The effect of number of bootstrap samples, trimming proportion and distribution to the results in bootstrap-t and percentile bootstrap methods

Bootstrap yöntemler, kestiricinin veya test istatistiğinin dağılımının bilinmediği durumlarda çıkarsama yapılmasını sağlayan ve eldeki rassal örneklemden tekrarlı olarak yapılan seçimler ile yeni örneklemler türetme ilkesine dayanan yöntemlerdir. Bootstrap yöntemlerde; tekrar sayısı, budanmış ortalama içeren bir yöntem ile birlikte kullanılırlarsa budama yüzdesi ve kitle dağılımının yöntemin performansını nasıl etkilediği tartışılmakta olan konulardır [1-7]. Bu çalışmada; tek örneklem hipotez testi yapmak amacıyla Tukey-McLaughlin testinin [8] bootstrap-t ile birlikte kullanımı ve yüzdelik bootstrap, iki örneklem hipotez testi yapmak amacıyla ise Yuen testinin [9] bootstrap-t ile birlikte kullanımı ve yüzdelik bootstrap yöntemi kullanılmıştır. Bahsedilen yöntemlerin performansları; farklı tekrar sayıları, budama yüzdeleri ve kitle dağılımları kullanılarak gerçekleşen 1. Tip hata değerlerine göre karşılaştırılmıştır. Karşılaştırma bir simülasyon çalışması ve ayrıca iki gerçek veri seti ile yapılmıştır. Kitle budanmış ortalaması için tek ve iki örneklemde hipotez testi yöntemi, budama yüzdesi ve tekrar sayısı için öneriler geliştirilmiştir.Bootstrap methods are procedures which enable to make inference when the distribution of estimator or test statistics is unknown, and based on the principle of generating new samples by using the original random sample with replacement. In bootstrap methods, how number of bootstrap samples, trimming proportion if they are used with a method that involves trimmed mean and population distribution affect the performance of the methods are issues that have been discussed [1-7]. In this study; with the aim of performing one sample hypothesis testing use of Tukey-McLaughlin test [8] with bootstrap-t and percentile bootstrap, and with the aim of performing two samples hypothesis testing use of Yuen test [9] with bootstrap-t and percentile bootstrap are used. The performances of these methods are compared in terms of actual type 1 error rates by using different number of bootstrap samples, trimming proportions and population distributions. The comparison is done with a simulation study by using theoretical distributions and two real data sets. Suggestions for the method to be used, trimming proportion and number of bootstrap samples are developed

Comparing Measures of Location When the Underlying Distribution Has Heavier Tails than Normal

In this study, two conventional (mean and median) and three robust (20% trimmed mean, one-step M-estimator, and modified one-step M-estimator) measures of location are compared in terms of theirasymptotic relative efficiencies and mean squared error when the underlying distribution is contaminatednormal. When n=20, one-step M-estimator was best in five, modified one-step M-estimator was best inthree, and 20% trimmed mean was best in one situation, when n=40, one-step M-estimator and modifiedone-step M-estimator were best in four, 20% trimmed mean was best in one sampling situation covered.&nbsp;</p

New Multilayer Neural Networks With NO Estimator and Winsorized Mean

Multilayer feed forward neural networks have been widely used for prediction, forecastingand classification over the past few years. However, it is a known fact that the mostlypreferred Mc - Culloch Pitts neuron model used in these network types does not give asuccessful prediction performance in data sets with outliers. Therefore, robust neuron modelsusing median and trimmed mean aggregation functions have been proposed. However, thesestudies were generally focused on time series forecasting. In this study, we developed newneuron models using NO estimator and the Winsorized mean for prediction, classification,and time series forecasting. NO is a quantile estimator with weights determined by using asubsampling approach. For estimating a population quantile, it uses all order statistics in asample and the accompanying weights of the order statistics are calculated from a BinomialDistribution. The proposed NO and Winsorized mean neuron models are not sensitive tooutlying observations. Back propagation, particle swarm optimization and artificial beecolony optimization algorithms were used when training multilayer neural networks andseveral activation functions such as sigmoid, hyperbolic, tangent, and rectified linear unitwere tried. All steps of the study were performed using statistical programming language R.The written functions of the proposed neural networks enable the prediction of newobservations and observing the change of errors at each iteration by providing a dynamic plot.The developed methods were applied on the real data sets and their performances werecompared with the existing ones. More successful results were achieved in terms of differentperformance criterions</p

Gözde NAVRUZ 1, * , A. Fırat Özdemir1

The frequently used way of comparing two independent groups is to compare in terms of some measure of location such as mean. For non-normal and heteroscedastic cases, trimmed mean, median or some other robust measures of location can be used instead. However, determination of the differences in the tails of the groups might be of interest. For this reason, comparing the lower and upper quantiles becomes an important issue. In this study, Harrell-Davis estimator and the default quantile estimator of R are compared in terms of actual Type I error rates. When quantiles close to zero or one are compared with small sample sizes Gumbel's estimator, and when quantiles close to median are compared with large sample sizes Harrell Davis estimator saved actual Type I error rate better

LP Methods for Fuzzy Regression and a New Approach

Linear Programming (LP) methods are commonly used to constructfuzzy linear regression (FLR) models. Probabilistic Fuzzy Linear Regression(PFLR) [9] and Unrestricted Fuzzy Linear Regression (UFLR) [3]are two of the mostly applied models that employ LP methods. In this study,a modified fuzzy linear regression model which use LP methods is proposed.PFLR, UFLR and proposed model compared in terms of mean squared error(MSE) and total fuzziness by using two simulated and one real data set.</p