Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median...Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median zero. Define the minimum L_1norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:展开更多
We study the asymptotic distribution of the L1 regression estimator under general condi-tions with matrix norming and possibly non i.i.d.errors.We then introduce an appropriate bootstrap procedure to estimate the dist...We study the asymptotic distribution of the L1 regression estimator under general condi-tions with matrix norming and possibly non i.i.d.errors.We then introduce an appropriate bootstrap procedure to estimate the distribution of this estimator and study its asymptotic properties.It is shown that this bootstrap is consistent under suitable conditions and in other situations the bootstrap limit is a random distribution.展开更多
For a linear model, let the error sequence be i.i.d, with common unknown density f(x), and (x) be a nonparametric estimator of f(x) based on the residuals. In this paper, on the basis of [1], we establish the L_1-norm...For a linear model, let the error sequence be i.i.d, with common unknown density f(x), and (x) be a nonparametric estimator of f(x) based on the residuals. In this paper, on the basis of [1], we establish the L_1-norm consistency, asymptotic normality and law of iterated logarithm for (x) under general condition. These results bring the asymptotic theory for estimation of error distributions to completion.展开更多
基金Project supported by the National Natural Science Foundation of China and also supported by the U. S. Office of Naval Research and Air Force Office of Scientific Research.
文摘Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median zero. Define the minimum L_1norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:
基金supported by J.C. Bose National Fellowship, Government of India
文摘We study the asymptotic distribution of the L1 regression estimator under general condi-tions with matrix norming and possibly non i.i.d.errors.We then introduce an appropriate bootstrap procedure to estimate the distribution of this estimator and study its asymptotic properties.It is shown that this bootstrap is consistent under suitable conditions and in other situations the bootstrap limit is a random distribution.
基金Project supported by the National Natural Science Foundation of China.
文摘For a linear model, let the error sequence be i.i.d, with common unknown density f(x), and (x) be a nonparametric estimator of f(x) based on the residuals. In this paper, on the basis of [1], we establish the L_1-norm consistency, asymptotic normality and law of iterated logarithm for (x) under general condition. These results bring the asymptotic theory for estimation of error distributions to completion.
