constructing general orthogonal fractional factorial split plot designs while the orthogonal design of split plot fractional factorial experiments has received much attention already there are still major voids in the literature first designs with one or more factors acting at more than two levels have not yet been considered second published work on nonregular fractional factorial split plot designs was either based only on plackett burman designs or on small nonregular designs with limited numbers of factors in this article we present a novel approach to designing general orthogonal fractional factorial split plot designs one key feature of our approach is that it can be used to construct two level designs as well as designs involving one or more factors with more than two levels moreover the approach can be used to create two level designs that match or outperform alternative designs in the literature and to create two level designs that cannot be constructed using existing methodology our new approach involves the use of integer linear programming and mixed integer linear programming and for large design problems it combines integer linear programming with variable neighborhood search we demonstrate the usefulness of our approach by constructing two level split plot designs of 16 96 runs an 81 run three level split plot design and a 48 run mixed level split plot design supplementary materials for this article are available online 2015 american statistical association and the american society for quality

component based discriminative classification for hidden markov models hidden markov models hmms have been successfully applied to a wide range of sequence modeling problems in the classification context one of the simplest approaches is to train a single hmm per class a test sequence is then assigned to the class whose hmm yields the maximum a posterior map probability this generative scenario works well when the models are correctly estimated however the results can become poor when improper models are employed due to the lack of prior knowledge poor estimates violated assumptions or insufficient training data to improve the results in these cases we propose to combine the descriptive strengths of hmms with discriminative classifiers this is achieved by training feature based classifiers in an hmm induced vector space defined by specific components of individual hidden markov models we introduce four major ways of building such vector spaces and study which trained combiners are useful in which context moreover we motivate and discuss the merit of our method in comparison to dynamic kernels in particular to the fisher kernel approach

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

algorithmic construction of efficient fractional factorial designs with large run sizes fractional factorial ff designs are widely used in practice and typically are chosen according to the minimum aberration criterion a sequential algorithm is developed for constructing efficient ff designs a construction procedure is proposed that allows a design to be constructed only from its minimum aberration projection in the sequential buildup process to efficiently identify nonisomorphic designs designs are categorized according to moment projection pattern a fast isomorphism checking procedure is developed by matching the factors using their delete one factor projections this algorithm is used to completely enumerate all 128 run designs of resolution 4 all 256 run designs of resolution 4 up to 17 factors all 512 run designs of resolution 5 all 1024 run designs of resolution 6 and all 2048 and 4 096 run designs of resolution 7 a method is proposed for constructing minimum aberration ma designs using only a partial catalog of some good designs three approaches to constructing good de

minimum aberration fractional factorial designs with large n xu has cataloged 165 minimum aberration ma regular fractional factorial ff designs with 2 levels and large run sizes n 128 m 8 64 factors n 256 m 9 28 109 119 n 512 m 10 25 238 246 n 1024 m 11 24 488 501 n 2048 m 12 23 and n 4096 m 13 24 such an extensive catalog was produced because of an improved algorithm we extend the catalog by 36 ma 2 level regular ff designs n 256 m 29 36 100 108 n 512 m 26 29 n 1024 m 25 28 n 2048 m 24 32 and n 4096 m 25 26 although such enumeration problems are notoriously difficult with increased n and or m we brought the newly solved problems within computational reach by changing the vital isomorphism check component of xu s algorithm here we present a new compact graph for solving regular design isomorphism problems and use the nauty program to solve the corresponding graph isomorphism problems supplemental appendices are available online

misspecified structural change threshold and markov switching models sudden perturbations of a large amplitude occur frequently in macroeconomic and financial time series a usual practice is to test linearity against a permanent structural change however changes can also be captured by nonlinear stationary models such that threshold and markov switching models in this paper we show that tests designed for a threshold alternative have also power against parameter instability originating from structural change or markov switching models on the other hand it is shown that tests for structural change have no power if the data are generated by a markov switching or threshold model therefore it appears that testing the null of parameter stability against a threshold alternative is a robust way to detect parameter instability in economic and financial time series a monte carlo analysis based on several models studied in the literature illustrates how the tests perform in practice

some risks in the construction and analysis of supersaturated designs a designed experiment in which the number of factors is at least as large as the number of runs is referred to as a supersaturated ss design recently these designs have received increased attention construction of such designs and analysis of data from them have been discussed by several authors our objective in this article is to examine these designs and methods for their analysis an important finding for practitioners is that the correlation structure inherent in ss designs can obscure real effects or promote nonreal effects whatever analysis method is used this problem can occur although all subsets regression is preferable to stepwise regression hence one should be cautious with the use of ss designs

