## Mathematical Statistics and Probability Theory: Volume A Theoretical Aspects Proceedings of the 6th Pannonian Symposium on Mathematical Statistics, Bad Tatzmannsdorf, Austria, September 14–20, 1986Madan L. Puri, P. Révész, Wolfgang Wertz, P. Bauer, F. Konecny The past several years have seen the creation and extension of a very conclusive theory of statistics and probability. Many of the research workers who have been concerned with both probability and statistics felt the need for meetings that provide an opportunity for personal con tacts among scholars whose fields of specialization cover broad spectra in both statistics and probability: to discuss major open problems and new solutions, and to provide encouragement for further research through the lectures of carefully selected scholars, moreover to introduce to younger colleagues the latest research techniques and thus to stimulate their interest in research. To meet these goals, the series of Pannonian Symposia on Mathematical Statistics was organized, beginning in the year 1979: the first, second and fourth one in Bad Tatzmannsdorf, Burgenland, Austria, the third and fifth in Visegrad, Hungary. The Sixth Pannonian Symposium was held in Bad Tatzmannsdorf again, in the time between 14 and 20 September 1986, under the auspices of Dr. Heinz FISCHER, Federal Minister of Science and Research, Theodor KERY, President of the State Government of Burgenland, Dr. Franz SAUERZOPF, Vice-President of the State Govern ment of Burgenland and Dr. Josef SCHMIDL, President of the Austrian Sta tistical Central Office. The members of the Honorary Committee were Pal ERDOS, WXadisXaw ORLICZ, Pal REVESz, Leopold SCHMETTERER and Istvan VINCZE; those of the Organizing Committee were Wilfried GROSSMANN (Uni versity of Vienna), Franz KONECNY (University of Agriculture of Vienna) and, as the chairman, Wolfgang WERTZ (Technical University of Vienna). |

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### Contents

Multivariate Extremal Models under NonClassical Situations | 1 |

Large Deviations and Bahadur Efficiency of Some Rank Tests of Independence | 11 |

On Some Observing and Replacement Policies | 25 |

On Strong Consistency of Kernel Estimators under Dependence Assumptions | 33 |

A Limit Theorem for Some Modified ChiSquare Statistics when the Number of Classes Increases | 43 |

Problems and Results on Random Walks | 59 |

On the Maximum Likelihood Method for Censored Bivariate Samples | 67 |

A Characterization Theorem Based on Truncated Moments and its Application to Some Distribution Families | 75 |

On Exponential Autoregressive Time Series Models | 147 |

Some Connections between Statistics and Control Theory | 155 |

Maximum Waiting Time when the Size of the Alphabet Increases | 169 |

On Bayes Inference in Contingency Tables | 179 |

Sequential Estimation Functions in Stochastic Population Processes | 189 |

Estimation Quadratic Polynomials with Applications to Square Root Normalizing Transformations | 205 |

A kSample Problems with Censored Data | 215 |

An Optimal kStopping Problem for the Poisson Process | 231 |

A Class of NonParametrically Constructed Parameter Estimators for a Stationary Autoregressive Model | 85 |

Selecting the Best Unknown Mean from Normal Populations Having a Common Unknown Coefficient of Variation | 97 |

The Extreme Linear Predictions of the MatrixValued Stationary Stochastic Processes | 113 |

Multivariate BSpline Analysis of Contingency Tables and Serial Correlation | 125 |

Discrimination between Stationary Gaussian Time Series | 139 |

A Statistical Approach to Relaxation in Glassy Materials | 245 |

255 | |

261 | |

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applications assume assumptions asymptotic normality autoregressive B-splines Bad Tatzmannsdorf Bahadur efficiency Bauer Bayes Bayes estimator bounded censored chi-square coefficient of variation condition consider constant convergence covariance credible intervals defined denote density function derived Dirichlet Dirichlet distributed distribution function equation Erdos exponential favourite values finite given Gupta Hence independent inequality integer large deviations Ledwina Lemma limit theorem Markov processes Math Mathematical Statistics matrix matrix-valued maximum likelihood mean multinomial distribution multivariate extremal normal distribution observations obtain optimal order statistics p-stable parameters Pearson Type Poisson process positive Probability Theory problem Proof properties quadratic random variables random walk regression Reidel Publishing Company Rukhin sample satisfies Schick Section selection rule sequence sequential estimation serial correlation Spearman's rho stationary Statistics and Probability stochastic subset selection test statistic tions unknown variance vector Wiener process