301 research outputs found
Numerical studies for the Rasch model with many items
No full textThis paper is concerned with numerical studies on the theoretical results obtained in Strasser [1] and [2]. These papers provide asymptotic expansions for conditional expectations of non i.i.d. Bernoulli trials and their application to the covariance structure of conditional maximum likelihood estimates for the Rasch model. In the present paper systematic numerical studies of the accuracy of the approximations given in Strasser [1] and [2] are presented. It is shown that the order of approximation claimed by the theoretical results can be established numerically. (author's abstract)Series: Research Report Series / Department of Statistics and Mathematic
Neuere Entwicklungen in der Konzentrationsmessung
No full textA general approach for the quantization of statistical data and distributionsis considered. The concept is closely related to the statistical measurementof concentration and to the mathematical theory of majorization. Inparticular, it is the theoretical basis of those compression algorithms whichare analysed by P¨otzelberger and Strasser (2001).</jats:p
Perturbation invariant estimates and incidental nuisance parameters
No full textIt is shown (Proposition (3.9)) that the asymptotic information bound which is valid for the estimation of a parameter in the structure (mixture) model remains valid in the functional model (incidental nuisance parameters) if only perturbation symmetric estimators (Definition (3.6)) are admitted. Pertur- bation symmetry is a property which is closely related to permutation symmetry (Theorem (3.4)). In particular, equicontinuous functions of empirical processes are perturbation symmetric (Theorem (3.3)). Thus, the results of this paper continue a discussion initiated by Bickel and Klaassen (1986), Pfanzagl (1993) and Strasser (1996) on permutation symmetry of estimators and the exclusion of superefficiency in the functional model. (authors' abstract)Series: Forschungsberichte / Institut für Statisti
The covariance structure of conditional maximum likelihood estimates
No full textIn this paper we consider conditional maximum likelihood (cml) estimates for
item parameters in the Rasch model under random subject parameters. We give
a simple approximation for the asymptotic covariance matrix of the cml-estimates.
The approximation is stated as a limit theorem when the number of item parameters
goes to infinity. The results contain precise mathematical information on the order
of approximation.
The results enable the analysis of the covariance structure of cml-estimates when
the number of items is large. Let us give a rough picture. The covariance matrix has
a dominating main diagonal containing the asymptotic variances of the estimators.
These variances are almost equal to the efficient variances under ml-estimation when
the distribution of the subject parameter is known. Apart from very small numbers
n of item parameters the variances are almost not affected by the number n. The
covariances are more or less negligible when the number of item parameters is large.
Although this picture intuitively is not surprising it has to be established in precise
mathematical terms. This has been done in the present paper.
The paper is based on previous results [5] of the author concerning conditional
distributions of non-identical replications of Bernoulli trials. The mathematical background
are Edgeworth expansions for the central limit theorem. These previous results
are the basis of approximations for the Fisher information matrices of cmlestimates.
The main results of the present paper are concerned with the approximation
of the covariance matrices.
Numerical illustrations of the results and numerical experiments based on the
results are presented in Strasser, [6]. (author's abstract
On the Asymptotic Theory of Permutation Statistics
No full textIn this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned by the sigma-field of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general contiguous alternatives with independent but not identically distributed observations. The proofs are based on results on limit theorems for exchangeable random variables by Strasser and Weber. The limit theorems under contiguous alternatives are consequences of an LAN-result for likelihood ratios of symmetrized product measures. The results of the paper have implications for statistical applications. By example it is shown that minimum variance partitions which are defined by observed data (e.g. by LVQ) lead to asymptotically optimal adaptive tests for the k-sample problem. As another application it is shown that conditional k-sample tests which are based on data-driven partitions lead to simple confidence sets which can be used for the simultaneous analysis of linear contrasts. (author's abstract)Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science
Author comment on RC4: 'Review of Strasser et al.: Rofental catchment', Adam Winstral, 02 Oct 2017
No full text
- …
