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On the uniqueness of minimal projections in Banach spaces

Szlachtowska E., Mielczarek D.

Opuscula Mathematica

2012

Vol. 32, no. 3

579-590

Let X be a uniformly convex Banach space with a continuous semi-inner product. We investigate the relation of orthogonality in X and generalized projections acting on X. We prove uniqueness of orthogonal and co-orthogonal projections.

On the maximum likelihood estimator in the generalized beta regression model

Rydlewski J. P., Mielczarek D.

Opuscula Mathematica

2012

Vol. 32, no. 4

761-774

The subject of this article is to present the beta – regression model, where we assume that one parameter in the model is described as a combination of algebraically independent continuous functions. The proposed beta model is useful when the dependent variable is continuous and restricted to the bounded interval. The parameters are obtained by maximum likelihood estimation. We prove that estimators are consistent and asymptotically normal.

Minimal and co-minimal projections in spaces of continuous functions

Mielczarek D.

Opuscula Mathematica

2010

Vol. 30, no. 4

457-464

Minimal and co-minimal projections in the space C[0, 1] are studied. We construct a minimal and co-minimal projection from C[0, 1] onto a subspace Y defined in the introduction.