new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

on the non negative garrotte estimator summary we study the non negative garrotte estimator from three different aspects consistency computation and flexibility we argue that the non negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form in particular we consider using the lasso the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non negative garrotte we prove that the non negative garrotte has the nice property that with probability tending to 1 the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables whereas such a property may not be valid for the initial estimators in general we show that the non negative garrotte can turn a consistent estimate into an estimate that is not only consistent in terms of estimation but also in terms of variable selection we also show that the non negative garrotte has a piecewise linear solution path using this fact we propose an efficient algorithm for computing the whole solution path for the non negative garrotte simulations and a real example demonstrate that the non negative garrotte is very effective in improving on the initial estimator in terms of variable selection and estimation accuracy

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

unified lasso estimation by least squares approximation we propose a method of least squares approximation lsa for unified yet simple lasso estimation our general theoretical framework includes ordinary least squares generalized linear models quantile regression and many others as special cases specifically lsa can transfer many different types of lasso objective functions into their asymptotically equivalent least squares problems thereafter the standard asymptotic theory can be established and the lars algorithm can be applied in particular if the adaptive lasso penalty and a bayes information criterion type tuning parameter selector are used the resulting lsa estimator can be as efficient as the oracle extensive numerical studies confirm our theory

stability analysis of the mixed traffic flow of cars and trucks using heterogeneous optimal velocity car following model abstract real world traffic flow usually contains a mixture of passenger vehicles pv and heavy vehicles hv in this paper the four types of car truck following combinations are considered the car following car case car following truck case truck following car case and truck following truck case the effect of different combinations on the stability of traffic flow is explored by converting the original bando s optimal velocity ov model to a heterogeneous form a new linear stability analysis method that can derive the stability criterion of the heterogeneous traffic flow mixed by cars and trucks is introduced moreover the effect of the proportions of the four car truck following combinations on traffic flow is examined through the trajectory analysis it concludes that the linear stability of the car truck mixed traffic flow is determined more by the proportions of the different car truck following scenarios rather than the numbers of the cars and trucks moreover cars and trucks can both stabilize and destabilize traffic flow depending on the density of the traffic flow and the parameters of the heterogeneous ov model

a new car following model considering the related factors of a gyroidal road abstract a novel car following model was proposed to describe the motion of the vehicles on a single lane gyroidal road we explore the related effects of gyroidal road upon uniform traffic flow analytically and numerically the analytical result shows that the related factors of gyroidal road including the friction coefficient radius of curvature and slope have great influences on the stability of the uniform flow respectively the modified kdv korteweg de vries equation is derived in the unstable area and the kink solution is obtained near the critical point a series of simulations are conducted to verify the effects upon uniform traffic flow under different road conditions it is shown that the amplitudes of the headway oscillation wave were affected by the friction coefficient radius of curvature and slope respectively the numerical results are in good agreement with the analytical results

modified basis functions for mpht splines abstract by allowing split in half in mesh refinement mpht splines modified polynomial splines over hierarchical t meshes were recently introduced to increase the flexibility of pht splines however some basis functions of mpht splines may severely decay as the basis functions of pht splines during the process of certain refinement of hierarchical t meshes this decay phenomenon may cause the isogeometric analysis matrices assembled by these basis functions to be ill conditioned to overcome this defect we present a method to modify the basis functions of mpht splines when the supports of the original truncated basis functions are rectangular domains hence the truncation operations are less used which alleviates the decay phenomenon of mpht splines in addition the modified basis functions preserve the good properties of the original mpht spline basis functions e g the partition of unity local support and linear independence numerical examples show that the condition numbers of isogeometric analysis matrices significantly decrease when new basis functions are applied