a bayesian variable selection approach for analyzing designed experiments with complex aliasing experiments using designs with complex aliasing patterns are often performed for example twolevel nongeometric plackett burman designs multilevel and mixed level fractional factorial designs two level fractional factorial designs with hard to control factors and supersaturated designs hamada and wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions their strategy provides a restricted search in a rather large model space however this article provides an efficient methodology based on a bayesian variable selection algorithm for searching the model space more thoroughly we show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models the proposed methodology is demonstrated with four examples three of which come from actual industrial experiments

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

a general approach to lagrange multiplier model diagnostics abstract a diagnostic test can be formulated by taking the current model as the null hypothesis and a particular form of misspecification as the alternative the general approach of this paper is to calculate the score for some alternative and base a test on its distribution under the null this distribution is derived in two theorems corresponding to different models such a test is a langrange multiplier test and is asymptotically optimal these tests can be formulated as ways of looking at the residuals for particular types of non randomness the tests are simple to calculate even when the alternative may be very complicated examples are given of tests for omitted variables and block recursive structures

experiments on the application of iohmms to model financial returns series input output hidden markov models iohmm are conditional hidden markov models in which the emission and possibly the transition probabilities can be conditioned on an input sequence for example these conditional distributions can be linear logistic or nonlinear using for example multilayer neural networks we compare the generalization performance of several models which are special cases of input output hidden markov models on financial time series prediction tasks an unconditional gaussian a conditional linear gaussian a mixture of gaussians a mixture of conditional linear gaussians a hidden markov model and various iohmms the experiments compare these models on predicting the conditional density of returns of market and sector indices note that the unconditional gaussian estimates the first moment with the historical average the results show that although for the first moment the historical average gives the best results for the higher moments the iohmms yielded significantly better performance as estimated by the out of sample likelihood

sequentially refined latin hypercube designs reusing every point the use of iteratively enlarged latin hypercube designs for running computer experiments has recently gained popularity in practice this approach conducts an initial experiment with a computer code using a latin hypercube design and then runs a follow up experiment with additional runs elaborately chosen so that the combined design set for the two experiments forms a larger latin hypercube design this augmenting process can be repeated multiple stages where in each stage the augmented design set is guaranteed to be a latin hypercube design we provide a theoretical framework to put this approach on a firm footing numerical examples are given to corroborate the derived theoretical results supplementary materials for this article are available online

indicator function and its application in two level factorial designs a two level factorial design can be uniquely represented by a polynomial indicator function therefore properties of factorial designs can be studied through their indicator functions this paper shows that the indicator function is an effective tool in studying two level factorial designs the indicator function is used to generalize the aberration criterion of a regular two level fractional factorial design to all two level factorial designs an important identity of generalized aberration is proved the connection between a uniformity measure and aberration is also extended to all two level factorial designs

screening strategies in the presence of interactions product and process improvement can involve a large number of factors that must be varied simultaneously understanding how factors interact is a key step in identifying those factors that have a substantial impact on the response this article gives the first comprehensive assessment and comparison of screening strategies for interactions using two level supersaturated designs group screening and a variety of data analysis methods including shrinkage regression and bayesian methods we develop novel methodology to allow application of bayesian methods in two stage group screening insights on using the strategies are provided through a variety of simulation scenarios and open issues are discussed supplementary materials are available online

blocked nonregular two level factorial designs this article discusses the optimal blocking criteria for nonregular two level designs we extend the optimal blocking criteria of cheng and wu to nonregular designs by adapting the g and g2 minimum aberration criteria discussed by tang and deng to define word length pattern for nonregular designs we extend the notion of word to nonregular designs through a polynomial representation of factorial designs we define treatment resolution and block resolution for evaluating the degrees of aliasing and confounding we propose four new criteria which we use to search for optimal blocking schemes of 12 run 16 run and 20 run two level orthogonal arrays

multi layer designs for computer experiments space filling designs such as latin hypercube designs lhds are widely used in computer experiments however finding an optimal lhd with good space filling properties is computationally cumbersome on the other hand the well established factorial designs in physical experiments are unsuitable for computer experiments owing to the redundancy of design points when projected onto a subset of factor space in this work we present a new class of space filling designs developed by splitting two level factorial designs into multiple layers the method takes advantage of many available results in factorial design theory and therefore the proposed multi layer designs mlds are easy to generate moreover our numerical study shows that mlds can have better space filling properties than optimal lhds

