comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

sample size estimation for the van elteren test a stratified wilcoxon mann whitney test the van elteren test is a type of stratified wilcoxon mann whitney test for comparing two treatments accounting for strata in this paper we study sample size estimation methods for the asymptotic version of the van elteren test assuming that the stratum fractions ratios of each stratum size to the total sample size and the treatment fractions ratios of each treatment size to the stratum size are known in the study design in particular we develop three large sample sample size estimation methods and present a real data example to illustrate the necessary information in the study design phase in order to apply the methods simulation studies are conducted to compare the performance of the methods and recommendations are made for method choice finally sample size estimation for the van elteren test when the stratum fractions are unknown is also discussed

transforming low discrepancy sequences from a cube to a simplex sequences of points with a low discrepancy are the basic building blocks for quasi monte carlo methods traditionally these points are generated in a unit cube to develop point sets on a simplex we will transform the low discrepancy points from the unit cube to a simplex an advantage of this approach is that most of the known results on low discrepancy sequences can be re used after introducing several transformations their efficiency as well as their quality will be evaluated we present a koksma hlawka inequality which says that under certain conditions the order of convergence using the new point set is the same as that of the original set

asymptotic normality of scrambled geometric net quadrature in a very recent work basu and owen found comput math 17 2017 467 496 propose the use of scrambled geometric nets in numerical integration when the domain is a product of s arbitrary spaces of dimension d having a certain partitioning constraint it was shown that for a class of smooth functions the integral estimate has variance o n 1 2 d log n s 1 for scrambled geometric nets compared to o n 1 for ordinary monte carlo the main idea of this paper is to expand on the work by loh ann statist 31 2003 1282 1324 to show that the scrambled geometric net estimate has an asymptotic normal distribution for certain smooth functions defined on products of suitable subsets of mathbb r d

transformations and hardy krause variation using a multivariable faa di bruno formula we give conditions on transformations tau 0 1 m to cal x where cal x is a closed and bounded subset of mathbb r d such that f circ tau is of bounded variation in the sense of hardy and krause for all f in c m cal x we give similar conditions for f circ tau to be smooth enough for scrambled net sampling to attain o n 3 2 epsilon accuracy some popular symmetric transformations to the simplex and sphere are shown to satisfy neither condition some other transformations due to fang and wang monogr statist appl probab 51 crc press boca raton fl 1993 satisfy the first but not the second condition we provide transformations for the simplex that makes f circ tau smooth enough to fully benefit from scrambled net sampling for all f in a class of generalized polynomials we also find sufficient conditions for conditional inversion in mathbb r 2 and for importance sampling to be of bounded variation in the sense of ha

calculation of power and sample size with bounded outcome scores the two sample wilcoxon rank sum test is the most popular non parametric test for the comparison of two samples when the underlying distributions are not normal although the underlying distributions need not be known in detail to calculate the null distribution of the test statistic parametric assumptions are often made to determine the power of the test or the sample size we encountered difficulties with this approach in the planning of a recent clinical trial in stroke patients it is shown that for power and sample size estimation it can be dangerous to apply the classical formulae routinely especially with outcome scores having a u shaped or a j shaped distribution as an example we have taken the barthel index a quality of life outcome measure in stroke patients further we have investigated alternative methods by means of monte carlo simulation the distributional characteristics of the estimated powers were compared our findings suggest more appropriate computer software is necessary for the calculation of power and sample size when efficacy is measured by a non parametric method

performance analysis of ofdm with wiener phase noise and frequency selective fading channel we analyze the effect of wiener phase noise on the capacity and signal to interference plus noise sinr ratio our analysis includes phase noise at the transmitter and receiver end of an ofdm communication link we see that the capacity and sinr are random variables whose distribution depends on the phase noise and the fading channel using a taylor series approximation we show that the random variable characterizing the phase noise in the performance metrics can be expressed as a sum of correlated gamma variables with rank deficient square root normalized covariance matrix the approximation holds well when the ratio between the subcarrier spacing and the 3db bandwidth of the oscillator power spectral density is at least one order of magnitude which for most practical oscillators is the case in earlier literature the probability density function of a sum of correlated gamma variables with full rank square root normalized covariance matrix was derived we extend these results to the rank deficient case and apply them to the random variable of our case with the probability density functions characterizing the phase noise and the fading channel at hand we proceed to obtain closed form statistical measures of capacity and sinr the simulations show the good agreement with our analytical expressions

power and sample size calculations for exact conditional tests with ordered categorical data we develop an algorithm for computing sample sizes equal or unequal for categorical data we illustrate its use in the two sample setting using the wilcoxon rank sum statistic but the algorithm accommodates the entire class of linear rank statistics and can be extended to include nonlinear rank statistics as well the sample size determinations can be based on either exact power or on a very precise monte carlo estimate of it to reduce the computations further power can be computed as a function of asymptotic critical values when the number of categories is not too small for the wilcoxon statistic we show that this approximation works well if there are more than five response categories

