joint monitoring of process mean and variance using exponentially weighted moving average control charts the performances of control charting schemes for thejoint monitoring of a process mean and a variance are evaluated and compared certain schemes are shown to be inadequate for this purpose and the potential risk of using these schemes alone is discussed a combined scheme consisting of a two sided exponentially weighted moving average ewma mean chart and a two sided ewma variance chart is found to perform well under several types of out of control situations a simple method is provided for approximating the average run length and the percentage points of a run length distribution of a combined ewma scheme a simple procedure is also proposed for the design of a combined ewma scheme

a unified theorem on sdp rank reduction we consider the problem of finding a low rank approximate solution to a system of linear equations in symmetric positive semidefinite matrices where the approximation quality of a solution is measured by its maximum relative deviation both above and below from the prescribed quantities we show that a simple randomized polynomial time procedure produces a low rank solution that has provably good approximation qualities our result provides a unified treatment of and generalizes several well known results in the literature in particular it contains as special cases the johnson lindenstrauss lemma on dimensionality reduction results on low distortion embeddings into low dimensional euclidean space and approximation results on certain quadratic optimization problems

signal separation by symmetric adaptive decorrelation stability convergence and uniqueness the performance of signal enhancement systems based on adaptive filtering is highly dependent on the quality of the noise reference in the lms algorithm signal leakage into the noise reference leads to signal distortion and poor noise cancellation the origin of the problem lies in the fact that lms decorrelates the signal estimate with the noise reference which in the case of signal leakage makes little sense an algorithm is proposed that decorrelates the signal estimate with a signal free noise estimate obtained by adding a symmetric filter to the classical structure the symmetric adaptive decorrelation sad algorithm no longer makes a distinction between signal and noise and is therefore a signal separator rather than a noise canceler stability and convergence are of the utmost importance in adaptive algorithms and hence are carefully studied apart from limitations on the adaptation constants stability around the desired solution can only be guaranteed for a subclass of signal mixtures furthermore the decorrelation criterion does not yield a unique solution and expressions for the phantom solutions are derived simulations with short fir filters confirm the predicted behavior

on the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues we derive some basic results on the geometry of semidefinite programming sdp and eigenvalue optimization i e the minimization of the sum of the k largest eigenvalues of a smooth matrix valued function we provide upper bounds on the rank of extreme matrices in sdps and the first theoretically solid explanation of a phenomenon of intrinsic interest in eigenvalue optimization in the spectrum of an optimal matrix the kth and k 1 st largest eigenvalues tend to be equal and frequently have multiplicity greater than two this clustering is intuitively plausible and has been observed as early as 1975 when the matrix valued function is affine we prove that clustering must occur at extreme points of the set of optimal solutions if the number of variables is sufficiently large we also give a lower bound on the multiplicity of the critical eigenvalue these results generalize to the case of a general matrix valued function under appropriate conditions

statistical process control for shifts in mean or variance using a changepoint formulation statistical process control spc involves ongoing checks to ensure that neither the mean nor the variability of the process readings has changed conventionally this is done by pairs of charts shewhart x and s or r charts cumulative sum charts for mean and for variance or exponentially weighted moving average charts for mean and variance the traditional methods of calculating the statistical properties of control charts are based on the assumption that the in control true mean and variance were known exactly and use these assumed true values to set center lines control limits and decision intervals the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample the random errors in the estimates lead to uncertain run length distribution of the resulting charts an attractive alternative to the traditional charting methods is a single chart using the unknown parameter likelihood ratio test for a change in mean and o

adaptive estimation of a quadratic functional by model selection we consider the problem of estimating s 2 when s belongs to some separable hilbert space and one observes the gaussian process y t langles t rangle sigmal t for all t epsilon mathbb h where l is some gaussian isonormal process this framework allows us in particular to consider the classical gaussian sequence model for which mathbb h l 2 mathbb n and l t sum lambda geq1 t lambda varepsilon lambda where varepsilon lambda lambda geq1 is a sequence of i i d standard normal variables our approach consists in considering some at most countable families of finite dimensional linear subspaces of mathbb h the models and then using model selection via some conveniently penalized least squares criterion to build new estimators of s 2 we prove a general nonasymptotic risk bound which allows us to show that such penalized estimators are adaptive on a variety of collections of sets for the parameter s depending on the family of models from which they are built in particular in the context of the gaussian sequence model a convenient choice of the family of models allows defining estimators which are adaptive over collections of hyperrectangles ellipsoids l p bodies or besov bodies we take special care to describe the conditions under which the penalized estimator is efficient when the level of noise sigma tends to zero our construction is an alternative to the one by efroimovich and low for hyperrectangles and provides new results otherwise