bayesian inference and state number determination for hidden markov models an application to the information content of the yield curve about inflation this paper is concerned with bayesian inference in hidden markov models focusing on switching regression models we propose a new methodology that delivers a joint estimation of the parameters and the number of regimes that have actually appeared in the studied sample the only prior information that is required on the latter quantity is an upper bound we implement a particle filter algorithm to compute the corresponding estimates applying this methodology to the information content of the yield curve regarding future inflation in four oecd countries we show that the predictive content for given country and combination of maturities is subject to regime switching

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

optimal foldover plans for two level fractional factorial designs a commonly used follow up experiment strategy involves the use of a foldover design by reversing the signs of one or more columns of the initial design defining a foldover plan as the collection of columns whose signs are to be reversed in the foldover design this article answers the following question given a 2k p design with k factors and p generators what is its optimal foldover plan we obtain optimal foldover plans for 16 and 32 runs and tabulate the results for practical use most of these plans differ from traditional foldover plans that involve reversing the signs of one or all columns there are several equivalent ways to generate a particular foldover design we demonstrate that any foldover plan of a 2k p fractional factorial design is equivalent to a core foldover plan consisting only of the p out of k factors furthermore we prove that there are exactly 2k p foldover plans that are equivalent to any core foldover plan of a 2k p design and demonstrate how these foldover plans can be const

some heteroskedasticity consistent covariance matrix estimators with improved finite sample properties abstract we examine several modified versions of the heteroskedasticity consistent covariance matrix estimator of hinkley 1977 and white 1980 on the basis of sampling experiments which compare the performance of quasi t statistics we find that one estimator based on the jackknife performs better in small samples than the rest we also examine the finite sample properties of using modified critical values based on edgeworth approximations as proposed by rothenberg 1984 in addition we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity consistent covariance matrix even in the absence of detected heteroskedasticity

impact of foreign exchange rate on oil companies risk in stock market during the recent years the importance of effective risk management has become extremely crucial value at risk var is a standard downside measure to explain the behavior of financial series as the garch models have been successfully applied in modeling the volatility structure of securities and other financial assets the var of garch models has turned into an important quantity to study in addition to garch family models the markov regime switching garch mrs garch models are a widely used approach to model financial volatility with potential structural breaks in this paper we evaluated the performance of the mrs garch models with the traditional arma garch family models for estimating var of the stock return of operating companies in the oil industry srocoi in irans stock market under the normal student t and ged distributions our findings showed that the mrs garch models outperform the arma garch family models to capture the characteristics of the srocois volatility additionally we evaluated impact of the foreign exchange rate fluctuations on the var of srocois that were calculated from the optimal models under two regimes usingardl model the results further demonstrated that foreign exchange rate fluctuations have significant and different impacts on the var of srocois across regimes we modeled srocois in irans stock market using mrs garch and arma garch family models mrs garch models under student t and ged distributions have better performance to capture srocois we estimated in sample and out of sample var of srocois from optima models we evaluated impact of the foreign exchange rate fluctuations on the var of srocois foreign exchange rate significantly effect on the var of srocois in different regimes

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

monte carlo methodology and the finite sample properties of instrumental variables statistics for testing nested and non nested hypotheses using monte carlo methodology this paper investigates the effect of dynamics and simultaneity on the finite sample properties of instrumental variables statistics for testing nested and nonnested hypotheses simple numerical analytical formulae response surfaces are obtained which closely approximate the statistics unknown size and power functions for a dynamic simultaneous equations model the analysis illustrates the value and limitations of asymptotic theory in interpreting finite sample properties two practical results arise the f form and the wald statistic is favored over its chi squared form and large sigma and small effective sample size strongly affect the test of over identifying restrictions and the cox type test copyright 1991 by the econometric society

a graph aided method for planning two level experiments when certain interactions are important in planning a fractional factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects in this article we propose a graph aided method to solve this problem for two level experiments first we choose the defining relations for a 2 n k design according to a goodness criterion such as the minimum aberration criterion then we construct all of the nonisomorphic graphs that represent the solutions to the problem of simultaneous estimation of main effects and two factor interactions for the given defining relations in each graph a vertex represents a factor and an edge represents the interaction between the two factors for the experiment planner the job is simple draw a graph representing the specified interactions and compare it with the list of graphs obtained previously our approach is a substantial improvement over taguchi s linear graphs

construction of orthogonal two level designs of user specified resolution where n 2 k fractional two level factorial designs are often used in the early stages of an investigation to screen for important factors traditionally 2 n k fractional factorial designs of resolution iii iv or v have been used for this purpose when the investigator is able to specify the set of nonnegligible factorial effects it is sometimes possible to obtain an orthogonal design with fewer runs than a standard textbook design by searching within a wider class of designs called parallel flats designs the run sizes in this class of designs do not necessarily need to be powers of 2 we discuss an algorithm for constructing orthogonal parallel flats designs to meet user specifications several examples illustrate the use of the algorithm

better foldover fractions for resolution iii 2k p designs this article describes a family of resolution iiidesigns for which the usual advice regarding foldover reversing all factors is ill advised the smallest such designs have 16 runs for designs in this family alternative foldover fractions not only increase the resolution to iv but also separate some of the aliased two factor interactions although resolution iv designs obtained by reversing all factors provide fewer than half the degrees of freedom for estimating two factor interactions the recommended foldovers for designs in this class permit estimation of many more two factor interactions this result implies that designs in this class make attractive initial designs even if they are not minimum aberration

columnwise pairwise algorithms with applications to the construction of supersaturated designs motivated by the construction of supersaturated designs we develop a class of algorithms called columnwise pairwise exchange algorithms they differ from the k exchange algorithms in two respects 1 they exchange columns instead of rows of the design matrix and 2 they employ a pairwise adjustment in the search for a better column the proposed algorithms perform very well in the construction of supersaturated designs both for a single criterion and for multiple criteria they are also applicable to the construction of designs that are not supersaturated

using the folded over 12 run plackett burman design to consider interactions this article demonstrates that the folded over 12 run plackett burman design is useful for considering up to 12 factors in 24 runs even if one anticipates that some two factor interactions may be significant the properties of this design are investigated and a sequential procedure for analyzing the data from such a design is proposed the performance of the procedure is investigated through the analysis of real and constructed examples and through a small simulation study applications to other folded over plackett burman designs are also briefly discussed

k circulant supersaturated designs a class of supersaturated designs called k circulant designs is explored these designs are constructed from cyclic generators by cycling k elements at a time the class of designs includes many es2 optimal designs some of which are already known and some of which are more efficient than known designs for model estimation under factor sparsity generators for the most efficient designs are listed and projection properties of some of the designs are explored we also illustrate that some k circulant supersaturated designs can be augmented with interaction columns to produce efficient designs for a larger number of factors or for estimating interactions

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

an asymptotic solution of the governing equation for the natural frequencies of a cantilevered coupled beam model abstract an asymptotic solution is presented for the natural frequencies mode shapes of a cantilevered coupled beam model a three term expansion is obtained for the frequency which shows good agreement with exact values over a wide range of the stiffness parameter the first three mode shapes are also presented for large and show good agreement for the first and second modes agreement for the third mode improves as gets larger the modeled structure behaves essentially as a shear beam except in the immediate neighborhood of the ends

a new class of supersaturated designs supersaturated designs are useful in situations in which the number of active factors is very small compared to the total number of factors being considered in this article a new class of supersaturated designs is constructed using half fractions of hadamard matrices when a hadamard matrix of order n is used such a design can investigate up to n 2 factors in n 2 runs results are given for n 60 extension to larger n is straightforward these designs are superior to other existing supersaturated designs and are easy to construct an example with real data is used to illustrate the ideas

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

analysis of time series subject to changes in regime abstract this paper introduces an em algorithm for obtaining maximum likelihood estimates of parameters for processes subject to discrete shifts in autoregressive parameters with the shifts themselves modeled as the outcome of a discrete valued markov process the simplicity of the em algorithm permits potential application of the approach to large vector systems

the small sample performance of the information matrix test abstract this paper reviews the information matrix im test procedure see white 1982 it investigates the size performance of several variants of the im test statistic and in particular exposes the nr2 variant of the test as proposed by chesher 1983 and lancaster 1984 as being extremely poor alternative nr2 im test statistics are considered and it appears that substantial improvements can be made by incorporating expected values of third derivatives of the log density into the im test calculation procedure interestingly these are exactly the sort of calculations that the chesher 1983 and lancaster 1984 variant avoids

design selection and classification for hadamard matrices using generalized minimum aberration criteria deng and tang 1999 and tang and deng 1999 proposed and justified two criteria of generalized minimum aberration for general two level fractional factorial designs the criteria are defined using a set of values called j characteristics in this article we examine the practical use of the criteria in design selection specifically we consider the problem of classifying and ranking designs that are based on hadamard matrices a theoretical result on j characteristics is developed to facilitate the computation the issue of design selection is further studied by linking generalized aberration with the criteria of efficiency and estimation capacity our studies reveal that generalized aberration performs quite well under these familiar criteria