promoting similarity of sparsity structures in integrative analysis with penalization abstractfor data with high dimensional covariates but small sample sizes the analysis of single datasets often generates unsatisfactory results the integrative analysis of multiple independent datasets provides an effective way of pooling information and outperforms single dataset and several alternative multi datasets methods under many scenarios multiple datasets are expected to share common important covariates that is the corresponding models have similarity in their sparsity structures however the existing methods do not have a mechanism to promote the similarity in sparsity structures in integrative analysis in this study we consider penalized variable selection and estimation in integrative analysis we develop an l0 penalty based method which explicitly promotes the similarity in sparsity structures computationally it is realized using a coordinate descent algorithm theoretically it has the selection and estimation consistency properties under a wide spectrum of simulation scenarios

c2 interpolation t splines abstract in this work we construct a class of c 2 interpolation t spline called it spline basis functions over regular t meshes a new rule for determining the local knot vectors of the it spline basis functions is designed the resulting it spline basis functions are always linearly independent for regular t meshes in order to guarantee the partition of unity and compact support properties of the it spline basis functions several modified schemes are developed an iteration adjustment algorithm for adjusting the points on it spline surface to the targeted points is proposed some applications of the new it spline basis functions in fitting bivariate functions and open 3d meshes solving numerical pdes and iga are given

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

nonconcave penalized likelihood with a diverging number of parameters a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by fan and li to simultaneously estimate parameters and select important variables they demonstrated that this class of procedures has an oracle property when the number of parameters is finite however in most model selection problems the number of parameters should be large and grow with the sample size in this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to as the sample size increases under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators furthermore the consistency of the sandwich formula of the covariance matrix is demonstrated nonconcave penalized likelihood ratio statistics are discussed and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions the asymptotic results are augmented by a simulation study and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary

l1 regularization path algorithm for generalized linear models summary we introduce a path following algorithm for l1 regularized generalized linear models the l1 regularization procedure is useful especially because it in effect selects variables according to the amount of penalization on the l1 norm of the coefficients in a manner that is less greedy than forward selection backward deletion the generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor corrector method of convex optimization selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths we suggest intuitive and flexible strategies for choosing appropriate values we demonstrate the implementation with several simulated and real data sets

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

approximate efficiency of a selection procedure for the number of regression variables we first show a simplification and a refinement of the result obtained by shibata 1976 it is an evaluation of the mean squared error of estimates of regression parameters when the number of regression variables is selected by a certain procedure the evaluation yields a good approximation to the efficiency of a selection procedure when the number of regression variables is small the approximate efficiency of fpe akaike 1970 aic akaike 1973 or cp mallows 1973 turns out to be not satisfactorily high although they are all asymptotically efficient in the sense of shibata 1981 based on such an approximation a procedure for choosing a out of the family fpe bhansali downham 1977 is suggested a further generalization is also developed consider a regression model y xji k l e where y yl yj is a vector of observations x is an n x k design matrix and f k fl1 fk 0 0 is a vector of regression parameters for simplicity we assume e el ej is a vector of independent normally distributed random variables with mean zero and variance a we call the above model model k in this paper we are concerned only with the problem of selecting the number k from a given range 1 k k under the model k we have a least squares estimate of the regression parameters 43 k h f1k which is a solution of x k x k k x k y here x k is an n x k submatrix consisting of the first k column vectors of the design matrix x hereafter f k is occasionally considered as the corresponding k dimensional vector with the undefined entries being zero suppose that observations yl yn come from a model ko 1 ko k with the regression parameter b such that f3k0 0 our main concern is the mean squared error

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

linear independence of the t spline blending functions associated with some particular t meshes based on the local refinement algorithm addressed in sederberg et al 2004 17 we analyze the linear independence of the bi cubic t spline blending functions corresponding to particular t meshes

one step sparse estimates in nonconcave penalized likelihood models fan and li propose a family of variable selection methods via penalized likelihood using concave penalty functions the nonconcave penalized likelihood estimators enjoy the oracle properties but maximizing the penalized likelihood function is computationally challenging because the objective function is nondifferentiable and nonconcave in this article we propose a new unified algorithm based on the local linear approximation lla for maximizing the penalized likelihood for a broad class of concave penalty functions convergence and other theoretical properties of the lla algorithm are established a distinguished feature of the lla algorithm is that at each lla step the lla estimator can naturally adopt a sparse representation thus we suggest using the one step lla estimator from the lla algorithm as the final estimates statistically we show that if the regularization parameter is appropriately chosen the one step lla estimates enjoy the oracle properties with good initial estimators computationally the one step lla estimation methods dramatically reduce the computational cost in maximizing the nonconcave penalized likelihood we conduct some monte carlo simulation to assess the finite sample performance of the one step sparse estimation methods the results are very encouraging

