lyapunov exponents for a duffing oscillator with the help of a parallel computer we perform a systematic computation of lyapunov exponents for a duffing oscillator driven externally by a force proportional to cos t in contrast to the familiar situation in discrete time systems where one finds windows of regularity embedded in intervals of chaos we find the continuous time duffing oscillator to contain a quite regular epetition of relatively self similar islands of chaos i e regions characterized by positive exponents embedded in large seas of regularity negative exponents we also investigate the effect of driving the oscillator with a jacobian elliptic function cn t m for m 0 one has cn t 0 cos t the usual trigonometric pumping for m 1 one has cn t 1 sech t a hyperbolic pumping when 0 m 1 the jacobian function is an intermediary double periodic function with periodicity depending on m and with fourier spectrum consisting of a regular train of narrow lines with varying envelope using m to tune the drive appropriately one may displace the islands of chaos in parameter space thus jacobian pumping provides a possible way of cleaning chaos in regions of the parameter space for periodically driven systems

non linear vibration of coupled duffing oscillators by an improved incremental harmonic balance method abstract the incremental harmonic balance method is improved by i reversing the order of increment and linearization to find the bifurcated solution branches ii using a fast fourier transform to compute the solution increments and the floquet matrix and iii finding the secondary path after a bifurcation by an improved arc length method a system of two duffing oscillators linked with a linear stiffness is taken as a numerical example the qualitative change of solution due to the change of the linking stiffness is studied in detail

contour regression a general approach to dimension reduction we propose a novel approach to sufficient dimension reduction in regression based on estimating contour directions of small variation in the response these directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response leading to simple and general contour regression scr and gcr methodology in comparison with existing sufficient dimension reduction techniques this contour based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions while maintaining sqrt n consistency and computational ease moreover it proves robust to departures from ellipticity we establish population properties for both scr and gcr and asymptotic properties for scr simulations to compare performance with that of standard techniques such as ordinary least squares sliced inverse regression principal hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses we demonstrate the use of contour based methods on a data set concerning soil evaporation

using the bootstrap to select one of a new class of dimension reduction methods dimension reduction in a regression analysis of response y given a p dimensional vector of predictors x reduces the dimension of x by replacing it with a lower dimensional linear combination x of the x s without specifying a parametric model and without loss of information about the conditional distribution of y given x we unify three existing methods sliced inverse regression sir sliced average variance estimate save and principal hessian directions phd into a larger class of methods each method estimates a particular candidate matrix essentially a matrix of parameters we introduce broad classes of dimension reduction candidate matrices and we distinguish estimators of the matrices from the matrices themselves given these classes of methods and several ways to estimate any matrix we now have the problem of selecting a particular matrix and estimation method we propose bootstrap methodology to select among candidate matrices estimators and dimension and in particular we investigate l

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

chaotic phase similarities and recurrences in a damped driven duffing oscillator we report strong evidence of remarkably close periodic repetitions of the structuring of the parameter space of a damped driven duffing oscillator as the amplitude of the drive increases families of period adding cascades and some intricate networks of periodic oscillations embedded in chaotic phases are also found to recur closely as the driving force grows such surprising regularities suggest that some hitherto unknown renormalization mechanism may be operating in higher codimension controlling the alternation of chaos and order in parameter space of certain flows

sparse sufficient dimension reduction existing sufficient dimension reduction methods suffer from the fact that each dimension reduction component is a linear combination of all the original predictors so that it is difficult to interpret the resulting estimates we propose a unified estimation strategy which combines a regression type formulation of sufficient dimension reduction methods and shrinkage estimation to produce sparse and accurate solutions the method can be applied to most existing sufficient dimension reduction methods such as sliced inverse regression sliced average variance estimation and principal hessian directions we demonstrate the effectiveness of the proposed method by both simulations and real data analysis

