国经济增长理论尚需改进的空间.     

Consistent House Allocation

In practice we often face the problem of assigning indivisible objects (e.g., schools, housing, jobs, offices) to agents (e.g., students, homeless, workers, professors) when monetary compensations are not possible. We show that a rule that satisfies consistency, strategy-proofness, and efficiency must be an efficient generalized priority rule; i.e., it must adapt to an acyclic priority structure, except – maybe – for up to three agents in each object’s priority ordering. We are grateful to the Editor and an anonymous referee for helpful comments and suggestions. L. Ehlers acknowledges financial support from the SSHRC (Canada)     

Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent. Supported by National Natural Science Foundation of China (Grant No. 10571159) and Specialized Research Fund for the Doctor Program of Higher Education (Grant No. 2002335090).     

On consistency of redescending M-kernel smoothers

M-estimators and M-kernel estimators with a redescending ψ-function are not in general consistent. This is often handled by means of coupling the estimator to a consistent one. Coupling the estimator to the (inconsistent) starting point improves the jump preserving properties. However, the consistency depends heavily on the shape of the density of the residuals. This paper shows inconsistency under convenient conditions as well as consistency – even at jump points – under somewhat stronger conditions. Research supported by the Friedrich Ebert Foundation and by grant Mu 1031/4-1/2 of the Deutsche Forschungsgemeinschaft     

Consistency,Value Relevance and Sufficiency of Book for Market Values in Five Japanese Conglomerates Over the Period 1950–2004

Market and accounting data for five Japanese conglomerates, Toyota, Fuji, Sony, Itochu and Sumitomo, are analysed over the period 1950 to 2004. Annual market value is regressed on three accounting and six macroeconomic variables, using a general‐to‐specific approach to construct simple error correction models for each of the five firms. The results show that in four of the five firms there is evidence of a long‐run relationship between market value and the net book value of assets, which can be interpreted, with increasing degrees of strength, as book values being either consistent with, value relevant for, or sufficient for market value.     

The effect of consistency in book-tax differences on analysts’ earnings forecasts: Evidence from forecast accuracy and informativeness

This study examines the relationship between the consistency of book-tax differences and the quality of analysts’ earnings forecasts. We find that the consistency of book-tax differences is associated with more accurate and informative forecasts. This suggests that the information embedded in the consistency of book-tax differences plays an important role in elevating the quality of analysts’ forecasts. Furthermore, the effect of consistency in book-tax differences on analyst forecast quality is greater for firms with noisier information environment. Finally, we find that the relation between consistency in book-tax differences and improvements in forecast accuracy and informativeness is stronger after the implementation of Regulation Fair Disclosure, which increased the role of public information in analysts’ forecasts.