car following model for autonomous vehicles and mixed traffic flow analysis based on discrete following interval abstract in this paper a discrete car following interval model for autonomous vehicles is proposed with the steady following and dynamic following intervals and the range of the steady following interval is established the stability conditions of the model are explored using linear stability analysis theory numerical simulation is used to verify the influence of the discrete following interval model on mixed traffic flow under small perturbations and hard braking the research results show that with the increase in the proportion of autonomous vehicles the stability of traffic flow is gradually enhanced in particular in the small perturbation condition the autonomous vehicle has a speed maintenance period in the steady following interval thereby reducing the influence of the preceding vehicle perturbations with the increase of the steady following interval the stability of traffic flow first increases and then decreases moreover when the length of steady following interval is constant with the increase of the minimum safety time headway the stability of traffic flow is gradually enhanced

analysis suitable t splines are dual compatible abstract in this paper we define dual compatible dc t splines and we prove that analysis suitable as t splines are dual compatible we show that the classical construction of a dual basis for tensor product t splines easily generalizes to dc t spline spaces and we discuss in the last section of the paper how it paves the way to a mathematical theory of as t splines

variable selection using mm algorithms variable selection is fundamental to high dimensional statistical modeling many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and or nonconcave this article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions these algorithms operate by perturbing the penalty function slightly to render it differentiable then optimizing this differentiable function using a minorize maximize mm algorithm mm algorithms are useful extensions of the well known class of em algorithms a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for em algorithms in particular we prove that when our mm algorithms converge they must converge to a desirable point we also discuss conditions under which this convergence may be guaranteed we exploit the newton raphson like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators our method performs well in numerical tests

generalised information criteria in model selection summary the problem of evaluating the goodness of statistical models is investigated from an information theoretic point of view information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data the proposed criteria are applied to the evaluation of models estimated by maximum likelihood robust penalised likelihood bayes procedures etc we also discuss the use of the bootstrap in model evaluation problems and present a variance reduction technique in the bootstrap simulation

hybrid non uniform recursive subdivision with improved convergence rates abstract this paper introduces a new non uniform subdivision surface representation called hybrid non uniform subdivision surface for short hnuss the subdivision scheme is constructed through two steps the first step inserts a set of edges and converts a valence n extraordinary point into a valence n face the second step combines both primal and dual subdivision schemes to define the subdivision rules the developed subdivision scheme generalizes bi cubic nurbs to arbitrary topology and is proved to be g 1 continuous for any valence extraordinary points and any non negative knot intervals the hnuss limit surface has comparable shape quality as non uniform subdivision via eigen polyhedron li et al 2016 and has better shape quality than all the other subdivision schemes in addition numerical experiments show that hnuss based isogeometric analysis yields improved convergence rates compared to any existing non uniform subdivision schemes

can the strengths of aic and bic be shared a conflict between model indentification and regression estimation a traditional approach to statistical inference is to identify the true or best model first with little or no consideration of the specific goal of inference in the model identification stage can the pursuit of the true model also lead to optimal regression estimation in model selection it is well known that bic is consistent in selecting the true model and aic is minimax rate optimal for estimating the regression function a recent promising direction is adaptive model selection in which in contrast to aic and bic the penalty term is data dependent some theoretical and empirical results have been obtained in support of adaptive model selection but it is still not clear if it can really share the strengths of aic and bic model combining or averaging has attracted increasing attention as a means to overcome the model selection uncertainty can bayesian model averaging be optimal for estimating the regression function in a minimax sense we show that the answers to these questions are basically in the negative for any model selection criterion to be consistent it must behave suboptimally for estimating the regression function in terms of minimax rate of covergence and bayesian model averaging cannot be minimax rate optimal for regression estimation

