splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

unicity in piecewise polynomial l 1 approximation via an algorithm our main result shows that certain generalized convex functions on a real interval possess a unique best l 1 approximation from the family of piecewise polynomial functions of fixed degree with varying knots this result was anticipated by kioustelidis in 11 however the proof given there is nonconstructive and uses topological degree as the primary tool in a fashion similar to the proof the comparable result for the l 2 case in 5 by contrast the proof given here proceeds by demonstrating the global convergence of an algorithm to calculate a best approximation over the domain of all possible knot vectors the proof uses the contraction mapping theorem to simultaneously establish convergence and uniqueness this algorithm was suggested by kioustelidis 10 in addition an asymptotic uniqueness result and a nonuniqueness result are indicated which analogize known results in the l 2 case

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

periodic harmonic functions on lattices and chebyshev polynomials abstract we shall give an explicit expression of the dimension of the space of harmonic functions on the cartesian product of path resp cycle graphs in terms of chebyshev polynomials of the second resp first kind as an application we obtain several identities among the dimensions some are new and some are known but obtained previously by other methods our motivation for this study is the lights out puzzle

σ game σ game and two dimensional additive cellular automata abstract the game introduced by sutner is a combinatorial game played on a graph g and is closely related to the automaton first studied by lindenmayer a related game is the game in this article we study the game game played on the rectangular grid 1 2 m 1 2 n we analyse the game by studying the divisibility properties of the polynomials p n which we have introduced here similar polynomials were earlier studied by sutner we give a simple algorithm for finding the number of solutions for the game and also give a necessary and sufficient condition for the existence of a unique solution for the game thus partially answering a question posed by sutner further we compute the number of solutions of the game when one of n m is of the form 2 k 1 finally we look at the game and the game played on cylinders and tori and give necessary and sufficient conditions for the existence of unique solutions for these games

space time block codes achieving full diversity with linear receivers in most of the existing space time code designs achieving full diversity is based on maximum likelihood ml decoding at the receiver that is usually computationally expensive and may not have soft outputs recently zhang liu wong introduced toeplitz codes and showed that toeplitz codes achieve full diversity when a linear receiver zero forcing zf or minimum mean square error mmse receiver is used motivated from zhang liu wong s results on toeplitz codes in this paper we propose a design criterion for space time block codes stbc in which information symbols and their complex conjugates are linearly embedded to achieve full diversity when zf or mmse receiver is used the complex orthogonal stbc ostbc satisfy the criterion as one may expect we also show that the symbol rates of stbc under this criterion are upper bounded by 1 subsequently we propose a novel family of stbc that satisfy the criterion and thus achieve full diversity with zf or mmse receiver our newly proposed stbc are constructed by overlapping the 2times2 alamouti code and hence named overlapped alamouti codes in this paper the new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas simulation results show that overlapped alamouti codes significantly outperform toeplitz codes for all numbers of transmit antennas and also outperform ostbc when the number of transmit antennas is above 4

dealing with label switching in mixture models summary in a bayesian analysis of finite mixture models parameter estimation and clustering are sometimes less straightforward than might be expected in particular the common practice of estimating parameters by their posterior mean and summarizing joint posterior distributions by marginal distributions often leads to nonsensical answers this is due to the so called label switching problem which is caused by symmetry in the likelihood of the model parameters a frequent response to this problem is to remove the symmetry by using artificial identifiability constraints we demonstrate that this fails in general to solve the problem and we describe an alternative class of approaches relabelling algorithms which arise from attempting to minimize the posterior expected loss under a class of loss functions we describe in detail one particularly simple and general relabelling algorithm and illustrate its success in dealing with the label switching problem on two examples

optimal grouping spacing stratification and piecewise constant approximation a variety of statistical problems of optimal grouping spacing and stratification are seen to be problems of optimal breakpoint selection for piecewise constant text l 2 0 1 approximation of certain functions this allows for the development of conditions that insure the existence and uniqueness of solutions a computational algorithm and simple approximate solutions in addition this approach is shown to provide insight into the relationships between the various problems considered

on the asymptotic distribution of scrambled net quadrature recently in a series of articles owen proposed the use of scrambled t m s nets and t s sequences in high dimensional numerical integration these scrambled nets and sequences achieve the superior accuracy of equidistribution methods while allowing for the simpler error estimation techniques of monte carlo methods the main aim of this article is to use stein s method to study the asymptotic distribution of the scrambled 0 m s net integral estimate in particular it is shown that for suitably smooth integrands on the s dimensional unit hypercube the estimate has an asymptotic normal distribution