trellis coded cochannel interference canceller for microcellular radio cochannel interference is a major impairment that limits the capacity of microcellular radio systems this paper proposes a trellis coded cochannel interference canceller which uses trellis coded modulation with maximum likelihood sequence estimation of both the desired signal and cochannel interference this technique permits operation even when the signal to interference ratio is 0 db computer simulation results show that this technique significantly reduces the bit error rate in microcellular systems with nakagami rice fading particularly when the average signal to interference ratio is 0 db however the technique requires 1 synchronization of the interference and the desired signal and 2 higher computational complexity than standard techniques

poincare maps of duffing type oscillators and their reduction to circle maps i analytic results bifurcation diagrams and plots of lyapunov exponents in the r omega plane for duffing type oscillators x 2rx v x omega t 0 exhibit a regular pattern of repeating self similar tongues with complex internal structure the authors demonstrate here that this behaviour is easily understood qualitatively and quantitatively from the poincare map of the system in action angle variables this map approaches the one dimensional form phi n 1 a c e rt cos phi n t pi omega provided e rt but not necessarily ce rt r and omega are small the authors derive asymptotic for small r omega formulae for a and c for a special class of potentials v they argue that these special cases contain all the information needed to treat the general case of potentials which obey v or 0 at all times the essential tools of the derivation are the use of action angle variables the adiabatic approximation and the introduction of a non oscillating reference solution of duffing s equation with respect to which the action angle variables have to be determined these allow the explicit construction of the poincare map in powers of e rt to first order the authors obtain the phi map which survives asymptotically to second order they obtain the two dimensional i phi map in the i direction it contracts by a factor e rt upon each iteration

reweighting to achieve elliptically contoured covariates in regression abstract we investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates in particular new estimation methods like sir sirii save and phd have been built around the assumption of elliptically contoured covariates finite samples of regression covariates may deviate from this ideal in practice and the method developed here termed voronoi weighting can be used to induce elliptical symmetry in such samples in a number of examples we show that reweighting cases by the voronoi method can substantially enhance various procedures for covariates that deviate from elliptical symmetry we show that voronoi weighting in conjunction with some trimming via the minimum volume ellipsoid method can be effective

likelihood based sufficient dimension reduction we obtain the maximum likelihood estimator of the central subspace under conditional normality of the predictors given the response analytically and in simulations we found that our new estimator can preform much better than sliced inverse regression sliced average variance estimation and directional regression and that it seems quite robust to deviations from normality

suppression of adjacent channel cochannel and intersymbol interference by equalizers and linear combiners we describe the ability of a linear equalizer combiner or decision feedback equalizer to suppress all received adjacent channel intersymbol and cochannel interference the emphasis is on values among transmitter bandwidth receiver bandwidth carrier spacing and antenna diversity which provide the best opportunities for interference suppression through analyses of the number of degrees of freedom and constraints in generalized zero forcing equalizers and partial comparisons to calculations of equalizer minimum mean square performance four results are obtained first with one antenna and a linear equalizer arbitrarily large receiver bandwidths allow for marginal improvements in spectral efficiency through decreased carrier spacing because the carrier spacing cannot be reduced to a value below the symbol rate without incurring unsuppressible interference second large receiver bandwidths assist multiple antennas in improving the spectral efficiency in that carrier spacing values may go below the symbol rate even in the presence of cochannel interference third the use of equalizers and linear combiners together with large receiver bandwidths allows large transmitter bandwidths to be used fourth for cochannel interference and intersymbol interference the number of interferers that may be suppressible by a generalized zero forcing linear equalizer combiner increases linearly with the product of the number of antennas and the truncated integer ratio of the total bandwidth to the symbol rate

stability transitions of certain exact periodic responses in undamped helmholtz and duffing oscillators abstract a linear stability analysis in which phase integral theory is used is applied to certain exact subharmonic responses of undamped helmholtz and duffing oscillators which are valid beyond the limits of perturbation theory infinite sequences of stability transitions are identified in terms of the mathieu parameters and their limiting behaviours are investigated