unraveling the rank one solution mystery of robust miso downlink transmit optimization a verifiable sufficient condition via a new duality result this paper concentrates on a robust transmit optimization problem for the multiuser multi input single output miso downlink scenario and under inaccurate channel state information csi this robust problem deals with a general rank transmit covariance design and follows a safe rate constrained formulation under spherically bounded csi uncertainties curiously simulation results in previous works suggested that the robust problem admits rank one optimal transmit covariances in most cases such a numerical finding is appealing because transmission with rank one covariances can be easily realized by single stream transmit beamforming this gives rise to a fundamentally important question namely whether we can theoretically identify conditions under which the robust problem admits a rank one solution in this paper we identify one such condition simply speaking we show that the robust problem is guaranteed to admit a rank one solution if the csi uncertainties are not too large and the multiuser channel is not too poorly conditioned to establish the aforementioned condition we develop a novel duality framework through which an intimate relationship between the robust problem and a related maximin problem is revealed our condition involves only a simple expression with respect to the multiuser channel and other system parameters in particular unlike other sufficient rank one conditions that have appeared in the literature ours is verifiable the application of our analysis framework to several other csi uncertainty models is also discussed

monitoring general linear profiles using multivariate exponentially weighted moving average schemes we propose a statistical process control scheme that can be implemented in industrial practice in which the quality of a process can be characterized by a general linear profile we start by reviewing the general linear profile model and the existing monitoring methods based on this we propose a novel multivariate exponentially weighted moving average monitoring scheme for such a profile we introduce two other enhancement features the variable sampling interval and the parametric diagnostic approach to further improve the performance of the proposed scheme throughout the article we use a deep reactive ion etching example from semiconductor manufacturing which has a profile that fits a quadratic polynomial regression model well to illustrate the implementation of the proposed approach

monitoring profiles based on nonparametric regression methods the use statistical process control spc in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries the spc problem with a nonlinear profile is particularly challenging this article proposes a novel scheme to monitor changes in both the regression relationship and the variation of the profile online it integrates the multivariate exponentially weighted moving average procedure with the generalized likelihood ratio test based on nonparametric regression the proposed scheme not only provides an effective spc solution to handle nonlinear profiles which are common in industrial practice but it also resolves the latent problem in popular parametric monitoring methods of being unable to detect certain types of changes due to a misspecified out of control model our simulation results demonstrate the effectiveness and efficiency of the proposed monitoring scheme in addition a systematic diagnostic approach is provided to locate t

approximation dans les espaces metriques et theorie de l estimation we investigate the relations between the speed of estimation and the metric structure of the parameter space especially in the case when its metric dimension is infinite given some distance d on generally hellinger distance in the case of n i i d variables we consider the minimax risk for n observations r n q mathop inf sup limits t n theta in theta text ie theta d q theta t n t n being any estimate of we shall look for functions r such that for positive constants c 1 q and c 2 q c 1 r q n r n q c2 r q n r n is the speed of estimation and we shall show under fairly general conditions including i i d variables and regular cases of markov chains and stationnary gaussian processes that r n is determined up to multiplicative constants by the metric structure of we shall also give a construction for some sort of universal estimates the risk of which is bounded by c 2 r q n in all cases where the preceding theory applies

should exponentially weighted moving average and cumulative sum charts be used with shewhart limits traditional shewhart control charts are usually considered effective for detecting large shifts in process parameters but ineffective for detecting small shifts for detecting small parameter shifts it is much better to use exponentially weighted moving average ewma control charts or cumulative sum cusum control charts but these charts are not considered as effective as shewhart charts for large parameter shifts it is frequently recommended that ewma or cusum charts be used in combination with a shewhart chart to gain the benefits of both types of charts so that both small and large shifts can be detected quickly here we consider the problem of process monitoring when a continuous process variable is being observed and the objective is to detect small or large shifts in either the process mean or the process standard deviation in this situation it is customary to use a combination of two control charts one chart designed to monitor and the other designed to monitor for this situation

