angled derivative approximation of the hyperbolic heat conduction equations numerical methods based upon angled derivative approximation are presented for a linear first order system of hyperbolic partial differential equations pdes the hyperbolic heat conduction equations these equations model the flow of heat in circumstances where the speed of thermal propagation is finite as opposed to the infinite wave speed inherent in the diffusion equation a basic angled derivative scheme is first developed which is second order accurate from this an enhanced angled derivative scheme is then developed which is fourth order accurate for courant numbers of one half and one both methods are explicit three level schemes which are conditionally stable careful treatment of initial and boundary conditions is provided which preserves overall order of accuracy and stability and suppresses any deleterious effects of spurious modes after establishing a necessary and sufficient stability condition of courant number less than or equal to one for both schemes their dissipative and dispersive properties are investigated a numerical example concerning the propagation of a thermal pulse train concludes this investigation

when should epidemiologic regressions use random coefficients summary regression models with random coefficients arise naturally in both frequentist and bayesian approaches to estimation problems they are becoming widely available in standard computer packages under the headings of generalized linear mixed models hierarchical models and multilevel models i here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed effects models now prevalent in epidemiology the argument invokes an antiparsimony principle attributed to l j savage which is that models should be rich enough to reflect the complexity of the relations under study it also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything often used to justify parsimony regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable selection algorithms and their attendant distortion of uncertainty assessments these points are illustrated with an analysis of data on diet nutrition and breast cancer

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

transferability of hydrological models and ensemble averaging methods between contrasting climatic periods understanding hydrological model predictive capabilities under contrasting climate conditions enables more robust decision making using differential split sample testing dsst we analyze the performance of six hydrological models for 37 irish catchments under climate conditions unlike those used for model training additionally we consider four ensemble averaging techniques when examining interperiod transferability dsst is conducted using 2 3 year noncontinuous blocks of i the wettest driest years on record based on precipitation totals and ii years with a more less pronounced seasonal precipitation regime model transferability between contrasting regimes was found to vary depending on the testing scenario catchment and evaluation criteria considered as expected the ensemble average outperformed most individual ensemble members however averaging techniques differed considerably in the number of times they surpassed the best individual model member bayesian model averaging bma and the granger ramanathan averaging gra method were found to outperform the simple arithmetic mean sam and akaike information criteria averaging aica here gra performed better than the best individual model in 51 86 of cases according to the nash sutcliffe criterion when assessing model predictive skill under climate change conditions we recommend i setting up dsst to select the best available analogues of expected annual mean and seasonal climate conditions ii applying multiple performance criteria iii testing transferability using a diverse set of catchments and iv using a multimodel ensemble in conjunction with an appropriate averaging technique given the computational efficiency and performance of gra relative to bma the former is recommended as the preferred ensemble averaging technique for climate assessment

least squares model averaging this paper considers the problem of selection of weights for averaging across least squares estimates obtained from a set of models existing model average methods are based on exponential akaike information criterion aic and bayesian information criterion bic weights in distinction this paper proposes selecting the weights by minimizing a mallows criterion the latter an estimate of the average squared error from the model average fit we show that our new mallows model average mma estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators in a simulation experiment we show that the mma estimator compares favorably with those based on aic and bic weights the proof of the main result is an application of the work of li 1987

combining multiple comparisons and modeling techniques in dose response studies the analysis of data from dose response studies has long been divided according to two major strategies multiple comparison procedures and model based approaches model based approaches assume a functional relationship between the response and the dose taken as a quantitative factor according to a prespecified parametric model the fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose response model multiple comparison procedures regard the dose as a qualitative factor and make very few if any assumptions about the underlying dose response model the primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect one approach is to evaluate the significance of contrasts between different dose levels while preserving the family wise error rate such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation we describe a unified strategy to the analysis of data from dose response studies which combines multiple comparison and modeling techniques we assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose response curve while preserving the family wise error rate the selected model is then used to provide inference on adequate doses

toward an objective and reproducible model choice via variable selection deviation various model selection methods can be applied to seek sparse subsets of the covariates to explain the response of interest in bioinformatics while such methods often offer very helpful predictive performances their selections of the covariates may be much less trustworthy indeed when the number of covariates is large the selections can be highly unstable even under a slight change of the data this casts a serious doubt on reproducibility of the identified variables for a sound scientific understanding of the regression relationship methods need to be developed to find the most important covariates that have higher chance to be confirmed in future studies such a method based on variable selection deviation is proposed and evaluated in this work

