direction of arrival estimation using parametric signal models we consider the problem of estimating the directions of arrival doas of narrowband sources with known center frequency the paper evaluates the potential improvement in estimation accuracy by using spatial temporal processing for signals obeying a deterministic parametric model one would expect that prior information about the temporal structure of the signals will yield some gain in performance by deriving the cramer rao bound crb on the doa estimates we quantify this gain and identify the cases for which the gain is significant we show that for the single source case spatial temporal processing does not yield any gain in performance relative to conventional spatial processing for multiple noncoherent signals incorporating temporal processing can achieve the single source performance yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array however spatial temporal processing cannot yield any gain in performance for multiple coherent signals

local clustering in scale free networks with hidden variables we investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices the class rules out self loops and multiple edges we focus on the regime where the hidden variables follow a power law with exponent 2 3 so that the degrees have infinite variance the natural cutoff h c characterizes the largest degrees in the hidden variable models and a structural cutoff h s introduces negative degree correlations disassortative mixing due to the infinite variance degrees we show that local clustering decreases with the hidden variable or degree we also determine how the average clustering coefficient c scales with the network size n as a function of h s and h c for scale free networks with exponent 2 3 and the default choices h s n 1 2 and h c n 1 1 this gives c n 2 lnn for the universality class at hand we characterize the extremely slow decay of c when 2 and show that for 2 1 say clustering starts to vanish only for networks as large as n 10 9

analysis of joint angle frequency estimation using esprit high resolution parameter estimation techniques have been applied to jointly estimate multiple signal parameters we consider the problem of determining the directions and center frequencies of a number of narrowband sources in a band of interest we present a joint angle frequency estimation method based on the multidimensional esprit algorithm a perturbation error analysis gives bounds on the parameter estimates and provides optimal values for the temporal and spatial smoothing parameters the analysis is shown to be consistent with simulation results

on the inefficiency of the adaptive design for monitoring clinical trials summary adaptive designs which allow the sample size to be modified based on sequentially computed observed treatment differences have been advocated recently for monitoring clinical trials although such methods have a great deal of appeal on the surface we show that such methods are inefficient and that one can improve uniformly on such adaptive designs using standard group sequential tests based on the sequentially computed likelihood ratio test statistic

efficient maximum likelihood doa estimation for signals with known waveforms in the presence of multipath we present a large sample maximum likelihood ml algorithm for estimating the directions of arrival doa s and signal amplitudes of known possibly coherent signals impinging on an array of sensors the algorithm is an extension of the deml method of li et al that handles coherent multipath that may be present in the signals the algorithm is computationally efficient because the nonlinear minimization step decouples into a set of minimizations of smaller dimension

performance of spatial smoothing algorithms for correlated sources the problem of identifying the angles of arrival of a set of plane waves impinging on a narrowband array of sensors and related spectral analysis problems have been addressed with a large number of algorithms one of the most popular techniques is the multiple signal classification music the major shortcoming of the music algorithm is that it performs poorly when the sources are highly correlated fortunately two algorithms exist to overcome this problem spatial smoothing ss and forward backward spatial smoothing fbss the performance of the ss technique depends on signal bearings and spatial separation for the same smoothing fbss can offer improved performance but this depends on the signal phases numerical results for the variance of the algorithms are given to illustrate the points made

forward backward spatial smoothing techniques for coherent signal identification a spatial smoothing scheme is further investigated in the context of coherent signal classification it is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously it is always possible to estimate any k directions of arrival using at most 3k 2 sensor elements this is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation by incorporating eigenstructure based techniques on this smoothed covariance matrix it then becomes possible to correctly identify all directions of arrival irrespective of their correlation

on information theoretic criteria for determining the number of signals in high resolution array processing an important problem in high resolution array processing is the determination of the number of signals arriving at the array information theoretic criteria provide a means to achieve this two commonly used criteria are the akaike information criterion aic and minimum descriptive length mdl criterion while the aic tends to overestimate even at a high signal to noise ratio snr the mdl criterion tends to underestimate at low or moderate snr by excluding irrelevant parameters a new log likelihood function has been chosen utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the aic and the mdl criterion computer simulations confirm that the modified criteria have superior performance