nondata aided i q mismatch and dc offset compensation for direct conversion receivers a digital signal processing technique is presented that can compensate for the frequency independent inphase quadrature i q mismatch and dc offset in zero intermediate frequency direct conversion receivers the proposed compensator consists of dc offset and i q mismatch estimators followed by a dc offset canceller and self image suppressor the estimators are nondata aided nda schemes that are derived by assuming that the desired signal is a random variable having an arbitrary circular symmetric distribution the cramer rao lower bounds crlbs for nda estimation are derived and the characteristics of the estimators are analyzed in terms of mean square errors in particular it is shown that for white gaussian distributed signals the accuracy of the estimates approaches the crlbs as the number of observed samples increases the characteristics of the proposed method as well as the validity of the analytical results are demonstrated through computer simulation

quadrature receiver mismatch calibration this article introduces nonlinear regression techniques to estimate gain and phase mismatches between the in phase i and quadrature q branches of a quadrature receiver under modest assumptions the system intrinsically follows a nonlinear regression model the algorithm is effective easily implemented customizable and requires few assumptions large sample jackknife and bootstrap techniques provide on line error assessment and parameter inference

moment inequalities for sums of random matrices and their applications in optimization in this paper we consider various moment inequalities for sums of random matrices which are well studied in the functional analysis and probability theory literature and demonstrate how they can be used to obtain the best known performance guarantees for several problems in optimization first we show that the validity of a recent conjecture of nemirovski is actually a direct consequence of the so called non commutative khintchine s inequality in functional analysis using this result we show that an sdp based algorithm of nemirovski which is developed for solving a class of quadratic optimization problems with orthogonality constraints has a logarithmic approximation guarantee this improves upon the polynomial approximation guarantee established earlier by nemirovski furthermore we obtain improved safe tractable approximations of a certain class of chance constrained linear matrix inequalities secondly we consider a recent result of delage and ye on the so called data driven distributionally robust stochastic programming problem one of the assumptions in the delage ye result is that the underlying probability distribution has bounded support however using a suitable moment inequality we show that the result in fact holds for a much larger class of probability distributions given the close connection between the behavior of sums of random matrices and the theoretical properties of various optimization problems we expect that the moment inequalities discussed in this paper will find further applications in optimization

nonparametric profile monitoring by mixed effects modeling in some applications the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables profile monitoring is for checking the stability of this relationship over time control charts for monitoring nonparametric profiles are useful when the relationship is too complicated to be described parametrically most existing control charts in the literature are for monitoring parametric profiles they require the assumption that within profile measurements are independent of each other which is often invalid in practice this article focuses on nonparametric profile monitoring when within profile data are correlated a novel control chart is suggested which incorporates local linear kernel smoothing into the exponentially weighted moving average ewma control scheme in this method within profile correlation is described by a nonparametric mixed effects model our proposed control chart is fast to compute and convenient to use numeric

a cramer rao lower bound for complex parameters an expression is derived for a cramer rao lower bound on the variance of unbiased estimators of complex parameters

a multivariate exponentially weighted moving average control chart a multivariate extension of the exponentially weighted moving average ewma control chart is presented and guidelines given for designing this easy to implement multivariate procedure a comparison shows that the average run length arl performance of this chart is similar to that of multivariate cumulative sum cusum control charts in detecting a shift in the mean vector of a multivariate normal distribution as with the hotelling s 2 and multivariate cusum charts the arl performance of the multivariate ewma chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter worst case scenarios show that hotelling s 2 charts should always be used in conjunction with multivariate cusum and ewma charts to avoid potential inertia problems examples are given to illustrate the use of the proposed procedure

a semidefinite relaxation scheme for multivariate quartic polynomial optimization with quadratic constraints we present a general semidefinite relaxation scheme for general n variate quartic polynomial optimization under homogeneous quadratic constraints unlike the existing sum of squares approach which relaxes the quartic optimization problems to a sequence of typically large linear semidefinite programs sdp our relaxation scheme leads to a possibly nonconvex quadratic optimization problem with linear constraints over the semidefinite matrix cone in mathbb r n times n it is shown that each alpha factor approximate solution of the relaxed quadratic sdp can be used to generate in randomized polynomial time an o alpha factor approximate solution for the original quartic optimization problem where the constant in o cdot depends only on problem dimension in the case where only one positive definite quadratic constraint is present in the quartic optimization problem we present a randomized polynomial time approximation algorithm which can provide a guaranteed relative approximation ratio of 1 o n 2