direct semiparametric estimation of single index models with discrete covariates abstract others have developed average derivative estimators of the parameter in the model e y x x g x where g is an unknown function and x is a random vector these estimators are noniterative and easy to compute but require that x be continuously distributed this article develops a noniterative easily computed estimator of for models in which some components of x are discrete the estimator is n consistent and asymptotically normal an application to data on product innovation by german manufacturers illustrates the estimator s usefulness

a continuation algorithm for discovering new chaotic motions in forced duffing systems we study a dynamical system described by the duffing equation under static plus large periodic excitation the bifurcation diagram in terms of the amplitude of the periodic excitation reveals that there are at least six cascades of period doubling bifurcations with the other parameters fixed at specific values these six sequences are further investigated by a continuation algorithm which is based on the principles of the shooting method combined with the newton method for solving nonlinear equations a runge kutta huta method has been used for solving the system of differential equations the final conclusion is that each of the six sequences is governed by feigenbaum s number 4 6692 from universality theory beyond the limit values derived for the amplitude of the periodic excitation new strange attractors are found

a constructive approach to the estimation of dimension reduction directions in this paper we propose two new methods to estimate the dimension reduction directions of the central subspace cs by constructing a regression model such that the directions are all captured in the regression mean compared with the inverse regression estimation methods e g j amer statist assoc 86 1991 328 332 j amer statist assoc 86 1991 316 342 j amer statist assoc 87 1992 1025 1039 the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable and have better performance than the inverse regression estimation methods for finite samples compared with the direct regression estimation methods e g j amer statist assoc 84 1989 986 995 ann statist 29 2001 1537 1566 j r stat soc ser b stat methodol 64 2002 363 410 which can only estimate the directions of cs in the regression mean the new methods can detect the directions of cs exhaustively consistency of the estimators and the convergence of corresponding algorithms are proved

fourier methods for estimating the central subspace and the central mean subspace in regression in regression with a high dimensional predictor vector it is important to estimate the central and central mean subspaces that preserve sufficient information about the response and the mean response using the fourier transform we have derived the candidate matrices whose column spaces recover the central and central mean subspaces exhaustively under the normality assumption of the predictors explicit estimates of the central and central mean subspaces are derived bootstrap procedures are used for determining dimensionality and choosing tuning parameters simulation results and an application to a real data are reported our methods demonstrate competitive performance compared with sir save and other existing methods the approach proposed in the article provides a novel view on sufficient dimension reduction and may lead to more powerful tools in the future

wavelet analysis of time series for the duffing oscillator the detection of order within chaos we consider a wavelet analysis of various time series for the duffing oscillator for which there is a potential maximum and a harmonic forcing term and we focus on time series that return to the region of the potential maximum when the dynamics is chaotic and the time series is highly nonstationary there are many significant higher harmonics in a fourier expansion and the usual fourier analysis is problematic especially for short total times we show that the wavelet analysis is a robust tool that may be used to obtain qualitative information for highly nonstationary time series specifically that it may be used to detect a small amplitude harmonic forcing term even when the dynamics is chaotic and even for short total times

quasiperiodic resonance and bifurcations of tori in the weakly nonlinear duffing oscillator abstract we study analytically and numerically the weakly nonlinear quasiconservative duffing oscillator under 2 periodic forcing utilizing the secondary averaging approach we derive approximate analytical expressions for the quasiperiodic response of the oscillator and for conditions of torus bifurcations the theoretical results are in good agreement with the numerical ones the structure of the bifurcation sets in the oscillator parameter space is similar to that of a one dimensional map with two extrema

