a constructive representation for the fourier dual of the zadoff chu sequences in this paper a complex matrix c consisting of a set of perfect sequences is studied the matrix c is constructed by taking the inverse discrete fourier transform idft of a diagonal matrix in which the diagonal elements comprise an arbitrary periodically perfect sequence gamma properties of the matrix c are presented in addition the fourier dual e of the matrix c is investigated when gamma is a zadoff chu sequence for the case of n even m 1 and g 0 an explicit representation for the matrix e is derived

generalized chirp like polyphase sequences with optimum correlation properties a new general class of polyphase sequences with ideal periodic autocorrelation function is presented the new class of sequences is based on the application of zadoff chu polyphase sequences of length n sm sup 2 where s and m are any positive integers it is shown that the generalized chirp like sequences of odd length have the optimum crosscorrelation function under certain conditions finally recently proposed generalized p4 codes are derived as a special case of the generalized chirp like sequence

optimal families of perfect polyphase sequences from the array structure of fermat quotient sequences we show that a p ary polyphase sequence of period p 2 from the fermat quotients is perfect that is its periodic autocorrelation is zero for all non trivial phase shifts we call this fermat quotient sequence we propose a collection of optimal families of perfect polyphase sequences using the fermat quotient sequences in the sense of the sarwate bound that is the cross correlation of two members in a family is upper bounded by p to investigate some relation between fermat quotient sequences and frank zadoff sequences and to construct optimal families including these sequences we introduce generators of p ary polyphase sequences of period p 2 using their p times p array structures we call an optimal generator to be the generator of some p ary polyphase sequences which are perfect and which gives an optimal family by the proposed construction finally we propose an algebraic construction for optimal generators as another main result a lot of optimal families of size p 1 can be constructed from these optimal generators some of which are known to be from the fermat quotient sequences or from the frank zadoff sequences but some families are new for p geq 11 the relation between the fermat quotient sequences and the frank zadoff sequences is determined as a by product

sufficient dimension reduction in regressions across heterogeneous subpopulations chiaromonte and co workers extended this method to regressions with qualitative predictors and developed a method partial sliced inverse regression under the assumption that the covariance matrices of the continuous predictors are constant across the levels of the qualitative predictor we extend partial sliced inverse regression by removing the restrictive homogeneous covariance condition this extension which significantly expands the applicability of the previous methodology is based on a new estimation method that makes use of a non linear least squares objective function

spreading sequences for multicarrier cdma systems the paper contains an analysis of the basic criteria for the selection of spreading sequences for the multicarrier cdma mc cdma systems with spectrum spreading in the frequency domain it is shown that the time domain crosscorrelation function between the spreading sequences is not a proper interference measure for the asynchronous mc cdma users therefore the spectral correlation function is introduced and together with the crest factor and the dynamic range of the corresponding multicarrier waveforms is used for the evaluation of mc cdma sequences some well known classes of sequences such as walsh gold orthogonal gold and zadoff chu sequences as well as legandre and golay complementary sequences are evaluated with respect to the aforementioned basic criteria it is also shown that the crest factors of the multicarrier spread spectrum waveforms based on the multilevel huffman sequences are very close to or even lower than the crest factor of a single sine wave

the mean curvature flow for isoparametric submanifolds a submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant we study the mean curvature flow with initial data an isoparametric submanifold in euclidean space and sphere we show that the mean curvature flow preserves the isoparametric condition develops singularities in finite time and converges in finite time to a smooth submanifold of lower dimension we also give a precise description of the collapsing

a construction of odd length generators for optimal families of perfect sequences in this paper we give a construction of optimal families of n ary perfect sequences of period n 2 where n is a positive odd integer for this we re define perfect generators and optimal generators of any length n which were originally defined only for odd prime lengths by park song kim and golomb in 2016 but investigate the necessary and sufficient condition for these generators for arbitrary length n based on this we propose a construction of odd length optimal generators by using odd prime length optimal generators for a fixed odd integer n and its odd prime factor p the proposed construction guarantees at least n p p 1 phi n p phi p phi p 1 phi n 2 inequivalent optimal generators of length n in the sense of constant multiples cyclic shifts and or decimations here phi cdot is euler s totient function from an optimal generator one can construct lots of different n ary optimal families of period n 2 all of which contain p text min 1 perfect sequences where p text min is the least positive prime factor of n