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

specification testing in markov switching time series models this paper develops a series of specification tests of markov switching time series models tests for omitted autocorrelation omitted arch misspecification of the markovian dynamics and omitted explanatory variables are proposed all of the tests can be constructed as a natural byproduct of the routine used to calculate the smoothed probability that a given observation came from a particular regime and do not require estimation of additional parameters the paper performs monte carlo analysis of the tests and briefly illustrates their use with an empirical application

serial correlation in latent discrete variable models abstract we consider the problems of estimation and testing in models with serially correlated discrete latent variables a particular case of this is the time series regression model in which a discrete explanatory variable is measured with error test statistics are derived for detecting serial correlation in such a model we then show that the likelihood function can be evaluated by a recurrence relation and thus maximum likelihood estimation is computationally feasible an illustrative example of these methods is given followed by a brief discussion of their applicability to a markov model of switching regressions

simulated annealing model search for subset selection in screening experiments the analysis of screening experiments based on nonregular designs can lead to a model selection problem in which the number of variables is large the number of trials is small and there are constraints on model structure common subset selection methods do not perform well in this setting we propose a new approach particularly well suited to screening the method uses an intentionally nonconvergent stochastic search to generate a large set of well fitting models each with the same number of variables model selection is then viewed as a feature extraction problem from this set an easy to use graphical method and an automatic approach are proposed to determine the best models computer code and additional supplementary materials are available online

additive heredity model for the analysis of mixture of mixtures experiments the mixture of mixtures mom experiment is different from the classical mixture experiment in that the mixture component in mom experiments known as the major component is made up of subcomponen

free vibrations of elastically connected stretched beams abstract a general theory for the determination of natural frequencies and mode shapes for a set of elastically connected axially loaded euler bernoulli beams is developed a normal mode solution is applied to a set of non dimensional coupled partial differential equations the natural frequencies are the eigenvalues of a matrix of differential operators the matrix operator is shown to be self adjoint leading to an orthogonality condition for the mode shapes in the special case of identical beams it is shown that the natural frequencies are organized into sets of intramodal frequencies in which each mode shape is a product of a spatial mode and a discrete mode an exact solution is available for the general case however the natural frequencies and mode shapes are then determined using a complicated numerical method a rayleigh ritz method using mode shapes of the corresponding unstretched beams is developed as an alternative

minimum aberration and model robustness for two level fractional factorial designs summary the performance of minimum aberration two level fractional factorial designs is studied under two criteria of model robustness simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived it is also shown that a minimum aberration design of resolution ilil or higher maximizes the number of two factor interactions which are not aliases of main effects and subject to that condition minimizes the sum of squares of the sizes of alias sets of two factor interactions this roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform it follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here examples are given to show that minimum aberration designs are indeed highly efficient

testing for regime switching we analyze use of a quasi likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a markov regime switching context this test exploits mixture properties implied by the regime switching process but ignores certain implied serial correlation properties when formulated in the natural way the setting is nonstandard involving nuisance parameters on the boundary of the parameter space nuisance parameters identified only under the alternative or approximations using derivatives higher than second order we exploit recent advances by andrews 2001 and contribute to the literature by extending the scope of mixture models obtaining asymptotic null distributions different from those in the literature we further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime switching tests we compare the size and power of our statistics to other useful tests for regime switching via monte carlo methods and find relatively good performance we apply our methods to reexamine the classic cartel study of porter 1983 and reaffirm porter s findings

