Bickel–Rosenblatt test for weakly dependent data

The aim of this paper is to analyze the Bickel–Rosenblatt test for simple hypothesis in case of weakly dependent data. Although the test has nice theoretical properties, it is not clear how to implement it in practice. Choosing different band-width sequences first we analyze percentage rejections of the test statistic under H0 by some empirical simulation analysis. This can serve as an approximate rule for choosing the bandwidth in case of simple hypothesis for practical implementation of the test. In the recent paper [12] a version of Neyman goodness-of-fit test was established for weakly dependent data in the case of simple hypotheses. In this paper we also aim to compare and discuss the applicability of these tests for both independent and dependent observations

Preliminary results of randomized controlled study on decompressive craniectomy in treatment of malignant middle cerebral artery stroke

Background and Objective. Studies on decompressive craniectomy (DCE) after a malignant middle cerebral artery (MCA) stroke in selected population show an increased probability of survival without increasing the number of very severely disabled. Cerebral infarct volume (CIV) as a triage criterion for performing surgery has not been discussed in literature. The aim of this study was to investigate the value of CIV and initial National Institutes of Health Stroke Scale (NIHHS) and Glasgow Coma Scale (GCS) scores as possible triage criteria in the surgical treatment of patients with " malignant" MCA stroke. Material and Methods. According to the study protocol, 28 patients with a malignant MCA stroke were included and analyzed prospectively. The patients were randomly divided either into the DCE plus best medical treatment (BMT) group or BMT alone group. CIV and NIHHSand GCS scores were measured at time of enrollment in every case. Clinical outcome was evaluated 1 year after the treatment. Results. Six patients survived: 5 in the DCE group (none of them was older than 60 years) and 1 in the BMT group (P=0.03/0.06).Among survivors, none had a cerebral infarct volume of more than 390 cm3 (P=0.05). Allsurvivors inthe DCE group had favorable outcomes. There was no significant difference inthe NIHSS and GCS scores between the groups and survivors/nonsurvivors (P>0.05). Conclusions. Decompressive surgery in the selected patients is likely to increase the probability of survival with a favorable outcome without increasing the number of severely disabled survivors. Patients with CIV of more than 390 cm3 may be bad candidates for DCE, and the prognosis is likely to be bad regardless the treatment strategy. The initial NIHHS and GCS scores did not prove any prognostic value in outcome.publishersversionPeer reviewe

Two‐sample problems in statistical data modelling

A common problem in mathematical statistics is to check whether two samples differ from each other. From modelling point of view it is possible to make a statistical test for the equality of two means or alternatively two distribution functions. The second approach allows to represent the two‐sample test graphically. This can be done by adding simultaneous confidence bands to the probability‐probability (P — P) or quantile‐quantile (Q — Q) plots. In this paper we compare empirically the accuracy of the classical two‐sample t‐test, empirical likelihood method and several bootstrap methods. For a real data example both Q — Q and P — P plots with simultaneous confidence bands have been plotted using the smoothed empirical likelihood and smoothed bootstrap methods. First published online: 09 Jun 201