experimental mimicry of duffing s equation abstract extensive analytical and numerical investigations have focused on duffing s equation however experimental work in a mechanics context has been limited to studying systems the stiffness characteristics of which can be approximated by a non linear cubic restoring force e g a buckled beam excited transversely or a rigid pendulum undergoing moderately large amplitude motion this work describes a novel experimental approach whereby a particle rigid body is contrived to mimic the behavior of duffing s equation this is a direct extension of the concept of a ball rolling on a double well potential energy surface both free and forced oscillations are considered illustrating familiar non linear dynamics features including competing steady state attractors hysteresis sensitivity to initial conditions subharmonic oscillations and chaos

structure in the bifurcation diagram of the duffing oscillator we identify four levels of structure in the bifurcation diagram of the two well periodically driven duffing oscillator plotted as a function of increasing control parameter t the period of the driving term the superstructure or bifurcation peninsula repeats periodically as t increases by ensuremath sim 2 ensuremath pi beginning and ending with symmetric period one orbits whose local torsions differ by 2 within each bifurcation peninsula there is a systematic window structure the primary window structure is due to newhouse and newhouse like orbits fine structure is due to a farey sequence of well ordered orbits between the primary windows hyperfine structure consists of very narrow windows associated with non well ordered orbits we construct a template for the duffing oscillator a two dimensional return map and a one dimensional return map which describes the systematics of orbit creation and annihilation all structures are identified by topological indices our predictions are based on and compatible with numerical computations

duffing equation with two periodic forcings the phase effect a weak additional sinusoidal perturbation is applied to the periodically forced nonlinear oscillator to suppress chaos numerical simulations show that the phase difference between the two sinusoidal forces plays a very important role in controlling chaos when the frequencies of these forces deviate from the resonance condition slightly a different type of intermittency alternation from regular motion to chaotic motion called breather here is observed if the phase difference follows a wiener process conventional intermittency is observed

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

stochastic jump and bifurcation of a duffing oscillator under narrow band excitation abstract the variance of the displacement the probability densities of the displacement velocity and amplitude and the joint probability density of the displacement and velocity of the stationary response of a duffing oscillator to narrow band gaussian random excitation for a number of combinations of the parameters of the oscillator and excitation obtained from digital simulation are presented based on these results the stochastic jump and bifurcation of the system are examined it is shown that for each combination of the parameters all the statistics of the stationary response are unique and independent of initial conditions in a certain domain of the parameter space there are two more probable motions in the stationary response and jumps may occur the jump is a transition from one more probable motion to another or vice versa outside of this domain the stationary response is either nearly gaussian or like a diffused limit cycle as the parameters cross the boundary of the domain the qualitative behavior of the stationary response changes and it is a special kind of bifurcation it is pointed out that some previous results and explanations on this problem are incorrect

relaxation in a duffing potential abstract the solution of the equation of motion for a particle in a duffing potential v x 1 x 2 2 2 x 4 4 1 2 0 for arbitrary anharmonicity strength is characterized by the presence of odd frequencies which implies that velocity and position autocorrelation functions of such an oscillator in a microcanonical ensemble are also characterized by odd frequencies it is however non trivial to determine whether such discrete frequencies also characterize the autocorrelation functions in a canonical ensemble as discussed recently by fronzoni et al j stat phys 41 1985 553 we recover and extend upon the results of fronzoni et al to show analytically via mori lee theory that essentially discrete i e well defined peaks with finite but small width temperature dependent frequencies characterize the autocorrelation functions in a canonical ensemble

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response 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

on efficient dimension reduction with respect to a statistical functional of interest we introduce a new sufficient dimension reduction framework that targets a statistical functional of interest and propose an efficient estimator for the semiparametric estimation problems of this type the statistical functional covers a wide range of applications such as conditional mean conditional variance and conditional quantile we derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals the linear functional the composite linear functional and the implicit functional in conjunction with our theoretical analysis we also propose a class of one step newton raphson estimators and show by simulations that they substantially outperform existing methods finally we apply the new method to construct the central mean and central variance subspaces for a data set involving the physical measurements and age of abalones which exhibits a strong pattern of heteroscedasticity