increasing the sample size when the unblinded interim result is promising increasing the sample size based on unblinded interim result may inflate the type i error rate and appropriate statistical adjustments may be needed to control the type i error rate at the nominal level we briefly review the existing approaches which allow early stopping due to futility or change the test statistic by using different weights or adjust the critical value for final test or enforce rules for sample size recalculation the implication of early stopping due to futility and a simple modification to the weighted z statistic approach are discussed in this paper we show that increasing the sample size when the unblinded interim result is promising will not inflate the type i error rate and therefore no statistical adjustment is necessary the unblinded interim result is considered promising if the conditional power is greater than 50 per cent or equivalently the sample size increment needed to achieve a desired power does not exceed an upper bound the actual sample size increment may be determined by important factors such as budget size of the eligible patient population and competition in the market the 50 per cent conditional power approach is extended to a group sequential trial with one interim analysis where a decision may be made at the interim analysis to stop the trial early due to a convincing treatment benefit or to increase the sample size if the interim result is not as good as expected the type i error rate will not be inflated if the sample size may be increased only when the conditional power is greater than 50 per cent if there are two or more interim analyses in a group sequential trial our simulation study shows that the type i error rate is also well controlled

adaptive and nonadaptive group sequential tests summary methods have been proposed for redesigning a clinical trial at an interim stage in order to increase power in order to preserve the type i error rate methods for unplanned design change have to be defined in terms of nonsufficient statistics and this calls into question their efficiency and the credibility of conclusions reached we evaluate schemes for adaptive redesign extending the theoretical arguments for use of sufficient statistics of tsiatis mehta 2003 and assessing the possible benefits of preplanned adaptive designs by numerical computation of optimal tests these optimal adaptive designs are concrete examples of optimal sequentially planned sequential tests proposed by schmitz 1993 we conclude that the flexibility of unplanned adaptive designs comes at a price and we recommend that the appropriate power for a study should be determined as thoroughly as possible at the outset then standard error spending tests possibly with unevenly spaced analyses provide efficient designs but it is still possible to fall back on flexible methods for redesign should study objective change unexpectedly once the trial is under way

adaptive group sequential designs for clinical trials combining the advantages of adaptive and of classical group sequential approaches a general method is presented integrating the concept of adaptive interim analyses into classical group sequential testing this allows the researcher to represent every group sequential plan as an adaptive trial design and to make design changes during the course of the trial after every interim analysis in the same way as with adaptive designs the concept of adaptive trial designing is thereby generalized to a large variety of possible sequential plans

evaluation of experiments with adaptive interim analyses summary a general method for statistical testing in experiments with an adaptive interim analysis is proposed the method is based on the observed error probabilities from the disjoint subsamples before and after the interim analysis formally an intersection of individual null hypotheses is tested by combining the twop values into a global test statistic stopping rules for fisher s product criterion in terms of critical limits for the p value in the first subsample are introduced including early stopping in the case of missing effects the control of qualitative treatment stage interactions is considered a generalization to three stages is outlined the loss of power when using the product criterion instead of the optimal classical test on the whole sample is calculated for the test of the mean of a normal distribution depending on increasing proportions of the first subsample in relation to the total sample size an upper bound on the loss of power due to early stopping is derived a general example is presented and rules for assessing the sample size in the second stage of the trial are given the problems of interpretation and precautions to be taken for applications are discussed finally the sources of bias for estimation in such designs are described

group sequential tests for delayed responses with discussion summary group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect a lack of an effect or concerns about patient safety in many studies the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond we formulate a new form of group sequential test which gives a proper treatment of these pipeline subjects these tests can be applied even when the continued accrual of data after the decision to stop the trial is unexpected we illustrate our methods through a series of examples we define error spending versions of these new designs which handle unpredictable group sizes and provide an information monitoring framework that can accommodate nuisance parameters such as an unknown response variance by studying optimal versions of our new designs we show how the benefits of lower expected sample size that are normally achieved by a group sequential test are reduced when there is a delay in response the loss of efficiency for larger delays can be ameliorated by incorporating data on a correlated short term end point fitting a joint model for the two end points but still making inferences on the original longer term end point we derive p values and confidence intervals on termination of our new tests

a new simultaneous estimation of directions of arrival and channel parameters in a multipath environment we present two new blind techniques for simultaneous estimation of the direction of arrival doa and the channel parameters for a uniform linear array in a multipath environment the first method is based on the sum of weighted complex exponentials and pade spl acute approximation and the second method determines the transfer function of a linear time invariant system given its impulse response for each method we introduce a rational function whose complex poles contain the desired doa the magnitude of its residues are the channel gains and the phase of its residues are in terms of the channel delays we also derive and numerically evaluate the pertinent crame spl acute r rao lower bound crlb for the estimation process our error analysis based on a perturbation series formulation of the parameter estimation reveals that doa and the channel parameters are extracted from a gaussian signal dependent noise for both methods the amount of computations are also determined some simulations are provided to assess the capabilities of the new methods