scrambled net variance for integrals of smooth functions hybrids of equidistribution and monte carlo methods of integration can achieve the superior accuracy of the former while allowing the simple error estimation methods of the latter one version randomized t m s nets has the property that the integral estimates are unbiased and that the variance is o 1 n for any square integrable integrand stronger assumptions on the integrand allow one to find rates of convergence this paper shows that for smooth integrands over s dimensions the variance is of order n 3 log n 3 1 compared to n 1 for ordinary monte carlo thus the integration errors are of order n 3 2 log n s 1 2 in probability this compares favorably with the rate n 1 log n s 1 for unrandomized t m s nets

on the sphere decoding complexity of high rate multigroup decodable stbcs in asymmetric mimo systems a space time block code stbc is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum likelihood ml decoded independently of the other symbol groups in this paper we show that the upper triangular matrix r encountered during the sphere decoding of a linear dispersion stbc can be rank deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas we then show that all known families of high rate rate greater than 1 multigroup decodable codes have rank deficient r matrix even when the rate is less than the number of transmit and receive antennas and this rank deficiency problem arises only in asymmetric mimo systems when the number of receive antennas is strictly less than the number of transmit antennas unlike the codes with full rank r matrix the complexity of the sphere decoding based ml decoder for stbcs with rank deficient r matrix is polynomial in the constellation size and hence is high we derive the ml sphere decoding complexity of most of the known high rate multigroup decodable codes and show that for each code the complexity is a decreasing function of the number of receive antennas

the asymptotic efficiency of randomized nets for quadrature an l 2 type discrepancy arises in the average and worst case error analyses for multidimensional quadrature rules this discrepancy is uniquely defined by k x y which serves as the covariance kernel for the space of random functions in the average case analysis and a reproducing kernel for the space of functions in the worst case analysis this article investigates the asymptotic order of the root mean square discrepancy for randomized 0 m s nets in base b for moderately smooth k x y the discrepancy is o n 1 log n s 1 2 and for k x y with greater smoothness the discrepancy is o n 3 2 log n s 1 2 where n b m is the number of points in the net numerical experiments indicate that the t m s nets of faure niederreiter and sobol do not necessarily attain the higher order of decay for sufficiently smooth kernels however niederreiter nets may attain the higher order for kernels corresponding to spaces of periodic functions

a density quantile function approach to optimal spacing selection in this paper design techniques for continuous parameter time series regression analysis are employed to develop a general approach to optimal spacing selection for the linear estimation of location and scale parameters by sample quantiles from uncensored or censored samples the spacings derived from this approach are asymptotically optimal in the sense that they result in near optimal asymptotic relative efficiencies for large values of k the number of spacing elements a comparison with the optimum efficiencies for several distribution types indicates that the asymptotically optimum spacings perform well for k 7 the regression framework is also utilized to develop sufficient conditions for optimal spacing unicity and to obtain asymptotically optimal spacings for quantile estimation

space time processing for x channels using precoders in this paper we investigate how to send space time codes with full diversity and low decoding complexity for x channels using precoders first we assume that we have 2 transmitters and 2 receivers each transmitter sends different codewords to each receiver at the same time we propose an orthogonal transmission scheme that combines space time block coding and array processing to achieve low complexity decoding and full diversity for transmitted signals to our best knowledge this is the first scheme which can achieve low complexity decoding and full diversity for any transmitted codeword in x channel when all the users transmit at the same time finally we show that under certain conditions our proposed scheme can be extended to a general case with any number of transmitters and receivers each with any number of antennas simulation results validate our theoretical analysis

chebyshev polynomials over finite fields and reversibility of σ automata on square grids using number theory on function fields and algebraic number fields we prove results about chebyshev polynomials over finite prime fields to investigate reversibility of two dimensional additive cellular automata on finite square grids for example we show that there are infinitely many primitive irreversible additive cellular automata on square grids when the base field has order two or three