generalized cross correlation properties of chu sequences in this paper detailed cross correlation properties for chu sequences are investigated all possible values of the cross correlation function of chu sequences are derived for any given sequence length and lag and the maximum magnitude distribution function n x which is defined as the number of all chu sequence pairs with length n whose maximum magnitude of the cross correlation function is nx is obtained also good lower and upper bounds on the maximum number of available chu sequences and a construction algorithm for the corresponding partial chu sequence set are proposed when the maximum magnitude of the cross correlation among the sequences is constrained numerical examples show that the proposed bounds are quite tight and the proposed construction algorithm is near optimal up to fairly large value of n

k means inverse regression li suggested the method of sliced inverse regression for dimension reduction in regressions with a univariate response in this article we extend that method to multivariate regressions by introducing a new way of performing the slicing this method applies for any number of response variables and may be particularly useful at the outset of an analysis before positing a multivariate model the emphasis is on application no new asymptotic theory is presented

aggregate inverse mean estimation for sufficient dimension reduction many well known sufficient dimension reduction methods investigate the inverse conditional moments of the predictors given the response the required linearity condition the number and ar

testing predictor contributions in sufficient dimension reduction we develop tests of the hypothesis of no effect for selected predictors in regression without assuming a model for the conditional distribution of the response given the predictors predictor effects need not be limited to the mean function and smoothing is not required the general approach is based on sufficient dimension reduction the idea being to replace the predictor vector with a lower dimensional version without loss of information on the regression methodology using sliced inverse regression is developed in detail

dimension reduction and semiparametric estimation of survival models in this paper we propose a new dimension reduction method by introducing a nominal regression model with the hazard function as the conditional mean which naturally retrieves information from complete data and censored data as well moreover without requiring the linearity condition the new method can estimate the entire central subspace consistently and exhaustively the method also provides an alternative approach for the analysis of censored data assuming neither the link function nor the distribution hence it exhibits superior robustness properties numerical studies show that the method can indeed be readily used to efficiently estimate survival models explore the data structures and identify important variables

multiple loci mapping via model free variable selection summary despite recent flourish of proposals o nv ariable selection genome wide multiple loci mapping remains to be challenging the majority of existing variable selection methods impose a model and often the homoscedastic linear model prior to selection however the true association between the phenotypical trait and the genetic markers is rarely known ap riori and the presence of epistatic interactions makes the association more complex than al inear relation model free variable selection o ers a useful alternative in th is context but the fact that the number of markers p often far exceeds the number of experimental units n renders all the existing model free solutions that require n p inapplicable in this article we examine a number of model free variable selection methods for small n large p regressions in the context of genome wide multiple loci mapping we propose and advocate a multivariate group wise adaptive penalization solution which requires no model prespecification and thus works for complex trait marker association and handles one variable at a time so that works for n p e ctiveness of the new method is demonstrated through bo th intensive simulations and a comprehensive real data analysis across 6100 gene expression traits

a systematic method for constructing sparse gaussian integer sequences with ideal periodic autocorrelation functions a gaussian integer is a complex number whose real and imaginary parts are both integers meanwhile a sequence is defined as perfect if and only if it has an ideal periodic auto correlation function this paper proposes a method for constructing sparse perfect gaussian integer sequences spgiss in which most of the sequence elements are zero the proposed spgiss are obtained by linearly combining four base sequences or their cyclic shift equivalents using nonzero gaussian integer coefficients of equal magnitudes each base sequence contains four nonzero elements belonging to the set pm 1 pm j the number of nonzero elements of the constructed spgiss depends on the choice of complex coefficients and cyclic shifts however each spgis has at most 16 nonzero elements irrespective of the sequence length a systematic investigation is performed into the properties of the spgiss and their fourier dual equivalents finally a general expression is derived for a perfect gaussian integer sequence pgis of length 4n where n is any positive integer and most of the sequence elements are nonzero

identifying regression outliers and mixtures graphically regressions in practice can include outliers and other unknown subpopulation structures for example mixtures of regressions occur if there is an omitted categorical predictor like gender or location and different regressions occur within each category the theory of regression graphics based on central subspaces can be used to construct graphical solutions to long standing problems of this type it is argued that in practice the central subspace automatically expands to incorporate outliers and regression mixtures thus methods of estimating the central subspace can be used to identify these phenomena without specifying a model examples illustrating the power of the theory are presented