modification of sample size in group sequential clinical trials in group sequential clinical trials sample size reestimation can be a complicated issue when it allows for change of sample size to be influenced by an observed sample path our simulation studies show that increasing sample size based on an interim estimate of the treatment difference can substantially inflate the probability of type i error in most practical situations a new group sequential test procedure is developed by modifying the weights used in the traditional repeated significance two sample mean test the new test has the type i error probability preserved at the target level and can provide a substantial gain in power with the increase of sample size generalization of the new procedure is discussed

adaptive sample size modification in clinical trials start small then ask for more we consider sample size re estimation in a clinical trial in particular when there is a significant delay before the measurement of patient response mehta and pocock have proposed methods in which sample size is increased when interim results fall in a promising zone where it is deemed worthwhile to increase conditional power by adding more subjects our analysis reveals potential pitfalls in applying this approach mehta and pocock use results of chen demets and lan to identify when increasing sample size but applying a conventional level significance test at the end of the trial does not inflate the type i error rate we have found the greatest gains in power per additional observation are liable to lie outside the region defined by this method mehta and pocock increase sample size to achieve a particular conditional power calculated under the current estimate of treatment effect this leads to high increases in sample size for a small range of interim outcomes whereas we have found it more efficient to make moderate increases in sample size over a wider range of cases if the aforementioned pitfalls are avoided we believe the broad framework proposed by mehta and pocock is valuable for clinical trial design working in this framework we propose sample size rules that apply explicitly the principle of adding observations when they are most beneficial the resulting trial designs are closely related to efficient group sequential tests for a delayed response proposed by hampson and jennison copyright 2015 john wiley sons ltd

maximum likelihood separation of constant modulus signals in this correspondence we derive a newton scoring algorithm for the maximum likelihood separation and direction of arrival doa estimation of constant modulus cm signals using a sensor array we present a rapidly converging scheme for the joint estimation of the signals and their directions based on their cm property we discuss initialization and show that the complexity is moderate

efficient group sequential designs when there are several effect sizes under consideration we consider the construction of efficient group sequential designs where the goal is a low expected sample size not only at the null hypothesis and the alternative taken to be the minimal clinically meaningful effect size but also at more optimistic anticipated effect sizes pre specified type i error rate and power requirements can be achieved both by standard group sequential tests and by more recently proposed adaptive procedures we investigate four nested classes of designs a group sequential tests with equal group sizes and stopping boundaries determined by a monomial error spending function the rho family b as a but the initial group size is allowed to be different from the others c group sequential tests with arbitrary group sizes and arbitrary boundaries fixed in advance d adaptive tests as c but at each analysis future group sizes and critical values are updated depending on the current value of the test statistic by examining the performance of optimal procedures within each class we conclude that class b provides simple and efficient designs with efficiency close to that of the more complex designs of classes c and d we provide tables and figures illustrating the performances of optimal designs within each class and defining the optimal procedures of classes a and b

are flexible designs sound flexible designs allow large modifications of a design during an experiment in particular the sample size can be modified in response to interim data or external information a standard flexible methodology combines such design modifications with a weighted test which guarantees the type i error level however this inference violates basic inference principles in an example with independent n mu 1 observations the test rejects the null hypothesis of mu or 0 while the average of the observations is negative we conclude that flexible design in its most general form with the corresponding weighted test is not valid several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests

designed extension of studies based on conditional power we propose a flexible method of extending a study based on conditional power the possibility for extension when the p value at the planned end is small but not statistically significant is built in to the design of the study the significance of the treatment difference at the planned end is used to determine the number of additional observations needed and the critical value necessary for use after accruing those additional observations it may therefore be thought of as a two stage procedure even though the observed treatment difference at stage 1 is used to make decisions the type i error rate is protected

a note on redundancy averaging it is well known that the performance of direction of arrival estimation and beamforming algorithms degrades in the presence of correlated signals since techniques like spatial and weighted smoothing which were developed for decorrelating the signals suffer from reduced effective aperture several authors have recently proposed redundancy averaging as an alternative spatial averaging method considering a two source signal model and the asymptotic case the authors show analytically that this technique results in an eigenstructure which is inconsistent with that of the underlying signal model in particular the resulting signal subspace fills up the whole m dimensional space where m is the array size and the resulting covariance matrix is not guaranteed to be nonnegative definite it is shown that complete decorrelation is not possible with this method even if the array size is infinitely large