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

estimating with partial statistics the parameters of ergodic finite markov sources parameter estimation based on data emitted from a finite ergodic markov source is discussed this can be considered an extension of the memoryless case first an asymptotically optimal estimator is suggested for the case where the parametric model is completely known for an unknown parametric model e g unknown noise distribution with training sequences available a necessary condition is given for the existence of a universally optimum estimate a universal estimate is then suggested that is asymptotically nearly optimal the results hold under fairly mild regularity conditions

functional quantization of gaussian processes quantization consists in studying the lr error induced by the approximation of a random vector x by a vector quantized version taking a finite number n of values for rm valued random vectors the theory and practice is quite well established and in particular the asymptotics as n of the resulting minimal quantization error for nonsingular distributions is well known it behaves like c x r m n 1 m this paper is a transposition of this problem to random vectors in an infinite dimensional hilbert space and in particular to stochastic processes xt t 0 1 viewed as l2 0 1 dt valued random vectors for gaussian vectors and the l2 error we present detailed results for stationary and optimal quantizers we further establish a precise link between the rate problem and shannon kolmogorov s entropy of x this allows us to compute the exact rate of convergence to zero of the minimal l2 quantization error under rather general conditions on the eigenvalues of the covariance operator typical rates are o logn a a 0 they are obtained for instance for the fractional brownian motion and the fractional ornstein uhlenbeck process the exponent a is closely related with the l2 regularity of the process

linear mixed models with flexible distributions of random effects for longitudinal data normality of random effects is a routine assumption for the linear mixed model but it may be unrealistic obscuring important features of among individual variation we relax this assumption by approximating the random effects density by the seminonparameteric snp representation of gallant and nychka 1987 econometrics 55 363 390 which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior controlled by a user chosen tuning parameter an advantage is that the marginal likelihood may be expressed in closed form so inference may be carried out using standard optimization techniques we demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality and we illustrate the approach via simulation and using longitudinal data from the framingham study

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

strong consistency of k means clustering a random sample is divided into the k clusters that minimise the within cluster sum of squares conditions are found that ensure the almost sure convergence as the sample size increases of the set of means of the k clusters the result is proved for a more general clustering criterion

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

closed form designs of complex orthogonal space time block codes of rates k 1 2k for 2k 1 or 2k transmit antennas in this correspondence we present systematic and closed form constructions of complex orthogonal space time block codes from complex orthogonal designs of rates k 1 2k for 2k 1 or 2k transmit antennas for any positive integer k

toward a preferred 4 x 4 space time block code a performance versus complexity sweet spot with linear filter decoding we develop a new 4 4 hadamard precoded quasi orthogonal space time block code qo stbc that enables highly effective near maximum likelihood near ml reliability based prioritized symbol detection using linear filters approximate block error rate minimization is being used to optimize the code rotation angle detailed computational complexity evaluation of the decoder in terms of real multiplications and additions shows significant complexity reduction for symbol alphabet sizes of interest numerical and simulation studies demonstrate negligible bit error rate degradation compared to the state of the art in bit error rate by ml decoded 4 4 codewords

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

σ automata and chebyshev polynomials a automaton is an additive binary cellular automaton on a graph for product graphs such as a grids and cylinders reversibility and periodicity properties of the corresponding automaton can be expressed in terms of a binary version of chebyshev polynomials we will give a detailed analysis of the divisibility properties of these polynomials and apply our results to the study of automata

clustering for sparsely sampled functional data we develop a flexible model based procedure for clustering functional data the technique can be applied to all types of curve data but is particularly useful when individuals are observed at a sparse set of time points in addition to producing final cluster assignments the procedure generates predictions and confidence intervals for missing portions of curves our approach also provides many useful tools for evaluating the resulting models clustering can be assessed visually via low dimensional representations of the curves and the regions of greatest separation between clusters can be determined using a discriminant function finally we extend the model to handle multiple functional and finite dimensional covariates and show how it can be applied to standard finite dimensional clustering problems involving missing data

on fast decodable space time block codes we focus on full rate fast decodable space time block codes stbcs for 2 times 2 and 4times2 multiple input multiple output mimo transmission we first derive conditions and design criteria for reduced complexity maximum likelihood ml decodable 2times2 stbcs and we apply them to two families of codes that were recently discovered next we derive a novel reduced complexity 4times2 stbc and show that it outperforms all previously known codes with certain constellations

on the uniqueness of best 0 1 approximation by piecewise polynomials with variable breakpoints in this paper a sufficient condition for the uniqueness of best l2 0 1 approximation by piecewise polynomials of order k with variable breakpoints is generalized from that of order 2 other extensions included here are nonuniqueness and eventual uniqueness results

