In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of $m$ different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia...

The paper deals with the experimental design which is optimal in the following sense: it satisfies the cost requirements simultaneously with a satisfactory precision of estimates. The underlying regression model is quadratic. The estimates of unknown parameters of the model are explicitly derived.

The paper discusses applications of permutation arguments in testing problems in linear models. Particular attention will be paid to the application in L₁-test procedures. Theoretical results will beaccompanied by a simulation study.

Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model.

Let (X, Y) be a random couple in S×T with unknown distribution P. Let (X1, Y1), …, (Xn, Yn) be i.i.d. copies of (X, Y), Pn being their empirical distribution. Let h1, …, hN:S↦[−1, 1] be a dictionary consisting of N functions. For λ∈ℝN, denote fλ:=∑j=1Nλjhj. Let ℓ:T×ℝ↦ℝ be a given loss function, which is convex with respect to the second variable. Denote (ℓ•f)(x, y):=ℓ(y; f(x)). We study the following penalized empirical risk minimization problem $${\widehat{\lambda }}^{\epsilon }:=\underset{\lambda \in {ℝ}^N}{argmin}\left[P_n(\ell •f_{\lambda })+\epsilon {\parallel \lambda \parallel }_{{\ell }_p}^p\right],$$ which is an empirical version of the problem $${\lambda }^{\epsilon }:=\underset{\lambda \in {ℝ}^N}{argmin}\left[P(\ell •f_{\lambda })+\epsilon {\parallel \lambda \parallel }_{{\ell }_p}^p\right]$$ (hereɛ≥0...

Necessary and sufficient conditions are derived for the inclusions $J_0\subset J$ and $J_0^{*}\subset J^{*}$ to be fulfilled where $J_0$, $J_0^{*}$ and $J$, $J^{*}$ are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models $G{M}_0=(y,X_0{\beta }_0,{\sigma }_0^2{V}_0)$ and $GM=(y,X\beta ,{\sigma }^{2}V)$, respectively.

This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, $\epsilon$-optimal solutions are considered. The setup is illustrated on consistency of a $\epsilon$-$M$-estimator in linear regression model.

This paper deals with an application of regression analysis to the regulation of the blood-sugar under diabetes mellitus. Section 2 gives a description of Gram-Schmidt orthogonalization, while Section 3 discusses the difference between Gauss-Markov estimation and Least Squares Estimation. Section 4 is devoted to the statistical analysis of the blood-sugar during the night. The response change of blood-sugar is explained by three variables: time, food and physical activity ("Bewegung"). At the beginning...

Generalizations of the additive hazards model are considered. Estimates of the regression parameters and baseline function are proposed, when covariates are random. The asymptotic properties of estimators are considered.

The aim of this work is to propose models to study the toxic effect of different concentrations of some standard mutagens in different colon cancer cell lines. We find estimates and, by means of an inverse regression problem, confidence intervals for the subtoxic concentration, that is the concentration that reduces by thirty percent the number of colonies obtained in the absence of mutagen.