streamwise feature selection in streamwise feature selection new features are sequentially considered for addition to a predictive model when the space of potential features is large streamwise feature selection offers many advantages over traditional feature selection methods which assume that all features are known in advance features can be generated dynamically focusing the search for new features on promising subspaces and overfitting can be controlled by dynamically adjusting the threshold for adding features to the model in contrast to traditional forward feature selection algorithms such as stepwise regression in which at each step all possible features are evaluated and the best one is selected streamwise feature selection only evaluates each feature once when it is generated we describe information investing and investing two adaptive complexity penalty methods for streamwise feature selection which dynamically adjust the threshold on the error reduction required for adding a new feature these two methods give false discovery rate style guarantees against overfitting they differ from standard penalty methods such as aic bic and ric which always drastically over or under fit in the limit of infinite numbers of non predictive features empirical results show that streamwise regression is competitive with on small data sets and superior to on large data sets much more compute intensive feature selection methods such as stepwise regression and allows feature selection on problems with millions of potential features

on the k 2 supercongruence of van hamme abstract we prove the last remaining case of the original 13 ramanujan type supercongruence conjectures due to van hamme from 1997 the proof utilizes classical congruences and a wz pair due to guillera additionally we mention some future directions concerning this type of supercongruence

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

efficient empirical bayes variable selection and estimation in linear models we propose an empirical bayes method for variable selection and coefficient estimation in linear regression models the method is based on a particular hierarchical bayes formulation and the empirical bayes estimator is shown to be closely related to the lasso estimator such a connection allows us to take advantage of the recently developed quick lasso algorithm to compute the empirical bayes estimate and provides a new way to select the tuning parameter in the lasso method unlike previous empirical bayes variable selection methods which in most practical situations can be implemented only through a greedy stepwise algorithm our method gives a global solution efficiently simulations and real examples show that the proposed method is very competitive in terms of variable selection estimation accuracy and computation speed compared with other variable selection and estimation methods

adapting to unknown sparsity by controlling the false discovery rate we attempt to recover an n dimensional vector observed in white noise where n is large and the vector is known to be sparse but the degree of sparsity is unknown we consider three different ways of defining sparsity of a vector using the fraction of nonzero terms imposing power law decay bounds on the ordered entries and controlling the lp norm for p small we obtain a procedure which is asymptotically minimax for l r loss simultaneously throughout a range of such sparsity classes the optimal procedure is a data adaptive thresholding scheme driven by control of the false discovery rate fdr fdr control is a relatively recent innovation in simultaneous testing ensuring that at most a certain fraction of the rejected null hypotheses will correspond to false rejections in our treatment the fdr control parameter qn also plays a determining role in asymptotic minimaxity if q lim qn 0 1 2 and also qn log n we get sharp asymptotic minimaxity simultaneously over a wide range of sparse parameter spaces and loss functions on the other hand q lim qn 1 2 1 forces the risk to exceed the minimax risk by a factor growing with q to our knowledge this relation between ideas in simultaneous inference and asymptotic decision theory is new our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors these new rules impose complexity penalization of the form 2 log potential model size actual model size we exhibit a close connection with fdr controlling procedures under stringent control of the false discovery rate

the variable selection problem abstract the problem of variable selection is one of the most pervasive model selection problems in statistical applications often referred to as the problem of subset selection it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors but there is uncertainty about which subset to use this vignette reviews some of the key developments that have led to the wide variety of approaches for this problem

on the transversal vibrations of a conveyor belt with a low and time varying velocity part ii the beam like case in this paper initial boundary value problems for a linear wave string equation are considered these problems can be used as simple models to describe the vertical vibrations of a conveyor belt for which the velocity is small with respect to the wave speed and is assumed to move with a time varying speed formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt it will also be shown that the truncation method cannot be applied to this problem in order to obtain approximations valid on long time scales

variational learning of a dirichlet process of generalized dirichlet distributions for simultaneous clustering and feature selection this paper introduces a novel enhancement for unsupervised feature selection based on generalized dirichlet gd mixture models our proposal is based on the extension of the finite mixture model previously developed in 1 to the infinite case via the consideration of dirichlet process mixtures which can be viewed actually as a purely nonparametric model since the number of mixture components can increase as data are introduced the infinite assumption is used to avoid problems related to model selection i e determination of the number of clusters and allows simultaneous separation of data in to similar clusters and selection of relevant features our resulting model is learned within a principled variational bayesian framework that we have developed the experimental results reported for both synthetic data and real world challenging applications involving image categorization automatic semantic annotation and retrieval show the ability of our approach to provide accurate models by distinguishing between relevant and irrelevant features without over or under fitting the data