poincare maps of duffing type oscillators and their reduction to circle maps ii methods and numerical results bifurcation diagrams and plots of lyapunov exponents in the r plane for duffing type oscillators exhibit a regular pattern of repeating self similar tongues with complex internal structure we demonstrate here how this behaviour is easily understood qualitatively and quantitatively from a poincare map of the system in action angle variables in the limit of large driving force or equivalently small driving frequency this map approaches the one dimensional form as derived in paper i this second paper describes our approach to calculating the various constants and functions introduced in paper i it gives numerical applications of the theory and tests its range of validity by comparison with results from the numerical integration of duffing type equations finally we show how to extend the range in the parameter space where the map is applicable

influences of harmonic coupling on bifurcations in duffing oscillator with bounded potential well abstract the dynamics of bifurcations in a dufhng oscillator with a bounded potential well is investigated special attention is paid to the prominent phenomena of repeated sets of symmetry and reverse symmetry breaking the harmonic balance method and floquet theory are employed to account for this peculiar phenomena

a paradox concerning nuisance parameters and projected estimating functions summary this paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters in a statistical model with unknown nuisance parameters the efficiency of an estimator of a parameter usually increases when the nuisance para meters are known however the opposite phenomenon can sometimes occur in this paper we elucidate the occurrence of this paradox by examining estimating functions in particular we focus on the projected estimating function which is defined by the projection of the score function on to a given estimating function a sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters in addition a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators

direction estimation in single index regressions we propose a general dimension reduction method that combines the ideas of likelihood correlation inverse regression and information theory we do not require that the dependence be confined to particular conditional moments nor do we place restrictions on the predictors or on the regression that are necessary for methods like ordinary least squares and sliced inverse regression although we focus on single index regressions the underlying idea is applicable more generally illustrative examples are presented

optimal escape from potential wells patterns of regular and chaotic bifurcation abstract the patterns of bifurcation governing the escape of periodically forced oscillations from a potential well over a smooth potential barrier are studied by numerical simulation both the generic asymmetric single well cubic potential and the symmetric twin well potential duffing oscillator are surveyed by varying three parameters forcing frequency forcing amplitude and damping coefficient the close relationship between optimal escape and nonlinear resonance within the well is confirmed over a wide range of damping subtle but significant differences are observed at higher damping ratios the possibility of indeterminate outcomes of jumps to and from resonance near optimal escape is cmppletely suppressed above a critical level of the damping ratio about 0 12 for the asymmetric single well oscillator coincidentally at almost the same level of damping the optimal escape condition becomes distinct from the apex in the f plane of the bistable regime this corresponds to the appearance of chaotic attractors which subsume both resonant and non resonant motions within one well at higher damping levels further changes occur involving conversions from chaotic saddle to regular saddle bifurcations these changes in optimal escape phenomena correspond to codimension three bifurcations at exceptional points in the space of three parameters these bifurcations are described in terms of homoclinic and heteroclinic structures of invariant manifolds and changes in accessible boundary orbits the same sequence of codimension three bifurcations is observed in both the twin well duffing oscillator and the asymmetric single well escape equation within the codimension three bifurcation patterns governing escape one particular codimension two global bifurcation involves a chaotic attractor explosion or interior crisis compounded with a blue sky catastrophe or boundary crisis of the exploded attractor this codimension two bifurcation has structure containing a form of predictive power knowledge of attractor bifurcations in part of the codimension two pattern permits inference of the attractor and basin bifurcations in the remainder this predictive power is applicable beyond the context of escape from potential wells quantitative correlation of bifurcation patterns between the two equations according to simple scaling laws is tested the unstable periodic orbits which figure most prominently in the major attractor basin bifurcations are of periods one and three their linking is conveniently interpreted by a three layer spiral horseshoe structure for the folding action in phase space within a well the structure of this 3 shoe implies a partial ordering among order three subharmonic saddle node bifurcations this helps explain the sequence of codimension three bifurcations near optimal escape some bifurcational precedence relations are known to follow from the linking of periodic orbits in a braid on a 3 shoe additional bifurcational precedence relations follow from a quantitative property of generic potential wells the dynamic hilltop saddle has a very large expanding multiplier over one cycle of forcing near fundamental resonance this quantitative property explains the close coincidence of codimension three bifurcations near the suppression of indeterminate outcomes an experimentalist s approach to identifying the three layer template structure from time series data is discussed including a consistency check involving poincare indices the bifurcation patterns emerging at higher damling values create favorable conditions for realizing experimental strategies to recognize optimal escape and locate it in parameter space strategies based solely on observations of quasi steady behavior while remaining always within one well are discussed

