Browsing by Subject "Robust regression"
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Item Open Access Asymptotic expansions for test statistics and tests for normality based on robust regression(Bilkent University, 1999) Önder, A. ÖzlemThis dissertation focuses on two different topics in econometrics. The first one is presented in Chapter 2 and is related to higher order asymptotic theory. The power of the Lagrange multiplier, Wald and likelihood ratio tests for the first order autoregressive model is compared through the approximations to the distributions of these three tests. The adequacy of the approximation is examined. The Wald and likelihood ratio tests are found to have superior performance than the Lagrange multiplier test. The comparisons are done according to stringency of the test statistics. As a second topic in Chapter 3, the dissertation examines the use of residuals from robust regression instead of OLS residuals in test statistics for the normality of the errors. According to simulation results their improvement over standard normality tests is found only in specialized circumstances. The applications on real data set show these conditions occur often enough in practice.Item Open Access Duality in robust linear regression using Huber's M-estimator(Elsevier, 1997-07) Pınar, M. Ç.The robust linear regression problem using Huber's piecewise-quadratic M-estimator function is considered. Without exception, computational algorithms for this problem have been primal in nature. In this note, a dual formulation of this problem is derived using Lagrangean duality. It is shown that the dual problem is a strictly convex separable quadratic minimization problem with linear equality and box constraints. Furthermore, the primal solution (Huber's M-estimate) is obtained as the optimal values of the Lagrange multipliers associated with the dual problem. As a result, Huber's M-estimate can be computed using off-the-shelf optimization software.Item Open Access A finite continuation algorithm for bound constrained quadratic programming(Society for Industrial and Applied Mathematics Publications, 1998) Madsen, K.; Nielsen, H. B.; Pınar, M. C.The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear ℓ1 minimization problem with quadratic terms. A smooth approximation to the linear ℓ1 function is used to obtain a parametric family of piecewise-quadratic approximation problems. The unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter. Thus, a finite continuation algorithm is designed. Results of extensive computational experiments are reported.Item Open Access On Newton's method for Huber's robust M-estimation problems in linear regression(Springer Netherlands, 1998) Chen, B.; Pınar, M. Ç.The Newton method of Madsen and Nielsen (1990) for computing Huber's robust M-estimate in linear regression is considered. The original method was proved to converge finitely for full rank problems under some additional restrictions on the choice of the search direction and the step length in some degenerate cases. It was later observed that these requirements can be relaxed in a practical implementation while preserving the effectiveness and even improving the efficiency of the method. In the present paper these enhancements to the original algorithm are studied and the finite termination property of the algorithm is proved without any assumptions on the M-estimation problems.