a comparison of snr estimation techniques for the awgn channel the performances of several signal to noise ratio snr estimation techniques reported in the literature are compared to identify the best estimator the snr estimators are investigated by the computer simulation of baseband binary phase shift keying psk signals in real additive white gaussian noise awgn and baseband 8 psk signals in complex awgn the mean square error is used as a measure of performance in addition to comparing the relative performances the absolute levels of performance are also established the simulated performances are compared to a published cramer rao bound crb for real awgn and a crb for complex awgn that is derived here some known estimator structures are modified to perform better on the channel of interest estimator structures for both real and complex channels are examined

finite time stability of impulsive reaction diffusion systems with and without time delay abstract this paper considers the finite time stability of impulsive reaction diffusion systems irdss we deal with two cases systems without time delay and systems with time delay when there is no delay in the considered system we obtain sufficient conditions to guarantee the finite time stability of irdss via two representations of impulsive sequences when time delay enters into irdss we adopt a comparison method to deal with the finite time stability and provide sufficient conditions ensuring the finite time stability we also present the differences of finite time stability and asymptotic stability for the irdss moreover in our sufficient conditions we show the effects of impulse diffusion and spatial domain on the finite time stability and discuss the effect of time delay on the stability numerical simulations are carried out to show the effectiveness of our obtained results

weighted rank regression for clustered data analysis we consider ranked based regression models for clustered data analysis a weighted wilcoxon rank method is proposed to take account of within cluster correlations and varying cluster sizes the asymptotic normality of the resulting estimators is established a method to estimate covariance of the estimators is also given which can bypass estimation of the density function simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure presence absence of outliers and different correlation values the proposed methods appear to perform well in particular the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers a real example is provided for illustration

a weighted multivariate sign test for cluster correlated data we consider the multivariate location problem with cluster correlated data a family of multivariate weighted sign tests is introduced for which observations from different clusters can receive different weights under weak assumptions the test statistic is asymptotically distributed as a chi squared random variable as the number of clusters goes to infinity the asymptotic distribution of the test statistic is also given for a local alternative model under multivariate normality optimal weights maximizing pitman asymptotic efficiency are provided these weights depend on the cluster sizes and on the intracluster correlation several approaches for estimating these weights are presented using pitman asymptotic efficiency we show that appropriate weighting can increase substantially the efficiency compared to a test that gives the same weight to each cluster a multivariate weighted t test is also introduced the finite sample performance of the weighted sign test is explored through a simulation study which shows that the proposed approach is very competitive a real data example illustrates the practical application of the methodology

marginal analyses of clustered data when cluster size is informative we propose a new approach to fitting marginal models to clustered data when cluster size is informative this approach uses a generalized estimating equation gee that is weighted inversely with the cluster size we show that our approach is asymptotically equivalent to within cluster resampling hoffman sen and weinberg 2001 biometrika 73 13 22 a computationally intensive approach in which replicate data sets containing a randomly selected observation from each cluster are analyzed and the resulting estimates averaged using simulated data and an example involving dental health we show the superior performance of our approach compared to unweighted gee the equivalence of our approach with wcr for large sample sizes and the superior performance of our approach compared with wcr when sample sizes are small

power and sample size estimation for the clustered wilcoxon test the wilcoxon rank sum test is widely used for two group comparisons of nonnormal data an assumption of this test is independence of sampling units both within and between groups which will be violated in the clustered data setting such as in ophthalmological clinical trials where the unit of randomization is the subject but the unit of analysis is the individual eye for this purpose we have proposed the clustered wilcoxon test to account for clustering among multiple subunits within the same cluster rosner glynn and lee 2003 biometrics 59 1089 1098 2006 biometrics 62 1251 1259 however power estimation is needed to plan studies that use this analytic approach we have recently published methods for estimating power and sample size for the ordinary wilcoxon rank sum test rosner and glynn 2009 biometrics 65 188 197 in this article we present extensions of this approach to estimate power for the clustered wilcoxon test simulation studies show a good agreement between estimated and empirical power these methods are illustrated with examples from randomized trials in ophthalmology enhanced power is achieved with use of the subunit as the unit of analysis instead of the cluster using the ordinary wilcoxon rank sum test