bat chirps with good properties zak space construction of perfect polyphase sequences previously a discretization of the linear fm chirp of length n kl 2 l and kl isin z was given and the conditions for its minimal zak space support were derived chirps satisfying these conditions are known as finite chirps in this work subsets of finite chirps of length n l 2 l a prime are examined the investigation leads to a new zak space construction of general polyphase sequence sets of size l 1 with optimal auto and cross correlation properties known as perfect sequence sets it is shown that perfect sequence sets are closely related to sets of finite chirps and in particular include the sets of zadoff chu sequences which are identical with subsets of finite chirps and the sets of generalized frank sequences which are identical with sets of modulations of finite chirps as special cases the entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group the construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group

principal hessian directions for regression with measurement error summary we consider a nonlinear regression problem with predictors with measurement error we assume that the response is related to unknown linear combinations of a p dimensional predictor vector through an unknown link function instead of observing the predictors we observe a surrogate vector with the property that its expectation is linearly related to the predictor vector with constant variance we use an important linear transformation of the surrogates based on the transformed variables we develop the modified principal hessian directions method for estimating the subspace of the effective dimension reduction space we derive the asymptotic variances of the modified principal hessian directions estimators several examples are reported and comparisons are made with the sliced inverse regression method of carroll li 1992

constant modulus and reduced papr block differential encoding for frequency selective channels frequency selective channels can be converted to a set of flat fading subchannels by employing orthogonal frequency division multiplexing ofdm conventional differential encoding on each subchannel however suffers from loss of multipath diversity and a very high peak to average power ratio papr which causes undesirable nonlinear effects to mitigate these effects we design a block differential encoding scheme over the subchannels that preserves multipath diversity and in addition results in constant modulus transmitted symbols this property is shown to ensure that the papr of the continuous time transmitted waveform is reduced by a large factor the maximum likelihood decoder for the proposed scheme conditioned on the current and previous received block is shown to have linear complexity in the number of subcarriers the constant modulus scheme will yield good bit error rate performance with full rate only if short blocks are used however one may mitigate this problem by relaxing the constant modulus requirement we show that in a practical ofdm system we can group the subcarriers into shorter subblocks in a certain manner and apply the constant modulus technique to each subblock thus we improve diversity at a very low decoder complexity and at the same time we introduce an upper bound on the discrete time papr which in turn may lead to appreciable reduction in continuous time papr depending on the system parameters finally in situations where we can sacrifice rate additional complex field coding may be used to exploit the multipath diversity provided by channels longer than those the simple scheme can handle

dimension reduction for the conditional kth moment in regression the idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction here we introduce the central kth moment subspace to capture information from the mean variance and so on up to the kth conditional moment of the regression new methods are studied for estimating these subspaces connections with sliced inverse regression are established and examples illustrating the theory are presented

a new class of zero correlation zone sequences in this correspondence two new methods for constructing sets of zero correlation zone zcz sequences are proposed these methods are based on perfect sequences and unitary matrices compared with previous methods the proposed methods can generate sets of nonbinary zcz sequences having a longer zero correlation zone the sequences obtained by these methods are suitable for approximately synchronized code division multiple access as cdma systems

on sliced inverse regression with high dimensional covariates sliced inverse regression is a promising method for the estimation of the central dimension reduction subspace cdr space in semiparametric regression models it is particularly useful in tackling cases with high dimensional covariates in this article we study the asymptotic behavior of the estimate of the cdr space with high dimensional covariates that is when the dimension of the covariates goes to infinity as the sample size goes to infinity strong and weak convergence are obtained we also suggest an estimation procedure of the bayes information criterion type to ascertain the dimension of the cdr space and derive the consistency a simulation study is conducted

