Nonparametric tests based on area-statistics

Area statistics are sample versions of areas occuring in a probability plot of two distribution functions F and G. This paper gives a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations such as testing equality of distributions against inequality or testing stochastic dominance in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distribution of these statistics can be calculated via recursion formulae. Two tables with critical values of the new statistics are added. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian Bridge. The distribution functions and quantiles thereof are obtained by Monte-Carlo-Simulation. Finally, the power of two new tests based on area statistics is compared to the power of tests based on corresponding supremum statistics, i.e. statistics of the Kolmogorov-Smirnov type. --Area Statistics,P-P-Plot,Functionals of Brownian Bridge,Monte Carlo Simulation,Nonparametric Tests,Recursion Formulae

Dependence of stock returns in bull and bear markets

Pearson's correlation coefficient is typically used for measuring the dependence structure of stock returns. Nevertheless, it has many shortcomings often documented in the literature. We suggest to use a conditional version of Spearman's rho as an alternative dependence measure. Our approach is purely nonparametric and we avoid any kind of model misspecification. We derive hypothesis tests for the conditional Spearman's rho in bull andbearmarkets and verify the tests by Monte Carlo simulation.Further, we study the daily returns of stocks contained in the German stock index DAX 30. We find some significant differences in dependence of stock returns in bull and bear markets. On the other hand the differences are not so strong as one might expect. --bear market,bootstrapping,bull market,conditional Spearman's rho,copulas,Monte Carlo simulation,stock returns

Shortest Distances as Enumeration Problem

We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements $(u, v, d(u, v))$ -- where $u$ and $v$ are vertices with shortest distance $d(u, v)$ -- are produced and listed one by one without repetition. The performance is measured in the RAM model of computation with respect to preprocessing time and delay, i.e., the maximum time that elapses between two consecutive outputs. This point of view reveals that specific types of output (e.g., excluding the non-reachable pairs $(u, v, \infty)$, or excluding the self-distances $(u, u, 0)$) and the order of enumeration (e.g., sorted by distance, sorted row-wise with respect to the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree. Excluding non-reachable pairs, or requesting the output to be sorted by distance, increases this delay to the order of the maximum degree. Further, for weighted graphs, a delay in the order of the average degree is also not possible without preprocessing or considering self-distances as output. In contrast, for SSSD we find that a delay in the order of the maximum degree without preprocessing is attainable and unavoidable for any of these requirements.Comment: Updated version adds the study of space complexit

TESTING FOR EFFICIENCY: A POLICY ANALYSIS WITH PROBABILITY DISTRIBUTIONS

The study evaluates the efficiency of government intervention using a vertical structured model including imperfectly competitive agricultural input markets, the bread grain market, and the imperfectly competitive food industry. To test for policy efficiency the actually observed bread grain policy is compared to a hypothetical efficient policy. To account for the sensitivity of the results in regard to the model parameter values computer-intensive simulation procedures and surface response functions are utilized.agricultural policy, efficient combination of policy instruments, statistical policy analysis, Productivity Analysis,

Was the Austrian agricultural policy least cost efficient?

The study evaluates the efficiency of government intervention using a vertical structured model including imperfectly competitive agricultural input markets, the bread grain market, and the imperfectly competitive food industry. To test for policy efficiency the actually observed bread grain policy is compared to a hypothetical efficient policy. To account for the sensitivity of the results in regard to the model parameter values computer-intensive simulation procedures and surface response functions are utilized.agricultural policy; efficient combination of policy instruments; statistical welfare analysis

On the politicization of intergovernmental fiscal relations in Germany after unification

A recent decision of the German Constitutional Court requires political decision makers to revise the system of intergovernmental transfers in order to limit free bargaining among state and federal government officials. The present paper provides empirical support for the thesis that political discretion has become increasingly important in the transfer negotiations after Unification. We attempt to show why political influences gained weight relative to economic considerations in the determination of net gains. This politicization of the fiscal transfer system appears to be a consequence of the inability of policy makers to agree on a fundamental reform in the early 1990's.

Magnetoelectric Cr_2 O_3 and relativity theory

Relativity theory is useful for understanding the phenomenology of the magnetoelectric effect of the antiferromagnet chromium sesquioxide Cr_2 O_3 in two respects: (i) One gets a clear idea about the physical dimensions of the electromagnetic quantities involved, in particular about the dimensions of the magnetoelectric moduli that we suggest to tabulate in future as dimensionless relative quantities; (ii) one can recognize and extract a temperature dependent, 4-dimensional pseudoscalar from the data of magnetoelectric experiments with Cr_2 O_3. This pseudoscalar piece of Cr_2 O_3 is odd under time reflections and parity transformations and is structurally related ("isomorphic") to the gyrator of electric network theory, the axion of particle physics, and the perfect electromagnetic conductor of electrical engineering.Comment: 9 pages latex, seminar at the Workshop on Magnetoelectric Interaction Phenomena in Crystals (MEIPIC-6), 25-28 Jan. 2009, Santa Barbara, US

Nonparametric inference for second order stochastic dominance

This paper deals with nonparametric inference for second order stochastic dominance of two random variables. If their distribution functions are unknown they have to be inferred from observed realizations. Thus, any results on stochastic dominance are in uenced by sampling errors. We establish two methods to take the sampling error into account. The first one is based on the asymptotic normality of point estimators, while the second one, relying on resampling techniques, can also cope with small sample sizes. Both methods are used to develop statistical tests for second order stochastic dominance. We argue, however, that tests based on resampling techniques are more useful in practical applications. Their power in small samples is estimated by Monte Carlo simulations for a couple of alternative distributions. We further show that these tests can also be used for testing for first order stochastic dominance, often having a higher power than tests specifically designed for first order stochastic dominance such as the Kolmogorov-Smirnov test or the Wilcoxon-Mann-Whitney test. The results of this paper are relevant in various fields such as finance, life testing and decision under risk. --second order stochastic dominance,nonparametric inference,permutation tests,Monte Carlo methods

Memory Bounded Open-Loop Planning in Large POMDPs using Thompson Sampling

State-of-the-art approaches to partially observable planning like POMCP are based on stochastic tree search. While these approaches are computationally efficient, they may still construct search trees of considerable size, which could limit the performance due to restricted memory resources. In this paper, we propose Partially Observable Stacked Thompson Sampling (POSTS), a memory bounded approach to open-loop planning in large POMDPs, which optimizes a fixed size stack of Thompson Sampling bandits. We empirically evaluate POSTS in four large benchmark problems and compare its performance with different tree-based approaches. We show that POSTS achieves competitive performance compared to tree-based open-loop planning and offers a performance-memory tradeoff, making it suitable for partially observable planning with highly restricted computational and memory resources.Comment: Presented at AAAI 201

A multivariate extension of the Lorenz curve based on copulas and a related multivariate Gini coefficient

We propose an extension of the univariate Lorenz curve and of the Gini coefficient to the multivariate case, i.e., to simultaneously measure inequality in more than one variable. Our extensions are based on copulas and measure inequality stemming from inequality in each single variable as well as inequality stemming from the dependence structure of the variables. We derive simple nonparametric estimators for both instruments and exemplary apply them to data of individual income and wealth for various countries