a log rank test for clustered data with informative within cluster group size the log rank test is a popular nonparametric test for comparing survival distributions among groups when data are organized in clusters of potentially correlated observations adjustments can be made to account for within cluster dependencies among observations eg tests derived from frailty models tests for clustered data can be further biased when the number of observations within each cluster and the distribution of groups within cluster are correlated with survival times phenomena known as informative cluster size and informative within cluster group size in this manuscript we develop a log rank test for clustered data that adjusts for the potentially biasing effect of informative cluster size and within cluster group size we provide the results of a simulation study demonstrating that our proposed test remains unbiased under cluster based informativeness while other candidate tests not accounting for the clustering structure do not properly maintain size furthermore our test exhibits power advantages under scenarios in which traditional tests are appropriate we demonstrate an application of our test by comparing time to functional progression between groups defined initial functional status in a spinal cord injury data set

a signed rank test for clustered data we consider the problem of comparing two outcome measures when the pairs are clustered using the general principle of within cluster resampling we obtain a novel signed rank test for clustered paired data we show by a simple informative cluster size simulation model that only our test maintains the correct size under a null hypothesis of marginal symmetry compared to four other existing signed rank tests further our test has adequate power when cluster size is noninformative in general cluster size is informative if the distribution of pair wise differences within a cluster depends on the cluster size an application of our method to testing radiation toxicity trend is presented

an envelope based feature for nda snr estimation signal to noise ratio snr estimation is essential in many communication systems moment based snr estimators are a type of envelope based estimator the performance of moment based estimators are known to decrease with increasing snr for nonconstant modulus signals in this paper an envelopebased feature is proposed to overcome the challenges posed by nonconstant modulus signals the feature extraction and estimation processes are presented and the results are shown the newly proposed estimator performs better than classical moment based estimators for modulations such as quadrature amplitude modulations qam and amplitude and phase shift keying apsk modulations

rank sum tests for clustered data the wilcoxon rank sum test is widely used to test the equality of two populations because it makes fewer distributional assumptions than parametric procedures such as the t test however the wilcoxon rank sum test can be used only if data are independent when data are clustered tests based on generalized estimating equations gees that generalize the t test have been proposed here we develop a rank sum test that can be used when data are clustered as an application we use our rank sum test to develop a nonparametric test of association between a genetic marker and a quantitative trait locus we also give a rank sum test for equivalence of three or more populations that generalizes the kruskal wallis test to situations with clustered data unlike previous rank tests for clustered data our proposal is valid when members of the same cluster belong to different groups or when the correlation between cluster members differs across groups

two sample rank tests under complex sampling rank tests are widely used for exploratory and formal inference in the health and social sciences with the widespread use of data from complex survey samples in medical and social research there is increasing demand for versions of rank tests that account for the sampling design we propose a general approach to constructing design based rank tests when comparing groups within a complex sample and when using a national survey as a reference distribution and illustrate both scenarios with examples we show that the tests have asymptotically correct levels and that the relative power of different rank tests is not greatly affected by complex sampling copyright 2013 oxford university press

snr estimation for nonconstant modulus constellations we propose a new technique to estimate the signal to noise ratio snr over the flat fading channel this is a nondata aided envelope based estimator that can be applied to nonconstant modulus constellations which is a feature not found in existing approaches we also analyze the performance of our estimators for both phase shift keying psk and non psk constellations by deriving their asymptotic variances and comparing with the crame spl acute r rao bounds crbs moreover we discuss how the snr estimates can be used to approximate the bit error rate ber and how the accuracy of the snr estimate is related to that of the ber estimate which justifies the necessity for the accurate estimation of snr the analytical performance is shown for both psk and non psk constellations such as 8 quadrature amplitude modulation qam and 16 qam monte carlo simulation results corroborate our analysis

efficient estimation for rank based regression with clustered data rank based inference is widely used because of its robustness this article provides optimal rank based estimating functions in analysis of clustered data with random cluster effects the extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations the performance of the proposed method is satisfactory even when the correlation structure is misspecified or when heteroscedasticity in variance is present finally a real dataset is analyzed for illustration

the nonparametric behrens fisher problem with dependent replicates purely nonparametric methods are developed for general two sample problems in which each experimental unit may have an individual number of possibly correlated replicates in particular equality of the variances or higher moments of the distributions of the data is not assumed even under the null hypothesis of no treatment effect thus a solution for the so called nonparametric behrens fisher problem is proposed for such models the methods are valid for metric count ordered categorical and even dichotomous data in a unified way point estimators of the treatment effects as well as their asymptotic distributions will be studied in detail for small sample sizes the distributions of the proposed test statistics are approximated using satterthwaite welch type t approximations extensive simulation studies show favorable performance of the new methods in particular in small sample size situations a real data set illustrates the application of the proposed methods