an application of a hill based response surface model for a drug combination experiment on lung cancer combination chemotherapy with multiple drugs has been widely applied to cancer treatment owing to enhanced efficacy and reduced drug resistance for drug combination experiment analysis response surface modeling has been commonly adopted in this paper we introduce a hill based global response surface model and provide an application of the model to a 512 run drug combination experiment with three chemicals namely ag490 u0126 and indirubin 3 monoxime i 3 m on lung cancer cells the results demonstrate generally improved goodness of fit of our model from the traditional polynomial model as well as the original hill model on the basis of fixed ratio drug combinations we identify different dose effect patterns between normal and cancer cells on the basis of our model which indicates the potential effectiveness of the drug combination in cancer treatment meanwhile drug interactions are analyzed both qualitatively and quantitatively the distinct interaction patterns between u0126 and i 3 m on two types of cells uncovered by the model could be a further indicator of the efficacy of the drug combination copyright 2014 john wiley sons ltd

generating systematic supersaturated designs practitioners are routinely faced with distinguishing between factors that have real effects and those whose apparent effects are due to random error when there are many factors the usual advice given is to run so called main effect designs resolution iii designs in the orthogonal case that require at least k 1 runs for investigating k factors this may be wasteful however if the goal is only to detect those active factors this is particularly true when the number of factors is large in such situations a supersaturated design can often save considerable cost a supersaturated design is a fraction of a factorial design composed of n observations where n k 1 when such a design is used the abandonment of orthogonality is inevitable this article examines the maximum number of factors that can be accommodated when the degree of the nonorthogonality is specified furthermore interesting properties of systematic supersaturated designs are revealed for example such a design may be adequate

incorporating prior information in optimal design for model selection an important use of experimental designs is in screening in which experimenters seek to identify significant effects both main effects and potentially interactions from a large set of candidate effects this article goes further than identification of effects introducing a design criterion that seeks to maximize the ability to discriminate between models motivated by the work of meyer steinberg and box the bayesian criterion is based on the hellinger distance between predictive distributions under competing models a bound for the criterion is obtained greatly improving interpretability the set of all possible models to compare is huge and not all models are equally plausible this challenge is addressed through prior distributions on the space of models that indicate preference for intuitively appealing models such as those with few effects more low order than high order effects and inheritance structure between active main effects and interactions techniques for evaluating the criterion a

semifolding 2 k p designs this article addresses the varied possibilities for following a two level fractional factorial with another fractional factorial half the size of the original experiment although follow up fractions of the same size as an original experiment are common practice in many situations a smaller followup experiment will sufiice peter john coined the term semifolding to describe using half of a foldover design existing literature does include brief mention and examples of semifolding but no thorough development of this follow up strategy after a quick examination of the estimation details for semlfoldmg the 24 1 iv design we focus on following 16 run fractions with a semifold design of eight runs two such examples are considered one in which the initial fraction ia resolution iv the other resolution iii a general result is proven for semifolding 2 k p iv designs conducting full foldover designs in two blocks is also recommended

two level designs to estimate all main effects and two factor interactions we study the design of two level experiments with n runs and n factors large enough to estimate the interaction model which contains all the main effects and all the two factor interactions yet an effect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two factor interactions orthogonal arrays oas favor main effect estimation however complete enumeration becomes infeasible for cases relevant for practitioners we develop a partial enumeration procedure for these cases and we establish upper bounds on the d efficiency for the interaction model based on arrays that have not been generated by the partial enumeration we also propose an optimal design procedure that favors main effect estimation designs created with this procedure have smaller d efficiencies for the interaction model than d optimal designs but standard errors for the main effects in this model are improved generated oas for 7 10 factors and 32 72 runs are smaller or have a higher d efficiency than the smallest oas from the literature designs obtained with the new optimal design procedure or strength 3 oas which have main effects that are not correlated with two factor interactions are recommended if main effects unbiased by possible two factor interactions are of primary interest d optimal designs are recommended if interactions are of primary interest supplementary materials for this article are available online 2017 american statistical association and the american society for quality

a note on foldover of 2k p designs with column permutations foldover is a commonly used follow up strategy in experimental designs all existing foldover designs were constructed by reversing the sign of columns of the initial design we propose a new methodology by allowing the permutation of columns in foldover focusing on resolution iv designs we show that almost all designs are better than existing results with respect to the minimum aberration criterion while augmenting a design by a foldover with column permutations may result in a nonregular combined design the proposed designs all have a resolution of 4 5 or higher for which no two factor interaction is fully aliased with any other two factor interactions

construction of maximin distance latin squares and related latin hypercube designs summarymaximin distance latin hypercube designs are widely used in computer experiments yet their construction is challenging based on number theory and finite fields we propose three algebraic methods to construct maximin distance latin squares as special latin hypercube designs we develop lower bounds on their minimum distances the resulting latin squares and related latin hypercube designs have larger minimum distances than existing ones and are especially appealing for high dimensional applications

