Identification Algorithm Based on the Approximate Least Absolute Deviation Criteria

Considering the situation that the least-squares (LS) method for system identification has poor robustness and the least absolute deviation (LAD) algorithm is hard to construct, an approximate least absolute deviation (ALAD) algorithm is proposed in this paper. The objective function of ALAD is constructed by introducing a deterministic function to approximate the absolute value function. Based on the function, the recursive equations for parameter identification are derived using Gauss-Newton iterative algorithm without any simplification. This algorithm has advantages of simple calculation and easy implementation, and it has second order convergence speed. Compared with the LS method, the new algorithm has better robustness when disorder and peak noises exist in the measured data. Simulation results show the efficiency of the proposed method.

Least Absolute Deviation Estimation of Autoregressive Conditional Duration Model

This paper studies the least absolute deviation estimation of the high frequency financial autoregressive conditional duration （ACD） model. The asymptotic properties of the estimator are studied given mild regularity conditions. Furthermore, we develop a Wald test statistic for the linear restriction on the parameters. A simulation study is conducted for the finite sample properties of our estimator. Finally, we give an empirical study of financial duration.

ROBUST ESTIMATES IN MULTIVARIATE NONPARAMETRIC REGRESSION VIA LEAST ABSOLUTE DEVIATIONS

Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)} , we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)| where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order r, it is shown that the optimal global convergence rate, n-r/(2r+J), is attained by the L1-norm based estimators.

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

Moderate Deviations for M-estimators in Linear Models with φ-mixing Errors

In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber＇s estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.

Approximation by randomly weighting method in censored regression model

Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the per-formance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.

RANDOM WEIGHTING METHOD FOR CENSORED REGRESSION MODEL

Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model.In this paper we extend the result to the censored regression model (or censored “Tobit” model).