a markov chain model for the multivariate exponentially weighted moving averages control chart abstract a markov chain approximation is used to determine the run length performance of a multivariate statistical process control chart the markov chain approach is widely used in the analysis of univariate control charts we extend the advantages of this type of analysis to a multivariate exponentially weighted moving averages control chart the analysis can be applied whenever the multivariate control statistic can be modeled as a markov chain and the run length performance depends on the off target mean only through the noncentrality parameter

a least angle regression control chart for multidimensional data in multidimensional applications it is very rare that all variables shift at the same time a statistical process control procedure would have superior efficiency when limited to the subset of variables likely responsible for the out of control conditions the key idea of this article consists of combining a variable selection method with a multivariate control chart to detect changes in both the mean and variability of a multidimensional process with gaussian errors in particular we develop a control chart for phase ii monitoring which integrates the least angle regression algorithm with a multivariate exponentially weighted moving average comparisons with related multivariate control schemes demonstrate the efficiency of the proposed control chart in a wide range of practical applications including profile and multistage process monitoring further the proposed scheme may also provide valuable diagnostic information for fault isolation supplemental materials including an r package are available

minimax estimation via wavelet shrinkage we attempt to recover an unknown function from noisy sampled data using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients the shrinkage can be tuned to be nearly minimax over any member of a wide range of triebel and besov type smoothness constraints and asymptotically minimax over besov bodies with p q linear estimates cannot achieve even the minimax rates over triebel and besov classes with p 2 so the method can significantly outperform every linear method e g kernel smoothing spline sieve in a minimax sense variants of our method based on simple threshold nonlinear estimators are nearly minimax our method possesses the interpretation of spatial adaptivity it reconstructs using a kernel which may vary in shape and bandwidth from point to point depending on the data least favorable distributions for certain of the triebel and besov scales generate objects with sparse wavelet transforms many real objects have similarly sparse transforms which suggests that these minimax results are relevant for practical problems sequels to this paper which was first drafted in november 1990 discuss practical implementation spatial adaptation properties universal near minimaxity and applications to inverse problems

outlier detection in functional observations with applications to profile monitoring the presence of outliers has serious adverse effects on the modeling and forecasting of functional data therefore outlier detection aiming at identifying abnormal functional curves from a dataset is quite important this article proposes a new testing procedure based on functional principal component analysis under mild conditions the null distribution of the test statistic is shown to be asymptotically pivotal with a well known asymptotic distribution simulation results demonstrate good finite sample performance of the asymptotic test and detection procedure finally by illustrating the connection between profile monitoring in statistical process control and outlier detection in functional data we apply the proposed approach to a real data example from a manufacturing process and show that it performs quite well in detecting outlying profiles supplementary material for this article is posted online on the journal web site

cusum charts with variable sampling intervals a standard cumulative sum cusum chart for controlling the process mean takes samples from the process at fixed length sampling intervals and uses a control statistic based on a cumulative sum of differences between the sample means and the target value this article proposes a modification of the standard cusum scheme that varies the time intervals between samples depending on the value of the cusum control statistic the variable sampling interval vsi cusum chart uses short sampling intervals if there is an indication that the process mean may have shifted and long sampling intervals if there is no indication of a change in the mean if the cusum statistic actually enters the signal region then the vsi cusum chart signals in the same manner as the standard cusum chart a markov chain approach is used to evaluate properties such as the average time to signal and the average number of samples to signal results show that the proposed vsi cusum chart is considerably more efficient than the standard cus

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

on maximization of quadratic form over intersection of ellipsoids with common center we demonstrate that if a1 a m are symmetric positive semidefinite n n matrices with positive definite sum and a is an arbitrary symmetric n n matrix then the relative accuracy in terms of the optimal value of the semidefinite relaxation max x tr ax mid tr a ix le1 i 1 m x succeq0 eqno hbox sdp of the optimization program x tax to max mid x ta ix le 1 i 1 m eqno hbox p is not worse than 1 frac 1 2 ln 2m 2 it is shown that this bound is sharp in order as far as the dependence on m is concerned and that a feasible solution x to p with x tax ge frac opt hbox rm sdp 2 ln 2m 2 eqno can be found efficiently this somehow improves one of the results of nesterov 4 where bound similar to is established for the case when all ai are of rank 1

