Gamma-Minimax Prediction for the Multinomial Distribution

Characterizations of gamma-minimax predictors for the linear combinations of the unknown parameter and the random variable having the multinomial distribution under arbitrary squared error loss are established in two situations – when the sample size is fixed and when the sample size is a realization of a random variable. It is always assumed that the available vague prior information about the unknown parameter can be described by a class of priors whose vector of first moments belongs to a suitable convex and compact set. Several known gamma-minimax and minimax results can be obtained from the characterizations derived in the present paper.     

Data driven rank test for the change point problem

Data driven test procedure for detection of change is introduced and its properties are studied. The new solution is max-type statistic related to data-driven rank tests for two-sample subproblems. Simulations show that the new test possesses high and stable power. The test is consistent at essentially any alternative. Asymptotic null distribution of the test is derived. The work of the first two authors has been partially supported by the grants GAČR 201/06/0186 and MSM 02160839.     

Distributions of stopping times in some sequential estimation procedures

A class of sequential estimation procedures is considered in the case when relevant data may become available only at random times. The exact distributions of the optimal stopping time and the number of observations at the moment of stopping are derived in some sequential procedures. The results obtained in an explicit form are applied to derive the expected time of observing the process, the average number of observations and the expected loss of sequential estimation procedures based on delayed observations. The use of the results is illustrated in a special model of normally distributed observations and the Weibull distributed lifetimes. The probabilistic characteristics are also derived for an adaptive sequential procedures and the behavior of the adaptive procedure is compared with the corresponding optimal sequential procedure.     

‘Taking on almost everyone?’ Migrant and employer recruitment strategies in a booming labour market

This paper explores the recruitment strategies of employers in the Irish Celtic Tiger boom labour market. It explores Irish employers' turn towards immigrants rather than pursuing other strategies such as raising productivity or mobilising alternative sources of labour. It demonstrates that during the boom years a more casualised approach to recruitment was favoured, privileging soft skills and competencies above credentialised skills. Immigrants became the employees of choice, not least because of issues of costs and obedience, but also because they brought new skills, in particular soft skills. Indeed, employers in some sectors developed a categorical preference for migrant workers as they recruited for attitude, work ethic and potential.     

Bayes sequential estimation for a particular exponential family of distributions under LINEX loss

The problem of sequentially estimating an unknown distribution parameter of a particular exponential family of distributions is considered under LINEX loss function for estimation error and a cost c > 0 for each of an i.i.d. sequence of potential observations X ₁, X ₂, . . . A Bayesian approach is adopted and conjugate prior distributions are assumed. Asymptotically pointwise optimal and asymptotically optimal procedures are derived.     

Minimax estimation of a cumulative distribution function by converting to a parametric problem

Let X = (X ₁,...,X _n ) be a sample from an unknown cumulative distribution function F defined on the real line . The problem of estimating the cumulative distribution function F is considered using a decision theoretic approach. No assumptions are imposed on the unknown function F. A general method of finding a minimax estimator d(t;X) of F under the loss function of a general form is presented. The method of solution is based on converting the nonparametric problem of searching for minimax estimators of a distribution function to the parametric problem of searching for minimax estimators of the probability of success for a binomial distribution. The solution uses also the completeness property of the class of monotone decision procedures in a monotone decision problem. Some special cases of the underlying problem are considered in the situation when the loss function in the nonparametric problem is defined by a weighted squared, LINEX or a weighted absolute error.     

Burn-in for a time-transformed exponential model

The problem of the optimal duration of a burn-in experiment is considered in the case of simultaneous testing n components with the conditionally independent time-transformed exponential life-times, given an unknown parameter. The explicit solution is derived by reformulation of the problem considered to an optimal stopping problem for a suitable defined three-dimensional Markov process and reduction to a free-boundary problem.     

Polish Public Sector Accounting in Transition: Evidence From the Mid 1990s

The Polish public sector is still under transition that began at the turn of 1989/1990. In the mid-1990s a new significant development in public sector accounting took place. A substantial differentiation of the accounting system was introduced. New elements and relationships appeared, along with general domination of the Accounting Act, tax regulations and the Budgetary Law. The system of basic regulation of accounting and reporting has also changed. There were also some changes in the auditing system. The enactment in 1994 of the Accounting Act has brought to light the political character and political importance of financial information in Poland. This paper presents the current mode of public sector accounting regulation and its relationship with the overall system of Polish accounting regulations. Much attention has been devoted to specific principles of public sector accounting and financial reporting in the public sector, and to government accounting. Some political contaminations and consequences of the current accounting system have been pointed out.     

Bayesian prediction in doubly stochastic Poisson process

A stochastic marked point process model based on doubly stochastic Poisson process is considered in the problem of prediction for the total size of future marks in a given period, given the history of the process. The underlying marked point process \((T_{i},Y_{i})_{i\ge 1}\) , where \(T_{i}\) is the time of occurrence of the \(i\) th event and the mark \(Y_{i}\) is its characteristic (size), is supposed to be a non-homogeneous Poisson process on \(\mathbb {R}_{+}^{2}\) with intensity measure \(P\times \varTheta \) , where \(P\) is known, whereas \(\varTheta \) is treated as an unknown measure of the total size of future marks in a given period. In the problem of prediction considered, a Bayesian approach is used assuming that \(\varTheta \) is random with prior distribution presented by a gamma process. The best predictor with respect to this prior distribution is constructed under a precautionary loss function. A simulation study for comparing the behavior of the predictors under various criteria is provided.