a q analogue of the j 2 supercongruence of van hamme abstract the l 2 supercongruence of van hamme was proved by swisher recently in this paper we provide a conjectural q analogue of the l 2 supercongruence of van hamme and prove a weaker form of it by using the q wz method in the same way we prove a complete q analogue of the following congruence k 0 n 6 k 1 2 k k 3 512 n k 0 mod 4 2 n 1 2 n n which was conjectured by z w sun and confirmed by b he we also provide a conjectural q analogue of another congruence proved by swisher

needles and straw in haystacks empirical bayes estimates of possibly sparse sequences an empirical bayes approach to the estimation of possibly sparse sequences observed in gaussian white noise is set out and investigated the prior considered is a mixture of an atom of probability at zero and a heavy tailed density y with the mixing weight chosen by marginal maximum likelihood in the hope of adapting between sparse and dense sequences if estimation is then carried out using the posterior median this is a random thresholding procedure other thresholding rules employing the same threshold can also be used probability bounds on the threshold chosen by the marginal maximum likelihood approach lead to overall risk bounds over classes of signal sequences of length n allowing for sparsity of various kinds and degrees the signal classes considered are nearly black sequences where only a proportion is allowed to be nonzero and sequences with normalized p norm bounded by for 0 and 0 1 simulations show excellent performance for appropriately chosen functions y the method is computationally tractable and software is available the extension to a modified thresholding method relevant to the estimation of very sparse sequences is also considered

spectral analysis for the transverse vibration of an axially moving timoshenko beam the use of frequency dependent spectral element matrix or exact dynamic stiffness matrix in structural dynamics is known to provide very accurate solutions while reducing the number of degrees of freedom to resolve the computational and cost problems thus in the present paper the spectral element model is formulated for the axially moving timoshenko beam under a uniform axial tension the high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions the effects of the axial velocity and axial tension on the vibration characteristics the dispersion relation and the stability of a moving timoshenko beam are analytically and numerically investigated

a note on visualizing response transformations in regression a new graphical method for assessing parametric transformations of the response in linear regression is given we simply regress the response variable y on the predictors find the fitted values and then dynamically plot the transformed response y against those fitted values by varying the transformation parameter until the plot is linear the method can be used also to assess the success of numerical response transformation methods and to discover influential observations modifications using robust estimators can be used as well

non linear parametric vibration and stability of axially moving visco elastic rayleigh beams abstract an axially moving visco elastic rayleigh beam with cubic non linearity is considered and the governing partial differential equation of motion for large amplitude vibration is derived through geometrical constitutive and dynamical relations by directly applying the method of multiple scales to the governing equations of motion and considering the solvability condition the linear and non linear frequencies and mode shapes of the system are analytically formulated in the presence of damping terms it can be seen that the amplitude is exponentially time dependent and as a result the non linear natural frequencies of the system will be time dependent for the resonance case through considering the solvability condition and routh hurwitz criterion the stability conditions are developed analytically eventually the effects of system parameters on the vibrational behavior stability and bifurcation points of the system are investigated through parametric studies

parallel maximum likelihood estimator for multiple linear regression models consistency and run time are important questions in performing multiple linear regression models in response we introduce a new parallel maximum likelihood estimator for multiple linear models we first provide an equivalent condition between the method and the generalized least squares estimator we also consider the rank of projections and the eigenvalue we then present consistency when a stable solution exists in this paper we describe several consistency theorems and perform experiments on consistency outlier and scalability finally we fit the proposed method onto bankruptcy data

multivariate statistical process control using lasso this article develops a new multivariate statistical process control spc methodology based on adapting the lasso variable selection method to the spc problem the lasso method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling which is especially useful in cases where the number of nonzero coefficients is small in multivariate spc applications process mean vectors often shift in a small number of components our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components using this connection between the two problems we propose a lasso based multivariate test statistic and then integrate this statistic into the multivariate ewma charting scheme for phase ii multivariate process monitoring we show that this approach balances protection against various shift levels and shift directions and thus provides an effective tool for multivariate spc applications this article