gaussian integer sequences with ideal periodic autocorrelation functions a gaussian integer is a complex number whose real and imaginary parts are both integers meanwhile a sequence is defined as perfect if and only if the out of phase value of the periodic autocorrelation function is equal to zero this paper presents two novel classes of perfect sequences constructed using two groups of base sequences the nonzero elements of these base sequences belong to the set 1 j a perfect sequence can be obtained by linearly combining these base sequences or their cyclic shift equivalents with arbitrary nonzero complex coefficients of equal magnitudes in general the elements of the constructed sequences are not gaussian integers however if the complex coefficients are gaussian integers then the resulting perfect sequences will be gaussian integer perfect sequences gipss in addition a periodic cross correlation function is derived which has the same mathematical expression as the investigated sequences finally the maximal energy efficiency of the proposed gipss is investigated

dimension reduction in regression without matrix inversion summary regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields sufficient dimension reduction provides a promising approach to such problems by restricting attention to d n linear combinations of the original p predictors however standard methods of sufficient dimension reduction require inversion of the sample predictor covariance matrix we propose a method for estimating the central subspace that eliminates the need for such inversion and is applicable regardless of the n p relationship simulations show that our method compares favourably with standard large sample techniques when the latter are applicable we illustrate our method with a genomics application

efficiency loss caused by linearity condition in dimension reduction linearity sometimes jointly with constant variance is routinely assumed in the context of sufficient dimension reduction it is well understood that when these conditions do not hold blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace surprisingly we discover that even if these conditions do hold using them will bring efficiency loss this paradoxical phenomenon is illustrated through sliced inverse regression and principal hessian directions the efficiency loss also applies to other dimension reduction procedures we explain this empirical discovery by theoretical investigation

polyphase codes for uplink ofdm cdma systems we propose a ofdm cdma system that employs polyphase codes to support variable spreading factors a systematic approach for constructing the polyphase code sequences of variable spreading factors is developed polyphase codes exhibit better auto and cross correlation properties than hadamard codes when employed in ofdm cdma systems polyphase codes result in certain structured multiple access interference mai caused by multipath analytical and numerical results show that ofdm cdma systems employing polyphase codes have better papr performance than those using hadamard codes the ber performance of the ofdm cdma system using polyphase codes is evaluated by numerical results and compared to that of the ofdm cdma system using hadamard codes with and without clipping

model free variable selection computing power has encouraged the modelling of data sets of ever increasing size data mining applications in finance marketing and bioinformatics are obvious examples a limitation of nearly all existing variable selection methods is the need to specify the correct model before selection when the number of predictors is large model formulation and validation can be difficult or even infeasible on the basis of the theory of sufficient dimension reduction we propose a new class of model free variable selection approaches the methods proposed assume no model of any form require no nonparametric smoothing and allow for general predictor effects the efficacy of the methods proposed is demonstrated via simulation and an empirical example is given

optimum sets of interference free sequences with zero autocorrelation zones a general construction of a particular class of zero correlation zone sequences is proposed the general construction produces the sets of so called interference free zero autocorrelation zone if zaz sequences where any two sequences from a set have all zero periodic cross correlation while each sequence has periodic autocorrelation equal to zero in multiple zones of non zero delays the length d of each such zaz has the maximum possible value d t 1 for given sequence length n tm and for the given number of sequences in the set m m as an important special case of the general construction we present the construction of generalized chirp like if zaz sequences that allow particularly simple implementation of the corresponding banks of matched filters

modulatable orthogonal sequences and their application to ssma systems a set of n 1 orthogonal sequences of period n sup 2 is proposed where n is a natural number each orthogonal sequence proposed can be modulated by n complex numbers of absolute value 1 so the modulated sequence is also orthogonal when n is an odd prime number the absolute value of the cross correlation function between any two of the n 1 orthogonal sequences is constant and satisfies the mathematical lower bound this property of the cross correlation function is not changed when each of the two orthogonal sequences is modulated by n complex numbers of absolute value 1 two spread spectrum multiple access ssma systems using these sequences are proposed one system is an asynchronous ssma system using the proposed sequences unmodulated the cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous ssma system using a set of orthogonal sequences the other system is a synchronous ssma system without cochannel interference which uses the modulated form of the proposed sequences

implications of influence function analysis for sliced inverse regression and sliced average variance estimation sliced inverse regression sliced inverse regression ii and sliced average variance estimation are three related dimension reduction methods that require relatively mild model assumptions as an approximation for the relative influence of single observations from large samples the influence function is used to compare the sensitivity of the three methods to particular observational types the analysis carried out here helps to explain why there is a lack of agreement concerning the preferability of these dimension reduction procedures in general an efficient sample version of the influence function is also developed and evaluated

