摘要:

After a survey on different results about the estimation of regression functions in inadquate models the risks of three estimators: the BLUE in the adequate model, the BLU Approgression and the biased OLSE in the inadequate model are calculated and compared. The optimality regions are discussed. On the basis of this results empirical composed procedures are proposed.

ISSN:0047-6277    

DOI:10.1080/02331887508801207

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

A random variableYwith the distributionPY⊝is considered. Based on a sample we have to astimate ψ(⊝). We look for optimal estimators which are robust against the loss function and robust against the sample distribution. A suitable approach for this are semi-orderings between distribution functions closely relsted to convex or monotone loss functions. The obtained results are applicable to estimators in the linear regression model, especially to the robutness of the usual GAUSS-MARKOV-estimator.

ISSN:0047-6277    

DOI:10.1080/02331887508801208

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In this paper the balanced two-way cross clossification model with random effects and without interactions is considered and it is proved-without assuming a specific distribution for the random effects-that the HENDERSON estimator is the uniformly best quadratic unbiased estimator.

ISSN:0047-6277    

DOI:10.1080/02331887508801209

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

This is a study of the robustness of the characteristics of usual tests for the comparison of a mean value with a given value or the comparision of two means, if the successive GAUSSian observations are not independent. The counter models (Xt),t∈N+, for non-independence are characterized by their authocorrelations and are such that EXt=μ, VarXt=σ2. Furthermore, M1is a stationary MARKOV process; M2is a stationary model so that the firstmauthocorrelation coeffficients are different from zero; M3is the model of the symmetry condition: ↭k∈N+: Corr (XtXt+k) = ρ = const,. It seems that the choice of these models covers a vast set of situations. – At first, conditions for a class M′ of models (including M1and M2) are established which, for instance, imply the quadratic mean convergence of the usual mean estimators (and variance estimators) to μ (and σ2) as well as the existence of a certain bias parameter. The bias equations for the samples, and for the test-power function, are established for each model. In the model M3the study is non-asymptotic, while in model M′ it is asumptotic. In all cases a bias parameter is obtained that is independent of the parameters being tested. Its value determines the sign and the amplitude of the bias. The bias is large also for the dependence levels in some cases. However, the amplitudes depend on the counter model; the tests become less robust when the autocorrelations increase in absolute value maintaining the same sign.

ISSN:0047-6277    

DOI:10.1080/02331887508801210

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Maximum likelihood estimates are obtained for the probilitiespkof the GALTON-WATSON branching process based on a sample (x0,x, …,xn) from the process. Some interesting models are considered by specializing thepk. A reasonable modification of the method kof observation is given for obtaining properties of the estimators (consistency, asymptotic normality).

ISSN:0047-6277    

DOI:10.1080/02331887508801211

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

The probability of the error of the second kind in the two-sample problems is often of the formfor a given θ in the alternative hypothesis, whereRm,nis a random variable converging in Pθ-probability to zero. Generalizing some results of H. CHERNOFF [1] we can show that probabilities of this type sometimes converge to zero with an exponecntial convergence rate, and we can compute this exponential convergence rate for probabilities of the error of the second kind for some two-sample tests.

ISSN:0047-6277    

DOI:10.1080/02331887508801213

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Results in the theory of the optimum design of regression experiments are used to develop experimental designs for detecting departures from a single regression model with quantitative factors. Because these designs may not be efficient for estimating the parameters of the model if it is adequate, multipurpose designs are developed which can be used both for model testing and parameter estimation. The properties of these designs are established using an extension of the KIEFER-WOLFOWITZ general equivalence theorem. This extension is then used to develop non-sequential designs for discriminating between several models. A sequential data-dependent strategy is derived from this non-sequential scheme and discussed in relationship to other sequential experimental strategies. The paper closes with a few remarks on numerical methods which have been found useful in the construction of experimental designs.

ISSN:0047-6277    

DOI:10.1080/02331887508801214

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

A survey of the latest results in nonparametric hypotheses testing and in nonparametric estimation is given. At first, two main hypotheses usually handled by rank tests, these of randomness and of symmetry, are defined and the locally most powerful rank tests for them described. Aymptotic efficiency considerations are included. In the second part, four rank-estimation procedures for the multiple regression model rue considered. Three of them (those of JUREČKOVÁ, JAECKEL and KOUL) are asymptotically equivalent one to another, the fourth one (KRAFT, VAN EEDEN) combines the classical least-squares estimate with ranks. If the supposed distribution equals to the real one, any of these procedures is asymptotically efficient, as may be seen from the correspondingasymptotic distributions.

ISSN:0047-6277    

DOI:10.1080/02331887508801215

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

An extension of a central limit theorem of F. EICKER for linear vector forms is used to derive conditions for the asymptotic normality of Least-Square Estimators in multivariate linear singular models with stochastically independent error terms. These conditions are shown to be necessary too in some cases. Several previous results concerning asymptotic normality of Least-Square Estimators in regular models are special cases of the theory developed in this paper.

ISSN:0047-6277    

DOI:10.1080/02331887508801216

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In this paper we consider the problems of estimation and prodiction for linear models in locally convex topological vector-spaces. Therefore let firstybe a random element in a locally convex topological vector-spaceHwhich is known to have an expectationEy∈L⫅Hand to have a set of covariancesV, whereVis a continuous semi-inner product onH*×H*. 12 conditions are shown to be equivaient in order that Gy(G:H→Ha linear operator) is a best linear unbiased continuous estimator (BLUCE) of Ey (GAUSS-MARKOV-theorem). After this we consider a random elementy*in a locally convex topological vector-spaceKsuch thatEy*=T(Ey) +l1:l1⫅L1⫅K,Ta linear operator. The optimal linear unbiased predictor (BLUP)G0y of y*is determined and the connection between estimation and prediction is ostablished. An introduetory section sketehes the historical development of the GAUSS-MARKOV-theorem while a second section is developing the essential mathematical tools for GAUSS-MARKOV-theory: a projection theorem for quasi-inner products and the (generalized) FARKAS-MINKOWSKI-theorem.

ISSN:0047-6277    

DOI:10.1080/02331887508801217

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor