EconStor Community:
http://hdl.handle.net/10419/175
2016-05-06T05:49:54ZConsistency of the kernel density estimator - a survey
http://hdl.handle.net/10419/39692
Title: Consistency of the kernel density estimator - a survey
Authors: Wied, Dominik; Weißbach, Rafael
Abstract: Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions is sufficient for strong consistency, proofs of exact convergence rates use deeper information about the underlying empirical processes. A unifying character, however, is that earlier and more recent proofs use bounds on the probability that a sum of random variables deviates from its mean.2010-01-01T00:00:00ZD-optimal plans for variable selection in data bases
http://hdl.handle.net/10419/41052
Title: D-optimal plans for variable selection in data bases
Authors: Schiffner, Julia; Weihs, Claus
Abstract: This paper is based on an article of Pumplün et al. (2005a) that investigates the use of Design of Experiments in data bases in order to select variables that are relevant for classification in situations where a sufficient number of measurements of the explanatory variables is available, but measuring the class label is hard, e. g. expensive or time-consuming. Pumplün et al. searched for D-optimal designs in existing data sets by means of a genetic algorithm and assessed variable importance based on the found plans. If the design matrix is standardized these D-optimal plans are almost orthogonal and the explanatory variables are nearly uncorrelated. Thus Pumplün et al. expected that their importance for discrimination can be judged independently of each other. In a simulation study Pumplün et al. applied this approach in combination with five classification methods to eight data sets and the obtained error rates were compared with those resulting from variable selection on the basis of the complete data sets. Based on the D-optimal plans in some cases considerably lower error rates were achieved. Although Pumplün et al. (2005a) obtained some promising results, it was not clear for different reasons if D-optimality actually is beneficial for variable selection. For example, D-efficiency and orthogonality of the resulting plans were not investigated and a comparison with variable selection based on random samples of observations of the same size as the D-optimal plans was missing. In this paper we extend the simulation study of Pumplün et al. (2005a) in order to verify their results and as basis for further research in this field. Moreover, in Pumplün et al. D-optimal plans are only used for data preprocessing, that is variable selection. The classification models are estimated on the whole data set in order to assess the effects of D-optimality on variable selection separately. Since the number of measurements of the class label in fact is limited one would normally employ the same observations that were used for variable selection for learning, too. For this reason in our simulation study the appropriateness of D-optimal plans for training classification methods is additionally investigated. It turned out that in general in terms of the error rate there is no difference between variable selection on the basis of D-optimal plans and variable selection on random samples. However, for training of linear classification methods D-optimal plans seem to be beneficial.2009-01-01T00:00:00ZInterventions in ingarch processes
http://hdl.handle.net/10419/41051
Title: Interventions in ingarch processes
Authors: Fokianos, Konstantions; Fried, Roland
Abstract: We study the problem of intervention effects generating various types of outliers in a linear count time series model. This model belongs to the class of observation driven models and extends the class of Gaussian linear time series models within the exponential family framework. Studies about effects of covariates and interventions for count time series models have largely fallen behind due to the fact that the underlying process, whose behavior determines the dynamics of the observed process, is not observed. We suggest a computationally feasible approach to these problems, focusing especially on the detection and estimation of sudden shifts and outliers. To identify successfully such unusual events we employ the maximum of score tests, whose critical values in finite samples are determined by parametric bootstrap. The usefulness of the proposed methods is illustrated using simulated and real data examples.2009-01-01T00:00:00ZOptimal designs for an interference model
http://hdl.handle.net/10419/41046
Title: Optimal designs for an interference model
Authors: Kunert, Joachim; Mersmann, Sabine
Abstract: Kunert and Martin (2000) determined optimal and efficient block designs in a model for field trials with interference effects, for block sizes up to 4. In this paper we use Kushner's method (Kushner, 1997) of finding optimal approximate designs to extend the work of Kunert and Martin (2000) to optimal designs with five or more plots per block. We give an overall upper bound a*t,b,k for the trace of the information matrix of any design and show that an universally optimal approximate design will have all its sequences from merely four different equivalence classes. We further determine the efficiency of a binary type I orthogonal array under the general p-criterion. We find that these designs achieve high efficiencies of more than 0:94.2009-01-01T00:00:00Z