an rkhs formulation of the inverse regression dimension reduction problem suppose that y is a scalar and x is a second order stochastic process where y and x are conditionally independent given the random variables 1 p which belong to the closed span l2 of x this paper investigates a unified framework for the inverse regression dimension reduction problem it is found that the identification of l2 with the reproducing kernel hilbert space of x provides a platform for a seamless extension from the finite to infinite dimensional settings it also facilitates convenient computational algorithms that can be applied to a variety of models

on almost linearity of low dimensional projections from high dimensional data this paper studies the shapes of low dimensional projections from high dimensional data after standardization let mathbf x be a p dimensional random variable with mean zero and identity covariance for a projection beta mathbf x beta 1 find another direction b so that the regression curve of b mathbf x against beta mathbf x is as nonlinear as possible we show that when the dimension of mathbf x is large for most directions beta even the most nonlinear regression is still nearly linear our method depends on the construction of a pair of p dimensional random variables mathbf w 1 mathbf w 2 called the rotational twin and its density function with respect to the standard normal density with this we are able to obtain closed form expressions for measuring deviation from normality and deviation from linearity in a suitable sense of average as an interesting by product from a given set of data we can find simple unbiased estimates of e f beta mathbf x t phi 1 t 1 2 and e lbrack e mathbf x mid beta beta mathbf x t 2 t 2 f 2 beta mathbf x t phi 2 1 t rbrack where phi 1 is the standard normal density f beta mathbf x is the density for beta mathbf x and the e is taken with respect to the uniformly distributed beta this is achieved without any smoothing and without resorting to any laborious projection procedures such as grand tours our result is related to the work of diaconis and freedman the impact of our result on several fronts of data analysis is discussed for example it helps establish the validity of regression analysis when the link function of the regression model may be grossly wrong a further generalization which replaces beta mathbf x by b mathbf x with b beta 1 ldots beta k for k randomly selected orthonormal vectors beta i i 1 ldots k helps broaden the scope of application of sliced inverse regression sir

a construction of multiple optimal zcz sequence sets with good cross correlation zero correlation zone zcz sequences are a class of spreading sequences having ideal auto correlation and cross correlation in a zone around the origin they have been extensively studied in recent years due to their important applications in quasi synchronous code division multiple access systems in this paper a construction of zcz sequence sets is proposed based on perfect nonlinear functions it generates multiple zcz sequence sets with the properties 1 each sequence is perfect in the sense that its out of phase auto correlation is always zero 2 each zcz sequence set is optimal with respect to the tang fan matsufuji bound in which all the sequences are pairwise cyclically distinct and 3 the maximum inter set cross correlation of multiple sequence sets achieves the well known sarwate bound

dimension reduction for conditional mean in regression in many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors and less concerned with the other aspects of the conditional distribution in this paper we develop dimension reduction methods that incorporate this consideration we introduce the notion of the central mean subspace cms a natural inferential object for dimension reduction when the mean function is of interest we study properties of the cms and develop methods to estimate it these methods include a new class of estimators which requires fewer conditions than phd and which displays a clear advantage when one of the conditions for phd is violated cms also reveals a transparent distinction among the existing methods for dimension reduction ols phd sir and save we apply the new methods to a data set involving recumbent cows

sliced regression for dimension reduction a new dimension reduction method involving slicing the region of the response and applying local kernel regression to each slice is proposed compared with the traditional inverse regression methods e g sliced inverse regression sir the new method is free of the linearity condition and has much better estimation accuracy compared with the direct estimation methods e g mave the new method is much more robust against extreme values and can capture the entire central subspace cs exhaustively to determine the cs dimension a consistent cross validation criterion is developed extensive numerical studies including a real example confirm our theoretical findings

partial period correlations of zadoff chu sequences and their relatives partial period correlations of sequences are an important performance measure of communication systems employing them but are known to be notoriously difficult to analyze in this paper we present a systematic approach to partial period correlations as a generalization of the paterson lothian approach for a pair of sequences not necessarily distinct we introduce the linear phase shifting sequences of one of them and analyze their full period correlations called the induced correlations with the other one by exploiting the induced correlations we obtain the partial period correlation properties of the given pair we then investigate zadoff chu sequences and give some theoretical results on their partial period autocorrelations including closed form expressions and the first and second moments we also derive an upper bound on the magnitudes of the partial period cross correlations of zadoff chu sequences finally we explore generalized chirp like discrete fourier transform sequences and show that their partial period cross correlations have the same magnitudes as the partial period autocorrelations of the employed zadoff chu sequence up to permutation