semidefinite relaxation bounds for indefinite homogeneous quadratic optimization this paper studies the relationship between the optimal value of a homogeneous quadratic optimization problem and its semidefinite programming sdp relaxation we consider two quadratic optimization models 1 min x c x mid x a k x ge 1 k 0 1 ldots m x in mathbb f n and 2 max x c x mid x a k x le 1 k 0 1 ldots m x in mathbb f n where mathbb f is either the real field mathbb r or the complex field mathbb c and a k c are symmetric matrices for the minimization model 1 we prove that if the matrix c and all but one of the a k s are positive semidefinite then the ratio between the optimal value of 1 and its sdp relaxation is upper bounded by o m 2 when mathbb f mathbb r and by o m when mathbb f mathbb c moreover when two or more of the a k s are indefinite this ratio can be arbitrarily large for the maximization model 2 we show that if c and at most one of the a k s are indefinite while other a k s are positive semidefinite then the ratio between the optimal value of 2 and its sdp relaxation is bounded from below by o 1 log m for both the real and the complex case this result improves the bound based on the so called approximate s lemma of ben tal nemirovski and roos siam j optim 13 2002 pp 535 560 when two or more of the a k s in 2 are indefinite we derive a general bound in terms of the problem data and the sdp solution for both optimization models we present examples to show that the derived approximation bounds are essentially tight

deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems due to their fundamental nature and numerous applications sphere constrained polynomial optimization problems have received a lot of attention lately in this paper we consider three such problems i maximizing a homogeneous polynomial over the sphere ii maximizing a multilinear form over a cartesian product of spheres and iii maximizing a multiquadratic form over a cartesian product of spheres since these problems are generally intractable our focus is on designing polynomial time approximation algorithms for them by reducing the above problems to that of determining the l 2 diameters of certain convex bodies we show that they can all be approximated to within a factor of log n n d 2 1 deterministically where n is the number of variables and d is the degree of the polynomial this improves upon the currently best known approximation bound of 1 n d 2 1 in the literature we believe that our approach will find further applications in the design of approximation algorithms for polynomial optimization problems with provable guarantees

x charts with variable sampling intervals the usual practice in using a control chart to monitor a process is to take samples from the process with fixed sampling intervals this article considers the properties of the chart when the sampling interval between each pair of samples is not fixed but rather depends on what is observed in the first sample the idea is that the time interval until the next sample should be short if a sample shows some indication of a change in the process and long if there is no indication of a change the proposed variable sampling interval vsi chart uses a short sampling interval if is close to but not actually outside the control limits and a long sampling interval if is close to target if is actually outside the control limits then the chart signals in the same way as the standard fixed sampling interval fsi chart properties such as the average time to signal and the average number of samples to signal are evaluated comparisons between the fsi and the vsi charts indicate that the vsi chart is substantially

approximation bounds for quadratic optimization with homogeneous quadratic constraints we consider the np hard problem of finding a minimum norm vector in n dimensional real or complex euclidean space subject to m concave homogeneous quadratic constraints we show that a semidefinite programming sdp relaxation for this nonconvex quadratically constrained quadratic program qp provides an o m 2 approximation in the real case and an o m approximation in the complex case moreover we show that these bounds are tight up to a constant factor when the hessian of each constraint function is of rank 1 namely outer products of some given so called steering vectors and the phase spread of the entries of these steering vectors are bounded away from pi 2 we establish a certain constant factor approximation depending on the phase spread but independent of m and n for both the sdp relaxation and a convex qp restriction of the original np hard problem finally we consider a related problem of finding a maximum norm vector subject to m convex homogeneous quadratic constraints we show that an sdp relaxation for this nonconvex qp provides an o 1 ln m approximation which is analogous to a result of nemirovski e math program 86 1999 pp 463 473 for the real case

approximation algorithms for homogeneous polynomial optimization with quadratic constraints in this paper we consider approximation algorithms for optimizing a generic multi variate homogeneous polynomial function subject to homogeneous quadratic constraints such optimization models have wide applications e g in signal processing magnetic resonance imaging mri data training approximation theory and portfolio selection since polynomial functions are non convex the problems under consideration are all np hard in general in this paper we shall focus on polynomial time approximation algorithms in particular we first study optimization of a multi linear tensor function over the cartesian product of spheres we shall propose approximation algorithms for such problem and derive worst case performance ratios which are shown to be dependent only on the dimensions of the model the methods are then extended to optimize a generic multi variate homogeneous polynomial function with spherical constraint likewise approximation algorithms are proposed with provable approximation performance ratios furthermore the constraint set is relaxed to be an intersection of co centered ellipsoids namely we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin and propose polynomial time approximation algorithms with provable worst case performance ratios numerical results are reported illustrating the effectiveness of the approximation algorithms studied