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Least empirical risk procedures in statistical inference

100%

Niemiro W.

Applicationes Mathematicae

1993-1995

tom 22

nr 1

55-67

We consider the empirical risk function $Q_n(α)={1\over n} \sum_{i=1}^n \cdot f(α,Z_i)$ (for iid $Z_i$'s) under the assumption that f(α,z) is convex with respect to α. Asymptotics of the minimum of $Q_n(α)$ is investigated. Tests for linear hypotheses are derived. Our results generalize some of those concerning LAD estimators and related tests.

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Selection strategies in projection methods for convex minimization problems

100%

Cegielski A., Dylewski R.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2002

tom 22

nr 1

97-123

We propose new projection method for nonsmooth convex minimization problems. We present some method of subgradient selection, which is based on the so called residual selection model and is a generalization of the so called obtuse cone model. We also present numerical results for some test problems and compare these results with some other convex nonsmooth minimization methods. The numerical results show that the presented selection strategies ensure long steps and lead to an essential acceleration of the convergence of projection methods.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Cegielski A.

1 Dylewski R.

1 Niemiro W.

1 2002

1 1993

Wyniki wyszukiwania

Least empirical risk procedures in statistical inference

Selection strategies in projection methods for convex minimization problems