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

a simple bit error probability analysis for square qam in rayleigh fading with channel estimation a new approach is presented for analyzing the bit error probability bep of square multilevel quadrature amplitude modulation over a nonselective rayleigh fading channel with imperfect channel estimation employing pilot symbol assisted modulation it is much simpler and more powerful than those in the literature and the average bep is obtained by calculating the bep for each individual bit the results are given in simple exact closed form expressions that do not require any numerical integration these expressions show explicitly the behavior of the bep as a function of various system parameters three channel estimation schemes are investigated it is shown that existing channel estimation schemes using sinc interpolation and gaussian interpolation can be improved

quasi monte carlo integration for twice differentiable functions over a triangle abstract we study quasi monte carlo integration for twice differentiable functions defined over a triangle we provide an explicit construction of infinite sequences of points including one by basu and owen 2015 as a special case which achieves the integration error of order n 1 log n 3 for any n 2 since a lower bound of order n 1 on the integration error holds for any linear quadrature rule the upper bound we obtain is best possible apart from the log n factor the major ingredient in our proof of the upper bound is the dyadic walsh analysis of twice differentiable functions over a triangle under a suitable recursive partitioning

on the error probability of linearly modulated signals on frequency flat ricean rayleigh and awgn channels the method used in aghamohammadi and meyr 1990 for finding the error probability of linearly modulated signals on rayleigh frequency flat fading channels has been applied to the more general case of ricean fading a signal received on a fading channel is subject to a multiplicative distortion md and to the usual additive noise following a compensation of the md the signal provided to the detector may be thought to include only a single additive distortion term final noise which comprises the effects of the original additive noise the md and the error in md compensation an exact expression for the probability density function of the final noise is derived this allows calculation of error probability for arbitrary types of linear modulations results for many cases of interest are presented furthermore as special cases of ricean fading error probability for rayleigh fading and non fading channels are obtained which either match the results or complete the approximate derivations formerly known from the literature

on the error probability of linearly modulated signals on rayleigh frequency flat fading channels consideration is given to optimal detection of linearly modulated signals subject to multiplicative rayleigh distributed distortion and additive white gaussian noise for coherent detection regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values a system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference producing a final additive noise term applied just before the detection which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references by determining the probability density function of this final noise term for arbitrary types of linear modulation it is possible to perform exact calculations of error probabilities

sample size determination for some common nonparametric tests abstract the article discusses the problem of determining the number of observations required by some common nonparametric tests so that the tests have power at least 1 against alternatives that differ sufficiently from the hypothesis being tested it is shown that the number of observations depends on certain simple probabilities a method is suggested for fixing the value of the appropriate probability when determining sample size

low discrepancy constructions in the triangle most quasi monte carlo research focuses on sampling from the unit cube many problems especially in computer graphics are defined via quadrature over the unit triangle quasi monte carlo methods for the triangle have been developed by pillards and cools j comput appl math 174 2005 pp 29 42 and by brandolini et al a koksma hlawka inequality for simplices in trends in harmonic analysis springer 2013 pp 33 46 this paper presents two quasi monte carlo constructions in the triangle with a vanishing discrepancy the first is a version of the van der corput sequence customized to the unit triangle it is an extensible digital construction that attains a discrepancy below 12 sqrt n the second construction rotates an integer lattice through an angle whose tangent is a quadratic irrational number it attains a discrepancy of o log n n which is the best possible rate previous work strongly indicated that such a discrepancy was possible but no constructions were available s

sample size calculation for the wilcoxon mann whitney test adjusting for ties in this paper we study sample size calculation methods for the asymptotic wilcoxon mann whitney test for data with or without ties the existing methods are applicable either to data with ties or to data without ties but not to both cases while the existing methods developed for data without ties perform well the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties we propose a new method which has a closed form formula and therefore is very easy to calculate in addition the new method can be applied to both data with or without ties simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

probability density functions for analyzing multi amplitude constellations in rayleigh and ricean channels this paper derives probability density functions pdfs to describe the behavior of data demodulated with imperfect channel estimation the pdfs apply to cases of flat rayleigh fading multiple diversity reception rayleigh fading and flat ricean fading these pdfs can be used to determine analytically both the symbol error rate and bit error rate for multi amplitude constellations with in phase and quadrature components thus avoiding the need for extensive computer simulation

a comparison of size and power calculations for the wilcoxon statistic for ordered categorical data this paper compares the accuracy of approximations to test size and power based on the score and the fisher information with calculations using edgeworth and cornish fisher approximations and demonstrates that in some cases one must exercise much care in using the simpler approximations