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

q analogues of dwork type supercongruences abstract in 1997 van hamme conjectured 13 ramanujan type supercongruences all of the 13 supercongruences have been confirmed by using a wide range of methods in 2015 swisher conjectured dwork type supercongruences related to the first 12 supercongruences of van hamme here we prove that the c 3 and j 3 supercongruences of swisher are true modulo p 3 r the original modulus is p 4 r by establishing q analogues of them our proof will use the creative microscoping method recently introduced by the author in collaboration with zudilin we also raise conjectures on q analogues of an equivalent form of the m 2 supercongruence of van hamme partially answering a question at the end of adv math 346 2019 329 358

stability in parametric resonance of axially moving viscoelastic beams with time dependent speed stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated the governing equation is derived from newton s second law the kelvin constitution relation and the geometrical relation when the axial speed is a constant mean speed with small harmonic variations the governing equation can be regarded as a continuous gyroscopic system under small periodically parametric excitations and a damping term the method of multiple scales is applied directly to the governing equation without discretization the stability conditions are obtained for combination and principal parametric resonance numerical examples are presented for beams with simple supports and fixed supports respectively to demonstrate the effect of viscoelasticity on the stability boundaries in both cases

controlling variable selection by the addition of pseudovariables we propose a new approach to variable selection designed to control the false selection rate fsr defined as the proportion of uninformative variables included in selected models the method works by adding a known number of pseudovariables to the real dataset running a variable selection procedure and monitoring the proportion of pseudovariables falsely selected information obtained from bootstrap like replications of this process is used to estimate the proportion of falsely selected real variables and to tune the selection procedure to control the fsr

steady state response of axially moving viscoelastic beams with pulsating speed comparison of two nonlinear models abstract principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed a nonlinear partial differential equation governing the transverse vibration is derived from the dynamical constitutive and geometrical relations under certain assumption the partial differential reduces to an integro partial differential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams the method of multiple scales is applied to two equations to calculate the steady state response closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms the stability of straight equilibrium and nontrivial steady state response are analyzed by use of the lyapunov linearized stability theory numerical examples are presented to highlight the effects of speed pulsation viscoelascity and nonlinearity and to compare results obtained from two equations

an algorithmic proof theory for hypergeometric ordinary and q multisum integral identities it is shown that every proper hypergeometric multisum integral identity orq identity with a fixed number of summations and or integration signs possesses a short computer constructible proof we give a fast algorithm for finding such proofs most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here we give many examples of the method including computer generated proofs of identities of mehta dyson selberg hille hardy q saalschutz and others the prospect of using the method for proving multivariate identities that involve an arbitrary number of summations integrations is discussed

infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations abstract the transverse vibrations of simply supported axially moving euler bernoulli beams are investigated the beam has a time varying axial velocity with viscous damping traveling beam eigenfunctions with infinite number of modes are considered approximate analytical solutions are sought using the method of multiple scales a perturbation technique a detailed analysis of the resonances in which upto four modes of vibration involved are performed stability analysis is treated for each type of resonance approximate stability borders are given for the resonances involving only two modes for higher number of modes involved in a resonance sample numerical examples are presented for stabilities

nonlinear vibrations of axially moving timoshenko beams under weak and strong external excitations in this paper nonlinear vibrations under weak and strong external excitations of axially moving beams are analyzed based on the timoshenko model the governing nonlinear partial differential equation of motion is derived from newton s second law accounting for the geometric nonlinearity caused by finite stretching of the beams the complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation the method of multiple scales is employed to investigate primary resonances nonsyntonic excitations superharmonic resonances and subharmonic resonances some numerical examples are presented to demonstrate the effects of a varying parameter such as axial speed external excitation amplitudes and nonlinearity on the response amplitudes for the first and second modes when other parameters are fixed the stability of the response amplitudes is investigated and the boundary of instability is located

quadratic programming feature selection identifying a subset of features that preserves classification accuracy is a problem of growing importance because of the increasing size and dimensionality of real world data sets we propose a new feature selection method named quadratic programming feature selection qpfs that reduces the task to a quadratic optimization problem in order to limit the computational complexity of solving the optimization problem qpfs uses the nystrom method for approximate matrix diagonalization qpfs is thus capable of dealing with very large data sets for which the use of other methods is computationally expensive in experiments with small and medium data sets the qpfs method leads to classification accuracy similar to that of other successful techniques for large data sets qpfs is superior in terms of computational efficiency