finite mixture modeling with mixture outcomes using the em algorithm summary this paper discusses the analysis of an extended finite mixture model where the latent classes corresponding to the mixture components for one set of observed variables influence a second set of observed variables the research is motivated by a repeated measurement study using a random coefficient model to assess the influence of latent growth trajectory class membership on the probability of a binary disease outcome more generally this model can be seen as a combination of latent class modeling and conventional mixture modeling the em algorithm is used for estimation as an illustration a random coefficient growth model for the prediction of alcohol dependence from three latent classes of heavy alcohol use trajectories among young adults is analyzed

latin hyperrectangle sampling for computer experiments latin hypercube sampling lhs is a popular method for evaluating the expectation of functions in computer experiments however when the expectation of interest is taken with respect to a nonuniform distribution the usual transformation to the probability space can cause relatively smooth functions to become extremely variable in areas of low probability consequently the equal probability cells inherent in hypercube methods often tend to sample an insufficient proportion of the total points in these areas this article introduces latin hyperrectangle sampling lhrs a generalization of lhs that allows for nonequal cell probabilities to address this problem a number of examples are given illustrating the improvement of the proposed methodology over lhs with respect to the variance of the resulting estimators extensions to orthogonal array based lhs stratified lhs and scrambled nets are also described

sampling designs for the detection of signals in noise sampling designs for the detection of sure signals in gaussian noise are considered both deterministic and random sampling schemes using optimal and nonoptimal detectors are presented and their performance is studied the analytical results are supplemented by comparison of performance for small and large sample size for some representative processes including the gauss markov and wiener processes

multidimensional σ automata p polynomials and generalised s matrices abstract in this article we study automata on finite multidimensional grids with different boundary conditions we obtain a natural representation of the global linear map of such automata in terms of kronecker products of matrices having a simple structure using this representation and properties of binary chebyshev polynomials we obtain necessary and sufficient condition for the invertibility of this map also in certain cases we relate this condition to the number theoretic properties of the number of dimensions and the lengths of the dimensions we generalise the notion of nearest neighbourhood to many dimensions and characterise invertibility of automata with such neighbourhoods

group decodable space time block codes with code rate 1 high rate space time block codes stbc with code rate 1 in multi input multi output mimo systems are able to provide both spatial multiplexing gain and diversity gain but have high maximum likelihood ml decoding complexity since group decodable quasi orthogonal code structure can reduce the decoding complexity we present in this paper systematic methods to construct group decodable high rate stbc with full symbol wise diversity gain for arbitrary transmit antenna number and code length we show that the proposed group decodable stbc can achieve high code rate that increases almost linearly with the transmit antenna number and the slope of this near linear dependence increases with the code length comparisons with existing low rate and high rate codes such as orthogonal stbc and algebraic stbc are conducted to show the decoding complexity reduction and good code performance achieved by the proposed codes

locally lattice sampling designs for isotropic random fields for predicting g v x z x dx where v is a fixed known function and z is a stationary random field a good sampling design should have a greater density of observations where v is relatively large in absolute value designs using this idea when g 0 1 have been studied for some time for g a region in two dimensions very little is known about the statistical properties of cubature rules based on designs with varying density this work proposes a class of designs that are locally parallelogram lattices but whose densities can vary the asymptotic variance of the cubature error for these designs is obtained for a class of isotropic random fields and an asymptotically optimal sequence of cubature rules within this class is found i conjecture that this sequence of cubature rules is asymptotically optimal with respect to all cubature rules

comparing two samples extensions of the t rank sum and log rank tests abstract i consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population i observe that the t rank sum and log rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice propose a criterion for identifying this problem in a particular data set and propose corresponding extensions of the conventional methods the proposed methods should be useful for both identifying and interpreting group differences

multigroup decodable stbcs from clifford algebras a space time block code stbc in k symbols variables is called a g group decodable stbc if its maximum likelihood ml decoding metric can be written as a sum of g terms for some positive integer g greater than one such that each term is a function of a subset of the k variables and each variable appears in only one term in this paper we provide a general structure of the weight matrices of multigroup decodable codes using clifford algebras without assuming that the number of variables in each group is the same a method of explicitly constructing the weight matrices of full diversity delay optimal multigroup decodable codes is presented for arbitrary number of antennas for the special case of 2 a number of transmit antennas we construct two subclass of codes 1 a class of 2 a group decodable codes with rate a 2 a 1 which is equivalently a class of single symbol decodable codes and 2 a class of 2a 2 group decodable codes with rate a 1 2 a 2 i e a class of double symbol decodable codes