unimodular perfect sequences of length p sup s a new class of unimodular perfect sequences of length p sup s where p is a prime is proposed an explicit secondary construction is provided this construction includes most of the previously known unimodular perfect sequences of length p sup s as special cases also the proposed construction is extended to sequences with autocorrelation over spl zopf sup s sub p sup k v sub m2 spl times spl zopf sub p sup m1 v sub k

optimal sufficient dimension reduction in regressions with categorical predictors though partial sliced inverse regression partial sir chiaromonte et al 2002 sufficient dimension reduction in regressions with categorical predictors ann statist 30 475 497 extended the scope of sufficient dimension reduction to regressions with both continuous and categorical predictors its requirement of homogeneous predictor covariances across the subpopulations restricts its application in practice when this condition fails partial sir may provide misleading results in this article we propose a new estimation method via a minimum discrepancy approach without this restriction our method is optimal in terms of asymptotic efficiency and its test statistic for testing the dimension of the partial central subspace always has an asymptotic chi squared distribution it also gives us the ability to test predictor effects an asymptotic chi squared test of the conditional independence hypothesis that the response is independent of a selected subset of the continuous predictors given the remaining predictors is obtained

a model free test for reduced rank in multivariate regression we propose a test of dimension in multivariate regression this test is in the spirit of tests on the rank of the coefficient matrix in a multivariate linear model but it does not require a prespecified model the test may be particularly useful at the outset of an analysis before a multivariate model is posited because it can lead to low dimensional summary plots that are inferred to contain all of the sample information on the multivariate mean function

on directional regression for dimension reduction we introduce directional regression dr as a method for dimension reduction like contour regression dr is derived from empirical directions but achieves higher accuracy and requires substantially less computation dr naturally synthesizes the dimension reduction estimators based on conditional moments such as sliced inverse regression and sliced average variance estimation and in doing so combines the advantages of these methods under mild conditions it provides exhaustive and consistent estimate of the dimension reduction space we develop the asymptotic distribution of the dr estimator and from that a sequential test procedure to determine the dimension of the central space we compare the performance of dr with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models finally we apply dr to analyze a data set concerning the identification of hand written digits

complex optimal sequences with constant magnitude for fast channel estimation initialization optimal sounding sequences which satisfy a certain autocorrelation property are useful for fast channel estimation techniques which are based on noniterative channel sounding methods we study optimal sequences consisting of complex symbols with constant magnitude an indirect sequence construction method is derived by considering the phase difference between sequence symbols our construction method includes periodic and nonperiodic optimal sequences and provides insight into the nature and properties of optimal sequences that are based on consecutive roots of unity phase difference sequences

generalized chirp like sequences with zero correlation zone in this paper a new construction of optimum sets of zero correlation zone zcz sequences derived from generalized chirp like gcl sequences is presented a special case with reduced alphabet size is also described in a set of gcl zcz sequences the length of the zero correlation zone d has the maximum possible value d t 1 for a given sequence length n tm and for a given number of sequences in the set m m many values of n can be decomposed into multiple products of two positive integers thus allowing for flexible tradeoff between the length of the zcz and the number of sequences in the set as the set of gcl zcz sequences is obtained by modulating a common carrier sequence with a set of orthogonal modulating sequences there is a possibility for efficient implementation of the corresponding bank of matched filters

sufficient dimension reduction via inverse regression a family of dimension reduction methods the inverse regression ir family is developed by minimizing a quadratic objective function an optimal member of this family the inverse regression estimator ire is proposed along with inference methods and a computational algorithm the ire has at least three desirable properties 1 its estimated basis of the central dimension reduction subspace is asymptotically efficient 2 its test statistic for dimension has an asymptotic chi squared distribution and 3 it provides a chi squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors current methods like sliced inverse regression belong to a suboptimal class of the ir family comparisons of these methods are reported through simulation studies the approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in slic