bayesian regression modeling with interactions and smooth effects abstract there have been many recent suggestions as to how to build and estimate flexible bayesian regression models using constructs such as trees neural networks and gaussian processes although there is much to commend these methods their implementation and interpretation can be daunting for practitioners this article presents a spline based methodology for flexible bayesian regression that is quite simple in terms of computation and interpretation smooth bivariate interactions are modeled in an economical and apparently novel way and prior distributions that penalize complexity are used predictions can be based on either model selection or model averaging taking computation interpretation and predictive performance into account the method is seen to perform well when applied to simulated and real data

improved heteroscedasticity consistent covariance matrix estimators summary the heteroscedasticity consistent covariance matrix estimator proposed by white 1980 is commonly used in practical applications and is implemented into a number of pieces of statistical software however although consistent it can display substantial bias in small to moderately large samples as shown by monte carlo simulations elsewhere this paper defines modified white estimators which are approximately bias free numerical results show that the modified estimators display much smaller bias than white s estimator in small samples we also show that the bias correction leads to some variance inflation in hypothesis testing based on heteroscedasticity consistent covariance matrix estimators numerical results suggest that tests based on the proposed bias corrected estimators typically display smaller size distortions

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

sparse estimators and the oracle property or the return of hodges estimator abstract we point out some pitfalls related to the concept of an oracle property as used in fan and li 2001 variable selection via nonconcave penalized likelihood and its oracle properties journal of the american statistical association 96 1348 1360 2002 variable selection for cox s proportional hazards model and frailty model annals of statistics 30 74 99 2004 new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis journal of the american statistical association 99 710 723 which are reminiscent of the well known pitfalls related to hodges estimator the oracle property is often a consequence of sparsity of an estimator we show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function in particular the maximal risk diverges to infinity whenever the loss function is unbounded for ease of presentation the result is set in the framework of a linear regression model but generalizes far beyond that setting in a monte carlo study we also assess the extent of the problem in finite samples for the smoothly clipped absolute deviation scad estimator introduced in fan and li 2001 variable selection via nonconcave penalized likelihood and its oracle properties journal of the american statistical association 96 1348 1360 we find that this estimator can perform rather poorly in finite samples and that its worst case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity

boosted classification trees and class probability quantile estimation the standard by which binary classifiers are usually judged misclassification error assumes equal costs of misclassifying the two classes or equivalently classifying at the 1 2 quantile of the conditional class probability function p y 1 x boosted classification trees are known to perform quite well for such problems in this article we consider the use of standard off the shelf boosting for two more general problems 1 classification with unequal costs or equivalently classification at quantiles other than 1 2 and 2 estimation of the conditional class probability function p y 1 x we first examine whether the latter problem estimation of p y 1 x can be solved with logitboost and with adaboost when combined with a natural link function the answer is negative both approaches are often ineffective because they overfit p y 1 x even though they perform well as classifiers a major negative point of the present article is the disconnect between class probability estimation and classification next we consider the practice of over under sampling of the two classes we present an algorithm that uses adaboost in conjunction with over under sampling and jittering of the data jous boost this algorithm is simple yet successful and it preserves the advantage of relative protection against overfitting but for arbitrary misclassification costs and equivalently arbitrary quantile boundaries we then use collections of classifiers obtained from a grid of quantiles to form estimators of class probabilities the estimates of the class probabilities compare favorably to those obtained by a variety of methods across both simulated and real data sets

variable selection in data mining building a predictive model for bankruptcy we predict the onset of personal bankruptcy using least squares regression although well publicized only 2 244 bankruptcies occur in our dataset of 2 9 million months of credit card activity we use stepwise selection to find predictors of these from a mix of payment history debt load demographics and their interactions this combination of rare responses and over 67 000 possible predictors leads to a challenging modeling question how does one separate coincidental from useful predictors we show that three modifications turn stepwise regression into an effective methodology for predicting bankruptcy our version of stepwise regression 1 organizes calculations to accommodate interactions 2 exploits modern decision theoretic criteria to choose predictors and 3 conservatively estimates p values to handle sparse data and a binary response omitting any one of these leads to poor performance a final step in our procedure calibrates regression predictions with these modifications stepwise regr