adaptive lasso for cox s proportional hazards model summary we investigate the variable selection problem for cox s proportional hazards model and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience the new method is based on a penalized log partial likelihood with the adaptively weighted l1 penalty on regression coefficients providing what we call the adaptive lasso estimator the method incorporates different penalties for different coefficients unimportant variables receive larger penalties than important ones so that important variables tend to be retained in the selection process whereas unimportant variables are more likely to be dropped theoretical properties such as consistency and rate of convergence of the estimator are studied we also show that with proper choice of regularization parameters the proposed estimator has the oracle properties the convex optimization nature of the method leads to an efficient algorithm both simulated and real examples show that the method performs competitively

the sparse laplacian shrinkage estimator for high dimensional regression we propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors this method is based on a combination of the minimax concave penalty and laplacian quadratic associated with a graph as the penalty function we call it the sparse laplacian shrinkage sls method the sls uses the minimax concave penalty for encouraging sparsity and laplacian quadratic penalty for promoting smoothness among coefficients associated with the correlated predictors the sls has a generalized grouping property with respect to the graph represented by the laplacian quadratic we show that the sls possesses an oracle property in the sense that it is selection consistent and equal to the oracle laplacian shrinkage estimator with high probability this result holds in sparse high dimensional settings with p n under reasonable conditions we derive a coordinate descent algorithm for computing the sls estimates simulation studies are conducted to evaluate the performance of the sls method and a real data example is used to illustrate its application

tuning parameter selectors for the smoothly clipped absolute deviation method summary the penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method it not only automatically and consistently selects the important variables but also produces estimators which are as efficient as the oracle estimator however these attractive features depend on appropriate choice of the tuning parameter we show that the commonly used generalized crossvalidation cannot select the tuning parameter satisfactorily with a nonignorable overfitting effect in the resulting model in addition we propose a bic tuning parameter selector which is shown to be able to identify the true model consistently simulation studies are presented to support theoretical findings and an empirical example is given to illustrate its use in the female labor supply data

as t splines linear independence and approximation abstract in this paper we define analysis suitable as t splines which include analysis suitable as t splines as a special case and maintain all the good mathematical properties as as t splines we prove that as t splines are always linear independent regardless of the knot values and show that the classical construction of the dual basis for tensor product b splines and as t splines can be generalized to as t spline spaces we also discuss how all of these issues pave the way to a mathematical theory for as t splines

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

asymptotic properties of criteria for selection of variables in multiple regression in normal linear regression analysis many model selection rules proposed from various viewpoints are available for the information criteria aic fpe c p pss and bic the asymptotic distribution of the selected model and the asymptotic quadratic risk based on each criterion are explicitly obtained

regularization parameter selections via generalized information criterion we apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators this approach relies heavily on the choice of regularization parameter which controls the model complexity in this paper we propose employing the generalized information criterion encompassing the commonly used akaike information criterion aic and bayesian information criterion bic for selecting the regularization parameter our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches we show that the bic type selector enables identification of the true model consistently and the resulting estimator possesses the oracle property in the terminology of fan and li 2001 in contrast however the aic type selector tends to overfit with positive probability we further show that the aic type selector is asymptotically loss efficient while the bic type selector is not

full velocity difference model for a car following theory in this paper we present a full velocity difference model for a car following theory based on the previous models in the literature to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in car following process than others this point is verified by numerical simulation then we investigate the property of the model using both analytic and numerical methods and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail

variable selection in semiparametric regression modeling in this paper we are concerned with how to select significant variables in semiparametric modeling variable selection for semiparametric regression models consists of two components model selection for nonparametric components and select significant variables for parametric portion thus it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel this leads to very heavy computational burden in this paper we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood the newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously this allows us to establish the sampling properties of the resulting estimate we first establish the rate of convergence of the resulting estimate with proper choices of penalty functions and regularization parameters we then establish the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component we investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi squared distribution which is independent of the nuisance parameters extensive monte carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures