We consider equalities between the ordinary least squares estimator (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathrm {OLSE} $$</EquationSource> </InlineEquation>), the best linear unbiased estimator (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathrm {BLUE} $$</EquationSource> </InlineEquation>) and the best linear unbiased predictor (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\mathrm {BLUP} $$</EquationSource> </InlineEquation>) in the general linear model <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\{ \mathbf y , \mathbf X \varvec{\beta }, \mathbf...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

We reveal the boundary bias problem of Birnbaum–Saunders, inverse Gaussian, and reciprocal inverse Gaussian kernel estimators (Jin and Kawczak, 2003; Scaillet, 2004) and re-formulate these estimators to solve the problem. We investigate asymptotic properties of a new class of asymmetric kernel...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

In this paper, we consider a class of semi-Markov processes, known as phase semi-Markov processes, which can be considered as an extension of Markov processes, but whose times between transitions are phase-type random variables. Based on the theory of generalized inverses, we derive expressions...

Efficient posterior simulators for two GARCH models with generalized hyperbolic disturbances are presented. The first model, GHt-GARCH, is a threshold GARCH with a skewed and heavy-tailed error distribution; in this model, the latent variables that account for skewness and heavy tails are...