mixtures of g priors for bayesian model averaging with economic application this paper examines the issue of variable selection in linear regression modeling where there is a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset in this context bayesian model averaging presents a formal bayesian solution to dealing with model uncertainty the main interest here is the effect of the prior on the results such as posterior inclusion probabilities of regressors and predictive performance the authors combine a binomial beta prior on model size with a g prior on the coefficients of each model in addition they assign a hyperprior to g as the choice of g has been found to have a large impact on the results for the prior on g they examine the zellner siow prior and a class of beta shrinkage priors which covers most choices in the recent literature the authors propose a benchmark beta prior inspired by earlier findings with fixed g and show it leads to consistent model selection inference is conducted through a markov chain monte carlo sampler over model space and g the authors examine the performance of the various priors in the context of simulated and real data for the latter they consider two important applications in economics namely cross country growth regression and returns to schooling recommendations for applied users are provided

calibration and empirical bayes variable selection for the problem of variable selection for the normal linear model selection criteria such as aic c p bic and ric have fixed dimensionality penalties such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical bayes formulation based on this calibration we propose empirical bayes selection criteria that use hyperparameter estimates instead of fixed choices for obtaining these estimates both marginal and conditional maximum likelihood methods are considered as opposed to traditional fixed penalty criteria these empirical bayes criteria have dimensionality penalties that depend on the data their performance is seen to approximate adaptively the performance of the best fixed penalty criterion across a variety of orthogonal and nonorthogonal set ups including wavelet regression empirical bayes shrinkage estimators of the selected coefficients are also proposed

a general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear time dependent internal boundary conditions abstract the subject of this paper is the development of a general solution procedure for the vibrations primary resonance and nonlinear natural frequency of systems with cubic nonlinearities subjected to nonlinear and time dependent internal boundary conditions this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements the equations of motion form a set of nonlinear partial differential equations with nonlinear time dependent and coupled internal boundary conditions the method of multiple timescales an approximate analytical method is applied directly to each partial differential equation of motion as well as coupled boundary conditions i e on each sub domain and the corresponding internal boundary conditions for a continuous system with intermediate elements which ultimately leads to approximate analytical expressions for the frequency response relation and nonlinear natural frequencies of the system these closed form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system moreover the suggested solution procedure is applied to a sample problem which is discussed in detail

on the predictive risk in misspecified quantile regression abstract in the present paper we investigate the predictive risk of possibly misspecified quantile regression functions the in sample risk is well known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple asymptotic characterizations of the associated bias also called expected optimism we propose estimates for the expected optimism and the predictive risk and establish their uniform consistency under mild conditions our results hold for models of moderately growing size and allow the quantile function to be incorrectly specified empirical evidence from our estimates is encouraging as it compares favorably with cross validation

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

benchmark priors for bayesian model averaging in contrast to a posterior analysis given a particular sampling model posterior model probabilities in the context of model uncertainty are typically rather sensitive to the speciflcation of the prior in particular difiuse priors on model speciflc parameters can lead to quite unexpected consequences here we focus on the practically relevant situation where we need to entertain a large number of sampling models and we have or wish to use little or no subjective prior information we aim at providing an automatic or benchmark prior structure that can be used in such cases we focus on the normal linear regression model with uncertainty in the choice of re gressors we propose a partly noninformative prior structure related to a natural conjugate g prior speciflcation where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j the consequences of difierent choices for g0j are examined we investigate theoretical properties such as consistency of the implied bayesian procedure links with classical information criteria are provided in addition we examine the flnite sample implications of several choices of g0j in a simulation study the use of the mc 3 algorithm of madigan and york 1995 combined with e cient coding in fortran makes it feasible to conduct large simulations in addition to posterior criteria we shall also compare the predictive performance of difierent priors a classic exam ple concerning the economics of crime will also be provided and contrasted with results in the literature the main flndings of the paper will lead us to propose a benchmark prior speciflcation in a linear regression context with model uncertainty

