The first Pannonian Symposium on Mathematical Statistics [held Bad Tatzmannsdorf from September 16th to 21st, 1979]

The first Pannonian Symposium on Mathematical Statistics was held at Bad Tatzmannsdorf (Burgenland/Austria) from September 16th to 21st, 1979. The aim of it was to furthe~ and intensify scientific cooperation in the Pannonian area, which, in a broad sense, can be understood to cover Hungary, the eastern part of Austria, Czechoslovakia, and parts of Poland, ¥ugoslavia and Romania. The location of centers of research in mathematical statistics and probability theory in this territory has been a good reason for the geographical limitation of this meeting. About 70 researchers attended this symposium, and 49 lectures were delivered; a considerable part of the presented papers is collected in this volume. Beside the lectures, vigorous informal discussions among the participants took place, so that many problems were raised and possible ways of solutions were attacked. We take the opportunity to thank Dr. U. Dieter (Graz), Dr. F. Konecny (Wien), Dr. W. Krieger (G8ttingen) and Dr. E. Neuwirth (Wien) for their valuable help in the refereeing work for this volume. The Pannonian Symposium could not have taken place without the support of several institutions: The Austrian Ministry for Research and Science, the State government of Burgenland, the Community Bad Tatzmannsdorf, the Kurbad Tatzmannsdorf AG, the Austrian Society for Information Science and Statistics, IBM Austria, Volksbank Oberwart, Erste Osterreichische Spar-Casse and Spielbanken AG Austria. The Austrian Academy of Sciences iv made possible the participation in the Symposium for several mathematicians. We express our gratitude to all these institutions for their generous help. Front Matter....Pages i-vi Improvement of Extrapolation in Multiple Time Series....Pages 1-12 Algorithmical Definition of Finite Binary Random Sequence....Pages 13-17 Some Remarks on the BMO Ф Spaces.....Pages 18-24 On Unbiased Estimation of a Common Mean of Two Normal Distributions....Pages 25-29 The Invariance Principle for Vector Valued Random Variables with Applications to Functional Random Limit Theorems....Pages 30-41 Iterated Logarithm Laws for the Square Integral of a Wiener Process....Pages 42-53 Asymptotic properties of the nonparametric survival curve estimators under variable censoring....Pages 54-72 A Local Central Limit Theorem on Some Groups....Pages 73-82 On the Statistics of Gibbsian Processes....Pages 83-93 Efficiency of Estimates in Nonregular Cases....Pages 94-109 Linear Forms in Random Variables Defined on a Homogeneous Markov Chain....Pages 110-121 Parallel processing of random sequences with priority....Pages 122-139 On the Existence of Minimal Complete Classes of Estimators....Pages 140-155 “Eine Bemerkung Zum Vergleich Von Zweiseitigen Testproblemen”....Pages 156-164 Duality of the maximal inequality for non-negative submartingales and of the convexity inequality of Burkholder....Pages 165-173 On a Hoeffding-Type Problem....Pages 174-181 Run-Test Discrimination Between Written Hungarian and Random Sequences....Pages 182-194 Recursive Estimation in the “Almost Smooth” Case....Pages 195-206 How Small are the Increments of a Wiener Sheet?....Pages 207-219 An Approach to the Formula L = λV Via the Theory of Stationary Point Processes on a Space of Compact Subsets of R k ....Pages 220-235 Sequential Estimates of a Regression Function by Orthogonal Series with Applications in Discrimination....Pages 236-244 The Asymptotic Distribution of Certain Goodness of Fit Test Statistics....Pages 245-253 Martingales with Directed Index Set....Pages 254-261 Extensions of Partial Homomorphisms in Probability Theory....Pages 262-265 A Remark on the Strong Law of Large Numbers for Random Indexed Sums....Pages 266-276 A Limit Theorem for Markov Renewal Processes....Pages 277-283 Remark to the Derivation of the Cramér.-Kréchet-Rao Inequality in the Regular Case....Pages 284-289 Nonparametric Density Estimators in Abstract and Homogeneous Spaces....Pages 290-301 Non-Ergodic Stationary Information Sources....Pages 302-305 Back Matter....Pages 306-308