generalized distributive law for ml decoding of space time block codes the problem of designing good space time block codes stbcs with low maximum likelihood ml decoding complexity has gathered much attention in the literature all the known low ml decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast decodable conditionally multigroup decodable structure of a code we refer to this well known technique of decoding stbcs as conditional ml cml decoding in this paper we introduce a new framework to construct ml decoders for stbcs based on the generalized distributive law gdl and the factor graph based sum product algorithm we say that an stbc is fast gdl decodable if the order of gdl decoding complexity of the code with respect to the constellation size m is strictly less than m where is the number of independent symbols in the stbc we give sufficient conditions for an stbc to admit fast gdl decoding and show that both multigroup and conditionally multigroup decodable codes are fast gdl decodable for any stbc whether fast gdl decodable or not we show that the gdl decoding complexity is strictly less than the cml decoding complexity for instance for any stbc obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable the gdl decoder provides about 12 times reduction in complexity compared to the cml decoder similarly for the golden code which is conditionally multigroup decodable the gdl decoder is only half as complex as the cml decoder

minimum light number of lit only σ game on a tree let t be a tree with leaves each vertex of t is assigned a state either lit or off an assignment of states to all the vertices of t is called a configuration the lit only s game allows the player to pick a lit vertex and change the states of all its neighbours we prove that for any initial configuration one can make a sequence of allowable moves to arrive at a configuration in which the number of lit vertices is no greater than email protected email protected we also give examples to show that the bound email protected email protected cannot be relaxed to email protected email protected

four group decodable space time block codes two new rate one full diversity space time block codes stbcs are proposed they are characterized by the lowest decoding complexity among the known rate one stbc arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection the first and the second codes are delay optimal if the number of transmit antennas is a power of 2 and even respectively the exact pairwise error probability is derived to allow for the performance optimization of the two codes compared with existing low decoding complexity stbc the two new codes offer several advantages such as higher code rate lower encoding decoding delay and complexity lower peak to average power ratio and better performance

optimal partitioning for linear mixed effects models applications to identifying placebo responders a longstanding problem in clinical research is distinguishing drug treated subjects that respond due to specific effects of the drug from those that respond to nonspecific or placebo effects of the treatment linear mixed effect models are commonly used to model longitudinal clinical trial data in this paper we present a solution to the problem of identifying placebo responders using an optimal partitioning methodology for linear mixed effects models since individual outcomes in a longitudinal study correspond to curves the optimal partitioning methodology produces a set of prototypical outcome profiles the optimal partitioning methodology can accommodate both continuous and discrete covariates the proposed partitioning strategy is compared and contrasted with the growth mixture modeling approach the methodology is applied to a two phase depression clinical trial where subjects in a first phase were treated openly for 12 weeks with fluoxetine followed by a double blind discontinuation phase where

a simple class of asymptotically optimal quantizers a simple class of quantizers is introduced which are asymptotically optimal as the number of quantization levels increases to infinity with respect to a mean r th power absolute error distortion measure these asymptotically optimal quantizers are very easy to compute their performance is evaluated for several distributions and compares favorably with the performance of the optimal quantizers in all cases for which the latter have been computed in addition their asymptotic robustness is studied under location scale and shape mismatch for several families of distributions

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

the influence of rounding errors on some nonparametric estimators of a density and its derivatives all continuous data is rounded to some extent and this rounding introduces errors into the estimation of the parent density and its derivatives in this paper we examine the influence of rounding errors on the two most popular types of nonparametric density estimator those based on kernels and those based on generalized fourier series our results lead directly to several important conclusions which are very relevant to the practical problems of density estimation

asymptotic optimality of regular sequence designs we study linear estimators for the weighted integral of a stochastic process the process may only be observed on a finite sampling design the error is defined in a mean square sense and the process is assumed to satisfy sacks ylvisaker regularity conditions of order r n o we show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators hereby we extend the results of sacks and ylvisaker for regularity r o or 1 and we confirm a conjecture by eubank smith and smith

uniqueness and eventual uniqueness of optimal designs in some time series models abstract earlier results on the uniqueness and eventual uniqueness of optimal designs for certain time series models are extended to a wider class of processes which includes those with covariance structures such as that of multiple integrals of brownian motion and brownian bridge processes the relationship between the problems of regression design for time series and piecewise polynomial approximation with free breakpoints is discussed and consequently asymptotic results obtained by sacks and ylvisaker 1970 are seen to hold under weaker assumptions for these processes