sprt and cusum in hidden markov models in this paper we study the problems of sequential probability ratio tests for parameterized hidden markov models we investigate in some detail the performance of the tests and derive corrected brownian approximations for error probabilities and expected sample sizes asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden markov chain data is established next we consider the cumulative sum cusum procedure for change point detection in this model based on the renewal property of the stopping rule cusum can be regarded as a repeated one sided sequential probability ratio test asymptotic optimality of the cusum procedure is proved in the sense of lorden 1971 motivated by the sequential analysis in hidden markov models wald s likelihood ratio identity and wald s equation for products of markov random matrices are also given we apply these results to several types of hidden markov models i i d hidden markov models switch gaussian regression and switch gaussian autoregression which are commonly used in digital communications speech recognition bioinformatics and economics

the coordinate exchange algorithm for constructing exact optimal experimental designs we describe the cyclic coordinate exchange algorithm for constructing d optimal and linear optimal experimental designs the algorithm uses a variant of the gauss southwell cyclic coordinate descent algorithm within the k exchange algorithm to achieve substantive reductions in required computing among its advantages are the following candidate sets which grow exponentially in the number of factors need not be explicitly constructed or enumerated convex design spaces or mixed convex by discrete design spaces are handled directly without the need for sophisticated nonlinear programming routines or candidate set adjustment for design problems having 10 or more factors the reductions in execution time are typically two or more orders of magnitude when compared to standard candidateset based procedures such as k exchange yet the designs produced exhibit no loss of efficiency

an efficient variable selection approach for analyzing designed experiments the analysis of experiments in which numerous potential variables are examined is driven by the principles of effect sparsity effect hierarchy and effect heredity we propose an efficient variable selection strategy to specifically address the unique challenges faced by such analysis the proposed methods are natural extensions of the lars general purpose variable selection algorithm they can be computed very rapidly and can find sparse models that better satisfy the goals of experiments simulations and real examples are used to illustrate the wide applicability of the proposed methods

construction of two level nonregular designs of strength three with large run sizes abstracttwo level orthogonal arrays of strength 3 permit the study of the main effects and the two factor interactions of the experimental factors these arrays are classified into regular and nonr

a two stage bayesian model selection strategy for supersaturated designs in early stages of experimentation one often has many candidate factors of which only few have significant influence on the response supersaturated designs can offer important advantages however standard regression techniques of fitting a prediction line using all candidate variables fail to analyze data from such designs stepwise regression may be used but has drawbacks as reported in the literature a two stage bayesian model selection strategy able to keep all possible models under consideration while providing a level of robustness akin to bayesian analyses incorporating noninformative priors is proposed the strategy is demonstrated on a well known dataset and compared to competing methods via simulation

projection properties of plackett and burman designs the projection properties of the 2 r q p fractional factorials are well known and have been used effectively in a number of published examples of experimental investigations the plackett and burman designs also have interesting projective properties knowledge of which allows the experimenter to follow up an initial plackett and burman design with runs that increase the initial resolution for the factors that appear to matter and thus permit efficient separation of effects of interest projections of designs into 2 5 dimensions are discussed and the 12 run case is given in detail a numerical example illustrates the practical uses of these projections

an analytic solution for estimating two dimensional hidden markov models two dimensional hidden markov model 2 d hmm is an extension of 1 d hmm to 2 d it provides a reasonable statistical method to model matrix data this paper presents some new strict definitions of 2 d hmm and proves the equivalence between them and gives a study of the three basic problems for 2 d hmm namely probability evaluation optimal state matrix and parameter estimation by using the ideal that the sequences of states on columns or rows of a 2 d hmm can be seen as states of a 1 d hmm several new formulae solving these problems are theoretically derived and further demonstrated by computer simulations

variable selection for proportional odds model in this paper we study the problem of variable selection for the proportional odds model which is a useful alternative to the proportional hazards model and might be appropriate when the proportional hazards assumption is not satisfied we propose to fit the proportional odds model by maximizing the marginal likelihood subject to a shrinkage type penalty which encourages sparse solutions and hence facilitates the process of variable selection two types of shrinkage penalties are considered the lasso and the adaptive lasso alasso penalty in the alasso penalty different weights are imposed on different coefficients such that important variables are more protectively retained in the final model while unimportant ones are more likely to be shrunk to zeros we further provide an efficient computation algorithm to implement the proposed methods and demonstrate their performance through simulation studies and an application to real data numerical results indicate that both methods can produce accurate and interpretable models and the alasso tends to work better than the usual lasso

