Walter Katzenbeisser

The exact power of two-sample location tests based on exceedance statistics against shift alternatives

The exact power of two-sample location tests based on exceedance statistics against shifts in exponential-, logistic- and rectangular distributions is derived. As an example; the exact power functions for the MANN-WHITNEY-WILCOXON, the MOOD-WESTENBERG and the MATHISEN test for shifts in exponential distributions is compared

Asymptotic results on the maximal deviation of simple random walks

This paper deals with the maximal one and two sided deviation of simple random walks. The remarkable asymptotic results of Kemperman, concerning the related conditional distribution functions are generalized. Moreover, exact enumeration formulae for the moments are given and their asymptotic equivalents are derived.

Simple Random Walk Statistics. Part I: Discrete Time Results

In a famous paper Dwass [I9671 proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows to extend Dwasss results in several ways, viz. arbitrary endpoints, horizontal steps, and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process. (authors abstract)

ON THE NUMBER OF TIMES WHERE A SIMPLE RANDOM WALK REACHES ITS MAXIMUM

Let Q, denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important r6le in probability and statistics. In this paper the distribution and the moments of Q, are considered and their asymptotic behavior is studied. (authors abstract)

Lattice Path Counting, Simple Random Walk Statistics, and Randomization: An Analytic Approach

In this paper an approach to lattice paths, simple random walks and randomized random walks is presented, which emphasizes the common features and permits to treat various aspects in a unified framework.

Some further results on the height of lattice paths

This paper deals with the joint and conditional distributions concerning the maximum of random walk paths and the number of times this maximum is achieved. This joint distribution was studied first by Dwass [1967]. Based on his result, the correlation and some conditional moments are derived. The main contributions are however asymptotic expansions concerning the conditional distribution and conditional moments. (authors abstract)

The Maximal Height of Simple Random Walks Revisited

In a recent paper Katzenbeisser and Panny (1996) derived distributional results for a number of so called simple random walk statistics defined on a simple random walk in the sense of Cox and Miller (1968) starting at zero and leading to state 1 after n steps, where 1 is arbitrary, but fix. In the present paper the random walk statistics Dn = the one-sided maximum deviation and Qn = the number of times where the maximum is achieved, are considered and distributional results are presented, when it is irrespective, where the random walk terminates after n steps. Thus, the results can be seen as generalizations of some well known results about (purely) binomial random walk, given e.g. in Revesz (1990). (authors abstract)

On the number of times a simple random walk reaches a onnegative height

The purpose of this note is to derive distributional properties of the random variable associated with the number of visits to state r r ≥ 0 during the interval [0,n] of a simple random walk. The random walk is defined in the sense of Cox and Miller, allowing for three step-types, arbitrary probabilities for these steps, and arbitrary terminating state after n steps. It is also shown that some well known results can be obtained as specializations of two general Theorems

Die relative asymptotische Effizienz der Prognoseschätzung mit einem ökonometrischen Modell

ZusammenfassungDie relative asymptotische Effizienz der Prognoseschätzung mit Hilfe der reduzierten Form eines ökonometrischen Modells wird untersucht, wobei die zwei Fälle „unrestricted“- und „derived reduced form“ betrachtet werden.SummaryThe relative asymptotic efficiency of forecasts by means of an econometric model, based on the “unrestricted”- and the “derived reduced form” is considered.