Konfidenbänder für strukturelle Modelle

Das Ziel dieser Arbeit ist die Konstruktion simultaner Konfidenzbänder für Strukturelle Modelle, die von Freitag (2000) und Freitag und Munk (2005) eingeführt wurden. Wir betrachten den zwei-Stichproben Fall. Dabei sind $X_1, \ldots, X_n$ und $Y_1, \ldots, Y_m$ zwei unabhängige Stichproben mit zugehörigen Verteilungsfunktionen $F_1$ beziehungsweise $F_2$. Das strukturelle Modell $F_1^{-1}(u) = \phi_1(F_2^{-1}(\phi_2(u,h)),h)$ (hier sind $\phi_1$ und $\phi_2$ zweimal differenzierbare reellwertige Funktionen) ist in der Lage verschiedene wichtige Zusammenhänge zwischen den Verteilungsfunktionen $F_1$ und $F_2$ darzustellen. Falls zum Beispiel $\phi_1(t,h) = t + h$ und $\phi_2(u,h) = u$ sind, bekommen wir das wichtige Lokationsmodell.Bei der Konstruktion der Konfidenzbänder schätzen wir zunächst den Parameter $h$, dieser Schätzer wird in die P-P Plot Funktion eingesetzt. Für diese Funktion werden dann mit Hilfe der zwei-Stichproben plug-in empirical Likelihood Methode die Konfidenzbänder konstruiert.Die Arbeit verallgemeinert Hjort's {\sl et al} (2004) Ergebnisse, in der die ein Stichprobe plug-in empirical Likelihood Methode definiert wurde. Eine plug-in Version für empirical Likelihood erlaubt es uns punktweise Konfidenzbänder zu konstruieren. Um simultane Konfidenzbänder zu bekommen, benutzen wir die Methode von Hall und Owen (1993), bei der empirical Likelihood die Gestalt der Bänder bestimmt und die Bootstrap-Methode das Konfidenzniveau festlegt.Claesken's {\sl et al.} (2003) Ergebnisse, bei denen die Konfidenzbänder für gewöhnliche P-P plot Funktionen bezüglich zweier Verteilungsfunktionen $F_1$ und $F_2$ konstruiert wurden, folgt in unserem Arbeit aus dem Spezialfall $\phi_1(t, h) = \phi_2(t, h) = t$. Dabei können die Konfidenzbänder für den P-P und Q-Q plot mit der gleichen Methode konstruiert werden. Dennoch beschränken wir uns auf die Konstruktion von P-P Plot Konfidenzbänder, da sie für strukturelle Modellen in einem gewissen Sinne vorteilhaft sind (siehe z.B. Holmgren im 1995). Darüberhinaus sind P-P Plots sehr interessant, da sie im engen Zusammenhang mit ROC-Kurven (Receiver Operating Characteristic) stehen, welche in der Medizin, Signaltheorie und Psychologie von Bedeutung sind (z.B. see Li, 1996).Speziel für Strukturelle Modelle haben wir eine glatte Version der empirical Likelihood bestimmt, welche die Methode der ein-Stichprobe empirical Likelihood von Chen and Hall (1993) benutzt. Für den Spezialfall des Lokationsmodell haben wir die asymptotischen Überdeckungsniveaus simuliert und Konfidenzbänder für reale Daten konstruiert.The goal of the thesis is to construct the simultaneous confidence bands for structural relationship models introduced by Freitag (2000), Freitag and Munk (2005). Consider the two-sample case, where $X_1, \ldots, X_n$ and $Y_1, \ldots, Y_m$ are independent samples with distribution functions $F_1$ and $F_2$ respectively. The structural relationship model $F_1^{-1}(u) = \phi_1(F_2^{-1}(\phi_2(u,h)),h)$, where $\phi_1$ and $\phi_2$ are some twice differentiable real-valued functions, describes several important relationships between the two distribution functions $F_1$ and $F_2$. For example, if $\phi_1(t,h) = t + h$ and $\phi_2(u,h) = u$ we get the well-known location model.To construct the bands, we first estimate the unknown structural parameter $h$ and plug it in the P-P (probability-probability) plot function of structural relationship models. Further the simultaneous bands have been constructed using the two-sample plug-in empirical likelihood method, which has been established in the thesis.The thesis generalizes Hjort {\sl et al.} (2004) work, where the one-sample plug-in empirical likelihood has been defined. A plug-in version of empirical likelihood allows us to derive the pointwise confidence bands. %for the P-P plot of general structural relationship models. To obtain the simultaneous confidence bands we have used the method introduced by Hall and Owen (1993), where the empirical likelihood method sets the shape of the bands and bootstrap sets the level of the test.Claesken's {\sl et al.} (2003) results, where the confidence bands have been constructed for the usual P-P plot of two distribution functions $F_1$ and $F_2$, follow from our results with functions $\phi_1(t,h) = \phi_2(t,h) = t$. We show also that the P-P and Q-Q (quantile-quantile) plots for the independent samples can be treated in the same way. However, in the context of structural relationship models we found P-P plots advantageous above Q-Q plots. P-P plots have become even more interesting because they are closely related to Receiver Operating Characteristic (ROC) curves, which are important in signal theory, psychology, medicine, etc. (cf. Li {\sl et al.}, 1996).We complete our work with establishing a smoothed version of plug-in empirical likelihood for structural relationship models. To do this we have used the smoothed empirical likelihood method, which has been introduced by Chen and Hall (1993) for the one-sample case. For the location model we simulated the coverage levels and constructed the simultaneous bands for some real data problems

Empirical Likelihood-Based ANOVA for Trimmed Means

In this paper, we introduce an alternative to Yuen’s test for the comparison of several population trimmed means. This nonparametric ANOVA type test is based on the empirical likelihood (EL) approach and extends the results for one population trimmed mean from Qin and Tsao (2002). The results of our simulation study indicate that for skewed distributions, with and without variance heterogeneity, Yuen’s test performs better than the new EL ANOVA test for trimmed means with respect to control over the probability of a type I error. This finding is in contrast with our simulation results for the comparison of means, where the EL ANOVA test for means performs better than Welch’s heteroscedastic F test. The analysis of a real data example illustrates the use of Yuen’s test and the new EL ANOVA test for trimmed means for different trimming levels. Based on the results of our study, we recommend the use of Yuen’s test for situations involving the comparison of population trimmed means between groups of interest

Neyman smooth goodness-of-fit tests for the marginal distribution of dependent data

Neyman’s smooth test, Goodness-of-fit, Strongly mixing process, Implied volatility,