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

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

asymptotic properties of the maximum likelihood estimator in regime switching econometric models abstract markov regime switching models have been widely used in numerous empirical applications in economics and finance however the asymptotic distribution of the maximum likelihood estimator mle has not been proven for some empirically popular markov regime switching models in particular the asymptotic distribution of the mle has been unknown for models in which some elements of the transition probability matrix have the value of zero as is commonly assumed in empirical applications with models with more than two regimes this also includes models in which the regime specific density depends on both the current and the lagged regimes such as the seminal model of hamilton 1989 and switching arch model of hamilton and susmel 1994 this paper shows the asymptotic normality of the mle and consistency of the asymptotic covariance matrix estimate of these models

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

construction of supersaturated designs through partially aliased interactions summary an n x n hadamard matrix can be used to construct a saturated 2 n 1 design with n runs furthermore if an interaction column for two of the columns of the matrix is not fully aliased with any column of the matrix this interaction column can be used as a supplementary column for studying an additional factor for some small hadamard matrices studied by plackett burman 1946 the number of such interaction columns is very large thus allowing the construction of supersaturated designs whose number of factors far exceeds the number of runs a general method of construction along these lines is proposed the efficiency of the constructed designs is studied by using three criteria

connections between two level designs of resolutions iii and v resolution iii designs are resolution iii designs in which no two factor interactions are confounded with one another they arise naturally in the search for small composite designs and were first suggested by hartley 1959 new results given here link resolution iii designs to resolution v designs enabling passage between the two types of designs to be made this means that previously untabulated resolution iii designs can be derived directly from known resolution v designs for example a hartley type composite design can be based on a 27 1 iii design derived from a 26 1 v design the usual composite design is based on a 27 1 v design double the number of factorial runs the resolution iii designs can also be usefully modified for specific industrial applications box and jones 1989 moreover the maximum number of factors it is possible to accommodate in a resolution iii design of a given size can be obtained directly from the known maximum for resolution v designs of the same size

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

detection of interactions in experiments on large numbers of factors one of the main advantages of factorial experiments is the information that they can offer on interactions when there are many factors to be studied some or all of this information is often sacrificed to keep the size of an experiment economically feasible two strategies for group screening are presented for a large number of factors over two stages of experimentation with particular emphasis on the detection of interactions one approach estimates only main effects at the first stage classical group screening whereas the other new method interaction group screening estimates both main effects and key two factor interactions at the first stage three criteria are used to guide the choice of screening technique and also the size of the groups of factors for study in the first stage experiment the criteria seek to minimize the expected total number of observations in the experiment the probability that the size of the experiment exceeds a prespecified target and the proportion of active individual factorial effects which are not detected to implement these criteria results are derived on the relationship between the grouped and individual factorial effects and the probability distributions of the numbers of grouped factors whose main effects or interactions are declared active at the first stage examples are used to illustrate the methodology and some issues and open questions for the practical implementation of the results are discussed

optimal foldover plans for two level nonregular orthogonal designs this article considers optimal foldover plans for nonregular designs by using the indicator function we define words with fractional lengths the extended word length pattern is then used to select among nonregular foldover designs some general properties of foldover designs are obtained using the indicator function we prove that the full foldover plan that reverses the signs of all factors is optimal for all 12 run and 20 run orthogonal designs the optimal foldover plans for all 16 run regular and nonregular orthogonal designs are constructed and tabulated for practical use optimal foldover plans for higher order orthogonal designs can be constructed in a similar manner

optimal semifoldover plans for two level orthogonal designs foldover is a widely used procedure for selecting follow up experimental runs as foldover designs require twice as many runs as the initial design they can be inefficient if the number of effects to be de aliased is smaller than the size of the original experiment semifolding refers to adding half of a foldover fraction and is a technique that has been investigated in recent literature for regular two level fractional factorial designs as an alternative to foldover in this article semifoldover plans for two level orthogonal factorial designs regular and nonregular are compared and ranked based on the concept of minimal dependent sets optimal plans are developed for selected 12 16 20 and 32 run designs a hidden projection property of optimal semifoldovers of 12 and 20 run orthogonal arrays is uncovered general properties of semifoldover designs are also discussed all initial designs considered in this article are included in the supplementary files available online