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

empirical extensions of the lasso penalty to reduce the false discovery rate in high dimensional cox regression models correct selection of prognostic biomarkers among multiple candidates is becoming increasingly challenging as the dimensionality of biological data becomes higher therefore minimizing the false discovery rate fdr is of primary importance while a low false negative rate fnr is a complementary measure the lasso is a popular selection method in cox regression but its results depend heavily on the penalty parameter usually is chosen using maximum cross validated log likelihood max cvl however this method has often a very high fdr we review methods for a more conservative choice of we propose an empirical extension of the cvl by adding a penalization term which trades off between the goodness of fit and the parsimony of the model leading to the selection of fewer biomarkers and as we show to the reduction of the fdr without large increase in fnr we conducted a simulation study considering null and moderately sparse alternative scenarios and compared our approach with the standard lasso and 10 other competitors akaike information criterion aic corrected aic bayesian information criterion bic extended bic hannan and quinn information criterion hqic risk information criterion ric one standard error rule adaptive lasso stability selection and percentile lasso our extension achieved the best compromise across all the scenarios between a reduction of the fdr and a limited raise of the fnr followed by the aic the ric and the adaptive lasso which performed well in some settings we illustrate the methods using gene expression data of 523 breast cancer patients in conclusion we propose to apply our extension to the lasso whenever a stringent fdr with a limited fnr is targeted copyright 2016 john wiley sons ltd

vibrations of an axially moving beam with time dependent velocity the dynamic response of an axially accelerating elastic tensioned beam is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is solved by using perturbation analysis principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for different flexural stiffness values and for the first two modes

general maximum likelihood empirical bayes estimation of normal means we propose a general maximum likelihood empirical bayes gmleb method for the estimation of a mean vector based on observations with i i d normal errors we prove that under mild moment conditions on the unknown means the average mean squared error mse of the gmleb is within an infinitesimal fraction of the minimum average mse among all separable estimators which use a single deterministic estimating function on individual observations provided that the risk is of greater order than log n 5 n we also prove that the gmleb is uniformly approximately minimax in regular and weak l p balls when the order of the length normalized norm of the unknown means is between log n k1 n 1 p 2 and n log n k2 simulation experiments demonstrate that the gmleb outperforms the james stein and several state of the art threshold estimators in a wide range of settings without much down side

multiple shrinkage and subset selection in wavelets this paper discusses bayesian methods for multiple shrinkage estimation in wavelets wavelets are used in applications for data denoising via shrinkage of the coefficients towards zero and for data compression by shrinkage and setting small coefficients to zero we approach wavelet shrinkage by using bayesian hierarchical models assigning a positive prior probability to the wavelet coefficients being zero the resulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear patterns we discuss fast computational implementations with a focus on easy to compute analytic approximations as well as importance sampling and markov chain monte carlo methods multiple shrinkage estimators prove to have excellent mean squared error performance in reconstructing standard test functions we demonstrate this in simulated test examples comparing various implementations of multiple shrinkage to commonly used shrinkage rules finally we illustrate our approach with an application to the so called glint data

some symmetric q congruences modulo the square of a cyclotomic polynomial abstract z h sun 2014 proved a symmetric congruence k 0 p 1 k 1 k f k 1 p k 0 p 1 k 1 k f k mod p 2 where p is an odd prime q is p integral p is the least non negative residue of modulo p and f k j 0 k 1 j k j f j this congruence implies several supercongruences of rodriguez villegas in this paper we give a q analogue of this congruence and prove some symmetric q congruences which also confirm two conjectures of guo and zeng 2014

local asymptotic coding and the minimum description length local asymptotic arguments imply that parameter selection via the minimum description length mdl resembles a traditional hypothesis test a common approximation for mdl estimates the cost of adding a parameter at about 1 2 log n bits for a model fit to n observations while accurate for parameters which are large on a standardized scale this approximation overstates the parameter cost near zero we find that encoding the parameter produces a shorter description length when the corresponding estimator is about two standard errors away from zero as in a traditional statistical hypothesis test

solvability condition in multi scale analysis of gyroscopic continua abstract the solvability condition is investigated for the method of multiple scales applied to gyroscopic continua the general framework of the multi scale analysis is proposed for a linear gyroscopic continuous system under small nonlinear time dependent disturbances the solvability condition is derived from the properties of the systems the condition holds only for appropriate boundary conditions the appropriateness of the boundary conditions can be examined for unperturbed linear systems an example is presented to highlight the requirements on the boundary conditions