graphics for regressions with a binary response abstract central dimension reduction subspaces which characterize the dependence of a response variable on one or more predictors are developed and then used to guide the construction and interpretation of graphics for regression problems with a binary response variable graphical methods requiring neither a link function nor residuals are suggested for both development and criticism of model components implied by the central dimension reduction subspace

n shift cross orthogonal sequences n shift cross orthogonal sequences and a complete complementary code derived from them are defined and discussed a general method for generating this code is also discussed a synchronous multiple user spread spectrum multiple system is proposed that uses n shift cross orthogonal sequences

new sequences design from weil representation with low two dimensional correlation in both time and phase shifts a new elementary expression of the construction first proposed by gurevich hadani and sochen is given which avoids the explicit use of the weil representation the sequences in this signal set are given by both multiplicative character and additive character of finite field fp such a signal set consists of p2 p 2 time shift distinct sequences the magnitude of the two dimensional autocorrelation function i e the ambiguity function in both time and phase of each sequence is upper bounded by 2 p at any shift not equal to 0 0 furthermore the magnitude of their fourier transform spectrum is less than or equal to 2 for a subset consisting of p p 2 phase shift distinct sequences in this signal set the magnitude of the ambiguity function of any pair is upper bounded by 4 p a proof is given through finding a new expression of the sequences in the finite harmonic oscillator system an open problem for directly establishing these assertions without involving the weil representation is addressed

sparse sliced inverse regression sliced inverse regression sir is an innovative and effective method for dimension reduction and data visualization of high dimensional problems it replaces the original variables with low dimensional linear combinations of predictors without any loss of regression information and without the need to prespecify a model or an error distribution however it suffers from the fact that each sir component is a linear combination of all the original predictors thus it is often difficult to interpret the extracted components by representing sir as a regression type optimization problem we propose in this article a new method called sparse sir that combines the shrinkage idea of the lasso with sir to produce both accurate and sparse solutions the efficacy of the proposed method is verified by simulation and a real data example is given

optimal design and placement of pilot symbols for channel estimation the problem of designing and placing pilot symbols for the estimation of frequency selective random channels is considered the channel is assumed to be a block fading model with finite impulse response fir for both single input single output siso and multiple input multiple output mimo channels under the assumption of independent and identical distributed channel taps the cramer rao bound crb on the mean square error mse of semi blind channel estimators is derived and minimized with respect to pilot symbols and their placement it is shown that the optimal strategy is to place pilot symbols satisfying certain orthogonality condition in such a way that data and pilot symbols with higher power are in the middle of the packet the results also indicate that the optimal pilot placements are independent of channel probability distribution for constant modulus symbols we show that the quasi periodic placement and its generalization in the multiuser case turn out to be optimal we further consider estimating channels with correlated taps and show that the previous placement strategy is also optimal among orthogonal pilot sequences

sufficient forecasting using factor models we consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect the dimensionality was first reduced via a high dimensional approximate factor model implemented by the principal component analysis using the extracted factors we develop a novel forecasting method called the sufficient forecasting which provides a set of sufficient predictive indices inferred from high dimensional predictors to deliver additional predictive power the projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi parametric approximate factor model is assumed our method is also applicable to cross sectional sufficient regression using extracted factors the connection between the sufficient forecasting and the deep learning architecture is explicitly stated the sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function the proposed method extends the sufficient dimension reduction to high dimensional regimes by condensing the cross sectional information through factor models we derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices we further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace our method and theory allow the number of predictors to be larger than the number of observations we finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables

a semiparametric approach to dimension reduction we provide a novel and completely different approach to dimension reduction problems from the existing literature we cast the dimension reduction problem in a semiparametric estimation framework and derive estimating equations viewing this problem from the new angle allows us to derive a rich class of estimators and obtain the classical dimension reduction techniques as special cases in this class the semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact the common assumption of linearity and or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression the semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example this article has online supplementary material

estimating sufficient reductions of the predictors in abundant high dimensional regressions we study the asymptotic behavior of a class of methods for sufficient dimension reduction in high dimension regressions as the sample size and number of predictors grow in various alignments it is demonstrated that these methods are consistent in a variety of settings particularly in abundant regressions where most predictors contribute some information on the response and oracle rates are possible simulation results are presented to support the theoretical conclusion