On optimality of the LR tests in the sense of exact slopes. II. Application to individual distributions
On optimality of the LR tests in the sense of exact slopes. I. General case
On optimality of the orthogonal block design
In the paper a usual block design with treatment effects fixed and block effects random is considered. To compare experimental design the asymptotic covariance matrix of a robust estimator proposed by Bednarski and Zontek (1996) for simultaneous estimation of shift and scale parameters is used. Asymptotically A- and D- optimal block designs in the class of designs with bounded block sizes are characterized.
On optimum experimental design for ridge estimates
On order statistics for random sample size having compound binomial and Poisson distributions
On orderings induced by the Loewner partial ordering
The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.
On orthogonal series estimation of bounded regression functions
The problem of nonparametric estimation of a bounded regression function , [a,b] ⊂ ℝ, d ≥ 1, using an orthonormal system of functions , k=1,2,..., is considered in the case when the observations follow the model , i=1,...,n, where and are i.i.d. copies of independent random variables X and η, respectively, the distribution of X has density ϱ, and η has mean zero and finite variance. The estimators are constructed by proper truncation of the function , where the coefficients are determined...
On parameter-effects arrays in non-linear regression models
Formulas for a new three- and four-dimensional parameter-effects arrays corresponding to transformations of parameters in non-linear regression models are given. These formulae make the construction of the confidence regions for parameters easier. An example is presented which shows that some care is necessary when a new array is computed.
On periodic autoregression with unknown mean
If the parameters of an autoregressive model are periodic functions we get a periodic autoregression. In the paper the case is investigated when the expectation can also be a periodic function. The innovations have either constant or periodically changing variances.
On perturbations of strongly admissible prior distributions
On pointwise adaptive curve estimation based on inhomogeneous data
We want to recover a signal based on noisy inhomogeneous data (the amount of data can vary strongly on the estimation domain). We model the data using nonparametric regression with random design, and we focus on the estimation of the regression at a fixed point x0 with little, or much data. We propose a method which adapts both to the local amount of data (the design density is unknown) and to the local smoothness of the regression function. The procedure consists of a local polynomial...
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
On precision of stochastic optimization based on estimates from censored data
In the framework of a stochastic optimization problem, it is assumed that the stochastic characteristics of optimized system are estimated from randomly right-censored data. Such a case is frequently encountered in time-to-event or lifetime studies. The analysis of precision of such a solution is based on corresponding theoretical properties of estimated stochastic characteristics. The main concern is to show consistency of optimal solution even in the random censoring case. Behavior of solutions...
On preservation under univariate weighted distributions
We derive some new results for preservation of various stochastic orders and aging classes under weighted distributions. The corresponding reversed preservation properties as straightforward conclusions of the obtained results for the direct preservation properties, are developed. Damage model of Rao, residual lifetime distribution, proportional hazards and proportional reversed hazards models are discussed as special weighted distributions to try some of our results.
On prior distributions which give rise to a dominated Bayesian experiment.
On probabilistic bounds inspired by interval arithmetic
On probabilities in certain multivariate distributions: their dependence on correlations
On probability of first order formulas in a given model
On quantile optimization problem based on information from censored data
Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore,...
On quasi-homogeneous copulas
Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.