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 Electronic Journal of Applied Statistical Analysis , 2008, DOI: 10.1285/i20705948v1n1p1 Abstract: Balanced groups ranked set samples method (BGRSS) is suggested for estimating the population mean with samples of size m=3k where (k=1,2,...). The BGRSS sample mean is considered as an estimator of the population mean. It is found that the BGRSS produces unbiased estimators with smaller variance than the commonly used simple random sampling (SRS) for symmetric distributions considered in this study. For asymmetric distributions that we considered, the BGRSS estimators have a small bias. A real data set is used to illustrate the BGRSS method.
 Janusz Garecki Physics , 2007, Abstract: Recently some authors concluded that the energy and momentum of the Fiedman universes, flat and closed, are equal to zero locally and globally (flat universes) or only globally (closed universes). The similar conclusion was also done for more general only homogeneous universes (Kasner and Bianchi type I). Such conclusions originated from coordinate dependent calculations performed only in comoving Cartesian coordinates by using the so-called {\it energy-momentum complexes}. By using new coordinate independent expressions on energy and momentum one can show that the Friedman and more general universes {\it needn't be energetic nonentity}.
 Julien Berestycki Mathematics , 2006, DOI: 10.1051/ps:2002009 Abstract: In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of these two types of fragmentations. We then give an explicit construction of homogeneous ranked fragmentations in terms of Poisson point processes. Finally we use this construction and classical results on records of Poisson point processes to study the small-time behavior of a ranked fragmentation.
 Respiratory Research , 2005, DOI: 10.1186/1465-9921-6-101 Abstract: Results from cross-sectional analysis, repeated measures on complete cases (ANOVA), and a multi-level analysis were compared. The scores on the dimension 'energy' of the Nottingham Health Profile (NHP) after transplantation were used to illustrate the differences between methods.Compared to repeated measures ANOVA, the cross-sectional and multi-level analysis included more patients, and allowed for a longer period of follow-up. In contrast to the cross sectional analyses, in the complete case analysis, and the multi-level analysis, the correlation between different time points was taken into account. Patterns over time of the three methods were comparable. In general, results from repeated measures ANOVA showed the most favorable energy scores, and results from the multi-level analysis the least favorable. Due to the separate subgroups per time point in the cross-sectional analysis, and the relatively small number of patients in the repeated measures ANOVA, inclusion of predictors was only possible in the multi-level analysis.Results obtained with the various methods of analysis differed, indicating some reduction of bias took place. Multi-level analysis is a useful approach to study changes over time in a data set where missing data, to reduce bias, make efficient use of available data, and to include predictors, in studies concerning the effects of LgTX on HRQL.Lung transplantation has become an accepted treatment option for appropriately selected patients with end-stage lung disease. Besides clinical outcome measures such as survival, Health Related Quality of Life (HRQL) has become an increasingly important endpoint in studies regarding the effectiveness of lung transplantation. Studies in which HRQL was included as an outcome measure generally report improvements across many domains of HRQL after lung transplantation [1-7]. The aim of the present study was twofold. First, to address the problem of missing data in the field of HRQL and lung transplantation, and
 Pakistan Journal of Statistics and Operation Research , 2011, DOI: 10.1234/pjsor.v7i2-sp.285 Abstract: This study investigates an application of Friedman statistic as a model selection methodology on post estimation data. The Friedman statistic is employed for testing the possible differences between related samples by ranking the data. Similarly, we suggest ranking of competing models based on a specific multiple comparison procedure for identifying differences between models. As a non-parametric test statistic, it does not make assumptions regarding the underlying distribution of data, however, this procedure may require a large dataset since it relies on post estimation comparisons.
 Statistics , 2012, Abstract: In this paper we tackle the ANOVA problem for directional data (with particular emphasis on geological data) by having recourse to the Le Cam methodology usually reserved for linear multivariate analysis. We construct locally and asymptotically most stringent parametric tests for ANOVA for directional data within the class of rotationally symmetric distributions. We turn these parametric tests into semi-parametric ones by (i) using a studentization argument (which leads to what we call pseudo-FvML tests) and by (ii) resorting to the invariance principle (which leads to efficient rank-based tests). Within each construction the semi-parametric tests inherit optimality under a given distribution (the FvML distribution in the first case, any rotationally symmetric distribution in the second) from their parametric antecedents and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simulation. We conclude by applying our findings on a real-data example involving geological data.
 Janusz Garecki Physics , 2012, Abstract: We show in the paper that Friedman universes can be created from empty, flat Minkowski spacetime by using suitable conformal rescaling of the spacetime metric.
 Mariusz P. Dabrowski Physics , 1995, DOI: 10.1006/aphy.1996.0057 Abstract: The non-singular, oscillating Friedman cosmology within the framework of General Relativity is considered. The general oscillatory solution given in terms of elliptic functions and the conditions for its existence are discussed. It is shown that the wall-like-matter and the small, but negative cosmological constant are required for oscillations. The oscillations can , in principle, be deep enough to allow standard hot universe processes like recombination and nucleosynthesis. It is shown that the wall-like-matter and string-like-matter can be interpreted as scalar fields with some potentials. This may give another candidate for the dark matter which may be compatible with observational data. For an exact elementary oscillatory solution it is shown that the associated scalar field potential is oscillating as well.
 Mathematics , 2006, DOI: 10.1214/009053606000000452 Abstract: It\^{o} processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such It\^{o} processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term. The proposed methodology, ANOVA for diffusions and It\^{o} processes,'' can be used to measure the statistical quality of a parametric model and, nonparametrically, the appropriateness of a one-regressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.
 Statistics , 2013, Abstract: Ranked set sampling is a sampling design which has a wide range of applications in industrial statistics, and environmental and ecological studies, etc.. It is well known that ranked set samples provide more Fisher information than simple random samples of the same size about the unknown parameters of the underlying distribution in parametric inferences. In this paper, we consider the uncertainty and information content of ranked set samples in both perfect and imperfect ranking scenarios in terms of Shannon entropy, R\'enyi and Kullback-Leibler (KL) information measures. It is proved that under these information measures, ranked set sampling design performs better than its simple random sampling counterpart of the same size. The information content is also a monotone function of the set size in ranked set sampling. Moreover, the effect of ranking error on the information content of the data is investigated.
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