rank based inference for covariate and group effects in clustered data in presence of informative intra cluster group size there have been numerous attempts to extend the wilcoxon rank sum test to clustered data recently one such rank sum test dutta datta 2016 biometrics 72 432 440 was developed to compare the group specific marginal distributions of outcomes in clustered data where the conditional distributions of outcomes depend on the number of observations from that group in a given cluster a phenomenon referred to as informative intra cluster group icg size however comparison of group specific marginal distributions may not be sufficient in presence of some potentially useful covariables that are observed in the study in addition not accounting for the effect of these covariates can lead to biased and misleading inference for the group comparisons thus the purpose of this article is twofold first we develop a method to estimate the covariate effects using rank based weighted estimating equations that are appropriate when the icg size is informative second we construct an aligned rank sum test based on the covariate adjusted outcomes asymptotic distributions of the r estimators and the test statistic are provided through simulation studies we show the importance of selecting proper weights in constructing the estimating equations when informativeness is present through the cluster or icg sizes we also demonstrate the superiority and the robustness of our method in comparison to regular parametric linear mixed models in clustered data we apply our method to analyze different real life data sets including a data on birthweights of rat pups in different litters and a dental data on tooth attachment loss

extension of the rank sum test for clustered data two group comparisons with group membership defined at the subunit level the wilcoxon rank sum test is widely used for two group comparisons for nonnormal data an assumption of this test is independence of sampling units both between and within groups in ophthalmology data are often collected on two eyes of an individual which are highly correlated in ophthalmological clinical trials randomization is usually performed at the subject level but the unit of analysis is the eye if the eye is used as the unit of analysis then a modification to the usual wilcoxon rank sum variance formula must be made to account for the within cluster dependence for some clustered data designs where the unit of analysis is the subunit group membership may be defined at the subunit level for example in some randomized ophthalmologic clinical trials different treatments may be applied to fellow eyes of some patients while the same treatment may be applied to fellow eyes of other patients in general binary eye specific covariates may be present scored as exposed or unexposed and one wishes to compare nonnormally distributed outcomes between exposed and unexposed eyes using the wilcoxon rank sum test while accounting for the clustering in this article we present a corrected variance formula for the wilcoxon rank sum statistic in the setting of eye subunit specific covariates we apply it to compare ocular itching scores in ocular allergy patients between eyes treated with active versus placebo eye drops where some patients receive the same eye drop in both eyes while other patients receive different eye drops in fellow eyes we also present comparisons between the clustered wilcoxon test and each of the signed rank tests and mixed model approaches and show dramatic differences in power in favor of the clustered wilcoxon test for some designs

nonparametric analysis of clustered multivariate data there is wide interest in extending univariate and multivariate nonparametric procedures to clustered and hierarchical data traditionally parametric mixed models have been used to account for the correlation structures among the dependent observational units in this work we extend multivariate nonparametric procedures for one sample and several sample location problems to clustered data settings the results are given for a general score function but with an emphasis on spatial sign and rank methods mixed models notation involving design matrices for fixed and random effects is used throughout the asymptotic variance formulas and limiting distributions of the test statistics under the null hypothesis and under a sequence of alternatives are derived as are the limiting distributions for the corresponding estimates the approach based on a general score function also shows for example how m estimates behave with clustered data efficiency studies demonstrate the practical advantages and disadvantag

pearson s chi square test and rank correlation inferences for clustered data pearson s chi square test has been widely used in testing for association between two categorical responses spearman rank correlation and kendall s tau are often used for measuring and testing association between two continuous or ordered categorical responses however the established statistical properties of these tests are only valid when each pair of responses are independent where each sampling unit has only one pair of responses when each sampling unit consists of a cluster of paired responses the assumption of independent pairs is violated in this article we apply the within cluster resampling technique to u statistics to form new tests and rank based correlation estimators for possibly tied clustered data we develop large sample properties of the new proposed tests and estimators and evaluate their performance by simulations the proposed methods are applied to a data set collected from a pet ct imaging study for illustration