multidimensional lindstedt poincare method for nonlinear vibration of axially moving beams abstract the multidimensional lindstedt poincare mdlp method is extended to the nonlinear vibration analysis of axially moving systems galerkin method is used to discretize the governing equations the forced response of an axially moving beam with internal resonance between the first two transverse modes is studied the fundamental harmonic resonance is studied the response curves exhibit the same internal resonance characteristics as that of non transferring thin plates and beams because all these systems possess cubic nonlinearity and similar frequency distribution the examples show that the results of the mdlp method agree reasonably well with that obtained by the incremental harmonic balance ihb method however the former is more straightforward and efficient for obtaining the solution

local causal and markov blanket induction for causal discovery and feature selection for classification part i algorithms and empirical evaluation we present an algorithmic framework for learning local causal structure around target variables of interest in the form of direct causes effects and markov blankets applicable to very large data sets with relatively small samples the selected feature sets can be used for causal discovery and classification the framework generalized local learning or gll can be instantiated in numerous ways giving rise to both existing state of the art as well as novel algorithms the resulting algorithms are sound under well defined sufficient conditions in a first set of experiments we evaluate several algorithms derived from this framework in terms of predictivity and feature set parsimony and compare to other local causal discovery methods and to state of the art non causal feature selection methods using real data a second set of experimental evaluations compares the algorithms in terms of ability to induce local causal neighborhoods using simulated and resimulated data and examines the relation of predictivity with causal induction performance our experiments demonstrate consistently with causal feature selection theory that local causal feature selection methods under broad assumptions encompassing appropriate family of distributions types of classifiers and loss functions exhibit strong feature set parsimony high predictivity and local causal interpretability although non causal feature selection methods are often used in practice to shed light on causal relationships we find that they cannot be interpreted causally even when they achieve excellent predictivity therefore we conclude that only local causal techniques should be used when insight into causal structure is sought in a companion paper we examine in depth the behavior of gll algorithms provide extensions and show how local techniques can be used for scalable and accurate global causal graph learning

a q microscope for supercongruences abstract by examining asymptotic behavior of certain infinite basic q hypergeometric sums at roots of unity that is at a q microscopic level we prove polynomial congruences for their truncations the latter reduce to non trivial super congruences for truncated ordinary hypergeometric sums which have been observed numerically and proven rarely a typical example includes derivation from a q analogue of ramanujan s formula n 0 4 n 2 n 2 n n 2 2 8 n 3 2 n 8 n 1 2 3 of the two supercongruences s p 1 p 3 p mod p 3 and s p 1 2 p 3 p mod p 3 valid for all primes p 3 where s n denotes the truncation of the infinite sum at the n th place and 3 stands for the quadratic character modulo 3

fast robust model selection in large datasets large datasets are increasingly common in many research fields in particular in the linear regression context it is often the case that a huge number of potential covariates are available to explain a response variable and the first step of a reasonable statistical analysis is to reduce the number of covariates this can be done in a forward selection procedure that includes selecting the variable to enter deciding to retain it or stop the selection and estimating the augmented model least squares plus t tests can be fast but the outcome of a forward selection might be suboptimal when there are outliers in this article we propose a complete algorithm for fast robust model selection including considerations for huge sample sizes because simply replacing the classical statistical criteria with robust ones is not computationally possible we develop simplified robust estimators selection criteria and testing procedures for linear regression the robust estimator is a one step weighted m estimato

dynamic stability in parametric resonance of axially accelerating viscoelastic timoshenko beams abstract this paper investigates dynamic stability of an axially accelerating viscoelastic beam undergoing parametric resonance the effects of shear deformation and rotary inertia are taken into account by the timoshenko thick beam theory the beam material obeys the kelvin model in which the material time derivative is used the axial speed is characterized as a simple harmonic variation about the constant mean speed the governing partial differential equations are derived from newton s second law euler s angular momentum principle and the constitutive relation the method of multiple scales is applied to the equations to establish the solvability conditions in summation and principal parametric resonances the sufficient and necessary condition of the stability is derived from the routh hurvitz criterion some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries

model complexity control for regression using vc generalization bounds it is well known that for a given sample size there exists a model of optimal complexity corresponding to the smallest prediction generalization error hence any method for learning from finite samples needs to have some provisions for complexity control existing implementations of complexity control include penalization or regularization weight decay in neural networks and various greedy procedures aka constructive growing or pruning methods there are numerous proposals for determining optimal model complexity aka model selection based on various asymptotic analytic estimates of the prediction risk and on resampling approaches nonasymptotic bounds on the prediction risk based on vapnik chervonenkis vc theory have been proposed by vapnik this paper describes application of vc bounds to regression problems with the usual squared loss an empirical study is performed for settings where the vc bounds can be rigorously applied i e linear models and penalized linear models where the vc dimension can be accurately estimated and the empirical risk can be reliably minimized empirical comparisons between model selection using vc bounds and classical methods are performed for various noise levels sample size target functions and types of approximating functions our results demonstrate the advantages of vc based complexity control with finite samples

some congruences involving fourth powers of central q binomial coefficients we prove some congruences on sums involving fourth powers of central q binomial coefficients as a conclusion we confirm the following supercongruence observed by long pacific j math 249 2011 405 418 sum limits k 0 p r 1 2 displaystyle 4k 1 over 256 k left matrix 2k cr k right 4 equiv p r quad left bmod p r 3 right where p 5 is a prime and r is a positive integer our method is similar to but a little different from the wz method used by zudilin to prove ramanujan type supercongruences

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

timoshenko beam column with generalized end conditions on elastic foundation dynamic stiffness matrix and load vector abstract the dynamic stiffness matrix and load vector of a timoshenko beam column resting on a two parameter elastic foundation with generalized end conditions are presented the proposed model includes the frequency effects on the stiffness matrix and load vector as well as the coupling effects of 1 bending and shear deformations along the member 2 translational and rotational lumped masses at both ends 3 translational and rotational masses uniformly distributed along its span 3 axial load tension or compression applied at both ends and 4 shear forces along the span induced by the applied axial load as the beam deforms according to the modified shear equation proposed by timoshenko the dynamic analyses of framed structures can be performed by including the effects of the imposed frequency 0 on the dynamic stiffness matrix and load vector while the static and stability analyses can be carried out by making the frequency 0 the proposed model and corresponding dynamic stiffness matrix and load vector represent a general solution capable to solve just by using a single segment per element the static dynamic and stability analyses of any elastic framed structure made of prismatic beam columns with semi rigid connections resting on two parameter elastic foundations analytical results indicate that the elastic behavior of framed structures made of beam columns is frequency dependent and highly sensitive to the coupling effects just mentioned three comprehensive examples are presented to show the capacities and validity of the proposed method and the obtained results are compared with the finite element method and other analytical approaches

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

indicator and stratification methods for missing explanatory variables in multiple linear regression abstract the statistical literature and folklore contain many methods for handling missing explanatory variable data in multiple linear regression one such approach is to incorporate into the regression model an indicator variable for whether an explanatory variable is observed another approach is to stratify the model based on the range of values for an explanatory variable with a separate stratum for those individuals in which the explanatory variable is missing for a least squares regression analysis using either of these two missing data approaches the exact biases of the estimators for the regression coefficients and the residual variance are derived and reported the complete case analysis in which individuals with any missing data are omitted is also investigated theoretically and is found to be free of bias in many situations though often wasteful of information a numerical evaluation of the bias of two missing indicator methods and the complete case analysis is reported the missing indi

analytical modeling of viscoelastic dampers for structural and vibration control different approaches to the mathematical modeling of viscoelastic dampers are addressed and their theoretical basis and performance are compared the standard mechanical model smm comprising linear springs and dashpots is shown to accurately describe the broad band rheological behavior of common viscoelastic dampers and be more efficient than other models such as the fractional derivative model and the modified power law the smm renders a prony series expression for the modulus and compliance functions in the time domain and the remarkable mathematical efficiency associated with the exponential basis functions of a prony series greatly facilitates model calibration and interconversion while cumbersome nonlinear regression is usually required for other models a simple collocation or least squares method can be used to fit the smm to available experimental data the model allows viscoelastic material functions to be readily determined either directly from the experimental data or through interconversion from a function established in another domain numerical examples on two common viscoelastic dampers demonstrate the advantages of the smm over fractional derivative and power law models detailed computational procedures for fitting and interconversion are discussed and illustrated published experimental data from a viscoelastic liquid damper and a viscoelastic solid damper are used in the examples

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