orthogonal array based latin hypercubes abstract in this article we use orthogonal arrays oa s to construct latin hypercubes besides preserving the univariate stratification properties of latin hypercubes these strength r oa based latin hypercubes also stratify each r dimensional margin therefore such oa based latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general latin hypercubes we prove that when used for integration the sampling scheme with oa based latin hypercubes offers a substantial improvement over latin hypercube sampling

a novel construction of multi group decodable space time block codes complex orthogonal design cod codes are known to have the lowest detection complexity among space time block codes stbcs however the rate of square cod codes decreases exponentially with the number of transmit antennas the quasi orthogonal design qod codes emerged to provide a compromise between rate and complexity as they offer higher rates compared to cod codes at the expense of an increase of decoding complexity through partially relaxing the orthogonality conditions the qod codes were then generalized with the so called g symbol and g group decodable stbcs where the number of orthogonal groups of symbols is no longer restricted to two as in the qod case however the adopted approach for the construction of such codes is based on sufficient but not necessary conditions which may limit the achievable rates for any number of orthogonal groups in this paper we limit ourselves to the case of unitary weight uw g group decodable stbcs for 2a transmit antennas where the weight matrices are required to be single thread matrices with non zero entries 1 j and address the problem of finding the highest achievable rate for any number of orthogonal groups this special type of weight matrices guarantees full symbol wise diversity and subsumes a wide range of existing codes in the literature we show that in this case an exhaustive search can be applied to find the maximum achievable rates for uw g group decodable stbcs with g 1 for this purpose we extend our previously proposed approach for constructing uw 2 group decodable stbcs based on necessary and sufficient conditions to the case of uw g group decodable stbcs in a recursive manner

estimation of parameters of the shifted gompertz distribution using least squares maximum likelihood and moments methods nonlinear least squares procedures for estimating the parameters of the shifted gompertz distribution are proposed simulation studies are carried out to compare weighted and unweighted least squares methods the maximum likelihood method and method of moments this work concludes that least squares methods via weighting factors to estimate the parameters of this probability distribution give a better performance than unweighted least squares methods showing the importance of weighting factors besides results of this simulation study show that a good performance is obtained using the maximum likelihood method and the estimators obtained with more bias are those of the method of moments

asymptotic quantization error of continuous signals and the quantization dimension extensions of the limiting qnanfizafion error formula of bennet are proved these are of the form d s k n f n beta b where n is the number of output levels d s k n f is the s th moment of the metric distance between quantizer input and output beta b 0 k s beta is the signal space dimension and f is the signal distribution if a suitably well behaved k dimensional signal density f x exists b b s k int f rho x dx 1 rho rho k s k and b s k does not depend on f for k 1 s 2 this reduces to bennett s formula if f is the cantor distribution on 0 1 0 and this k equals the fractal dimension of the cantor set 12 13 random quantization optimal quantization in the presence of an output information constraint and quantization noise in high dimensional spaces are also investigated

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

orthogonal column latin hypercubes and their application in computer experiments abstract latin hypercubes have been frequently used in conducting computer experiments in this paper a class of orthogonal latin hypercubes that preserves orthogonality among columns is proposed applying an orthogonal latin hypercube design to a computer experiment benefits the data analysis in two ways first it retains the orthogonality of traditional experimental designs the estimates of linear effects of all factors are uncorrelated not only with each other but also with the estimates of all quadratic effects and bilinear interactions second it can facilitate nonparametric fitting procedures because one can select good space filling designs within the class of orthogonal latin hypercubes according to selection criteria

the clustering of regression models method with applications in gene expression data summary identification of differentially expressed genes and clustering of genes are two important and complementary objectives addressed with gene expression data for the differential expression question many per gene analytic methods have been proposed these methods can generally be characterized as using a regression function to independently model the observations for each gene various adjustments for multiplicity are then used to interpret the statistical significance of these per gene regression models over the collection of genes analyzed motivated by this common structure of per gene models we proposed a new model based clustering method the clustering of regression models method which groups genes that share a similar relationship to the covariate s this method provides a unified approach for a family of clustering procedures and can be applied for data collected with various experimental designs in addition when combined with per gene methods for assessing differential expression that employ the same regression modeling structure an integrated framework for the analysis of microarray data is obtained the proposed methodology was applied to two microarray data sets one from a breast cancer study and the other from a yeast cell cycle study