marginal association measures for clustered data the use of correlation coefficients in measuring the association between two continuous variables is common but regular methods of calculating correlations have not been extended to the clustered data framework for clustered data in which observations within a cluster may be correlated regular inferential procedures for calculating marginal association between two variables can be biased this is particularly true for data in which the number of observations in a given cluster is informative for the association being measured in this paper we apply the principle of inverse cluster size reweighting to develop estimators of marginal correlation that remain valid in the clustered data framework when cluster size is informative for the correlation being measured these correlations are derived as analogs to regular correlation estimators for continuous independent data namely pearson s and kendall s we present the results of a simple simulation study demonstrating the appropriateness of our proposed estimators and the inherent bias of other inferential procedures for clustered data we illustrate their use through an application to data from patients with incomplete spinal cord injury in the usa

a rank sum test for clustered data when the number of subjects in a group within a cluster is informative the wilcoxon rank sum test is a popular nonparametric test for comparing two independent populations groups in recent years there have been renewed attempts in extending the wilcoxon rank sum test for clustered data one of which datta and satten 2005 journal of the american statistical association 100 908 915 addresses the issue of informative cluster size i e when the outcomes and the cluster size are correlated we are faced with a situation where the group specific marginal distribution in a cluster depends on the number of observations in that group i e the intra cluster group size we develop a novel extension of the rank sum test for handling this situation we compare the performance of our test with the datta satten test as well as the naive wilcoxon rank sum test using a naturally occurring simulation model of informative intra cluster group size we show that only our test maintains the correct size we also compare our test with a classical signed rank test based on averages of the outcome values in each group paired by the cluster membership while this test maintains the size it has lower power than our test extensions to multiple group comparisons and the case of clusters not having samples from all groups are also discussed we apply our test to determine whether there are differences in the attachment loss between the upper and lower teeth and between mesial and buccal sites of periodontal patients

cramer rao lower bound and em algorithm for envelope based snr estimation of nonconstant modulus constellations signal to noise ratio snr estimation for linearly modulated signals is addressed in this letter focusing on envelope based estimators which are robust to carrier offsets and phase jitter and on the challenging case of nonconstant modulus constellations for comparison purposes the true cramer rao lower bound is numerically evaluated obtaining an analytical expression in closed form for the asymptotic case of high snr values which quantifies the performance loss with respect to coherent estimation as the maximum likelihood algorithm is too complex for practical implementation an expectation maximization em approach is proposed achieving a good tradeoff between complexity and performance for medium to high snrs finally a hybrid scheme based on em and moments based estimates is suggested which performs close to the theoretical limit over a wide snr range

within cluster resampling within cluster resampling is proposed as a new method for analysing clustered data although the focus of this paper is clustered binary data the within cluster resampling asymptotic theory is general for many types of clustered data within cluster resampling is a simple but computationally intensive estimation method its main advantage over other marginal analysis methods such as generalised estimating equations liang zeger 1986 zeger liang 1986 is that it remains valid when the risk for the outcome of interest is related to the cluster size which we term nonignorable cluster size we present theory for the asymptotic normality and provide a consistent variance estimator for the within cluster resampling estimator simulations and an example are developed that assess the finite sample behaviour of the new method and show that when both methods are valid its performance is similar to that of generalised estimating equations

incorporation of clustering effects for the wilcoxon rank sum test a large sample approach the wilcoxon rank sum test is frequently used in statistical practice for the comparison of measures of location when the underlying distributions are far from normal or not known in advance an assumption of the ordinary rank sum test is that individual sampling units are independent in many ophthalmologic clinical trials the early treatment for diabetic retinopathy scale etdrs is a principal endpoint used for measuring the level of diabetic retinopathy this is an ordinal scale and it is natural to consider the wilcoxon rank sum test for the comparison of the level of diabetic retinopathy between treatment groups however under this design unlike the usual wilcoxon rank sum test the subject is the unit of randomization but the eye is the unit of analysis furthermore a person will tend to have different but correlated etdrs scores for fellow eyes thus we propose a correction to the variance of the wilcoxon rank sum statistic that accounts for clustering effects and that can be used for both balanced same number of subunits per cluster or unbalanced different number of subunits per cluster data both in the presence or absence of ties with p value adjusted accordingly in this article we present large sample theory and simulation results for this test procedure and apply it to diabetic retinopathy data from type i diabetics in the sorbinil retinopathy trial