dimension reduction for non elliptically distributed predictors second order methods summary many classical dimension reduction methods especially those based on inverse conditional moments require the predictors to have elliptical distributions or at least to satisfy a linearity condition such conditions however are too strong for some applications li and dong 2009 introduced the notion of the central solution space and used it to modify first order methods such as sliced inverse regression so that they no longer rely on these conditions in this paper we generalize this idea to second order methods such as sliced average variance estimation and directional regression in doing so we demonstrate that the central solution space is a versatile framework we can use it to modify essentially all inverse conditional moment based methods to relax the distributional assumption on the predictors simulation studies and an application show a substantial improvement of the modified methods over their classical counterparts

oscillatory behavior of solutions of forced second order differential equations with alternating coefficients abstract in this paper we study the oscillatory behavior of solutions of the forced second order nonlinear ordinary functional differential equation x t g x t p t d dt sufficient conditions are established for all solutions of the equation to be oscillatory as well as bounded

weak and strong uniform consistency of kernel regression estimates we study the estimation of a regression function by the kernel method under mild conditions on the window the bandwidth and the underlying distribution of the bivariate observations x i y i we obtain the weak and strong uniform convergence rates on a bounded interval these results parallel those of silverman 1978 on density estimation and extend those of schuster and yakowitz 1979 and collomb 1979 on regression estimation

groupwise dimension reduction in many regression applications the predictors fall naturally into a number of groups or domains and it is often desirable to establish a domain specific relation between the predictors and the response in this article we consider dimension reduction that incorporates such domain knowledge the proposed method is based on the derivative of the conditional mean where the differential operator is constrained to the form of a direct sum this formulation also accommodates the situations where dimension reduction is focused only on part of the predictors as such it extends partial dimension reduction to cases where the blocked predictors are continuous through simulation and real data analyses we show that the proposed method achieves greater accuracy and interpretability than the dimension reduction methods that ignore group information furthermore the new method does not require the stringent conditions on the predictor distribution that are required by existing methods

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

bifurcation analysis of two coupled periodically driven duffing oscillators bifurcation diagrams and phase diagrams of two coupled periodically driven identical duffing oscillators are presented it is shown that the global pattern of bifurcation curves in parameter space consists of repeated subpatterns similar to the superstructure observed for single periodically driven strictly dissipative oscillators the subpattern itself however is different from that of a single duffing oscillator due in particular to hopf bifurcations that are newly added to the bifurcation scenario

on estimating regression based causal effects using sufficient dimension reduction summary in many causal inference problems the parameter of interest is the regression causal effect defined as the conditional mean difference in the potential outcomes given covariates in this paper we discuss how sufficient dimension reduction can be used to aid causal inference and we propose a new estimator of the regression causal effect inspired by minimum average variance estimation the estimator requires a weaker common support condition than propensity score based approaches and can be used to estimate the average causal effect for which it is shown to be asymptotically super efficient its finite sample properties are illustrated by simulation

continuous extension of the geometric control method in this paper we give a continuous version valid for flows of the geometric control method introduced by toroczkai et al 1994 and constructed for mappings on 2d poincare sections this method does not require explicit knowledge of the dynamics just a rough location of the periodic orbit and a single parameter easily computed from four data points applicability in numerical and real experiments is discussed

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