incorporating baseline measurements into the analysis of crossover trials with time to event endpoints two period two treatment 2 2 crossover designs are commonly used in clinical trials for continuous endpoints it has been shown that baseline pretreatment measurements collected before the start of each treatment period can be useful in improving the power of the analysis methods to achieve a corresponding gain for censored time to event endpoints have not been adequately studied we propose a method in which censored values are treated as missing data and multiply imputed using prespecified parametric event time models the event times in each imputed data set are then log transformed and analyzed using a linear model suitable for a 2 2 crossover design with continuous endpoints with the difference in period specific baselines included as a covariate results obtained from the imputed data sets are synthesized for point and confidence interval estimation of the treatment ratio of geometric mean event times using model averaging in conjunction with rubin s combination rule we use simulations to illustrate the favorable operating characteristics of our method relative to two other methods for crossover trials with censored time to event data ie a hierarchical rank test that ignores the baselines and a stratified cox model that uses each study subject as a stratum and includes period specific baselines as a covariate application to a real data example is provided

the impact of baseline covariates on the efficiency of statistical analyses of crossover designs we investigate the impact of baseline covariates on the efficiency of statistical analyses of crossover designs for practical considerations we contemplate two different baseline methods study baselines and period dependent baselines for each baseline method we establish analytical upper bounds for the relative efficiency of a large class of crossover designs the totally balanced designs under a model with the baseline covariates as compared with the model without the baseline covariates we present numerical details based on these bounds for assorted scenarios and reveal implications of these results copyright 2012 john wiley sons ltd

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

jackknife model averaging abstract we consider the problem of obtaining appropriate weights for averaging m approximate misspecified models for improved estimation of an unknown conditional mean in the face of non nested model uncertainty in heteroskedastic error settings we propose a jackknife model averaging jma estimator which selects the weights by minimizing a cross validation criterion this criterion is quadratic in the weights so computation is a simple application of quadratic programming we show that our estimator is asymptotically optimal in the sense of achieving the lowest possible expected squared error monte carlo simulations and an illustrative application show that jma can achieve significant efficiency gains over existing model selection and averaging methods in the presence of heteroskedasticity

capture recapture estimation using finite mixtures of arbitrary dimension reversible jump markov chain monte carlo rjmcmc methods are used to fit bayesian capture recapture models incorporating heterogeneity in individuals and samples heterogeneity in capture probabilities comes from finite mixtures and or fixed sample effects allowing for interactions estimation by rjmcmc allows automatic model selection and or model averaging priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models in contrast to likelihood based methods to demonstrate the approach we analyze the standard snowshoe hare and cottontail rabbit data sets from ecology a reliability testing data set

least squares forecast averaging abstract this paper proposes forecast combination based on the method of mallows model averaging mma the method selects forecast weights by minimizing a mallows criterion this criterion is an asymptotically unbiased estimate of both the in sample mean squared error mse and the out of sample one step ahead mean squared forecast error msfe furthermore the mma weights are asymptotically mean square optimal in the absence of time series dependence we show how to compute mma weights in forecasting settings and investigate the performance of the method in simple but illustrative simulation environments we find that the mma forecasts have low msfe and have much lower maximum regret than other feasible forecasting methods including equal weighting bic selection weighted bic aic selection weighted aic bates granger combination predictive least squares and granger ramanathan combination

frequentist model average estimators the traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance without acknowledging the additional uncertainty introduced by model selection this often means underreporting of variability and too optimistic confidence intervals we build a general large sample likelihood apparatus in which limiting distributions and risk properties of estimators post selection as well as of model average estimators are precisely described also explicitly taking modeling bias into account this allows a drastic reduction in complexity as competing model averaging schemes may be developed discussed and compared inside a statistical prototype experiment where only a few crucial quantities matter in particular we offer a frequentist view on bayesian model averaging methods and give a link to generalized ridge estimators our work also leads to new model selection criteria the methods are illustrated with real data applications

the barendregt cube with definitions and generalised reduction in this paper we propose to extend the barendregt cube by generalisings reduction and by adding definition mechanisms generalised reduction allows contracting more visible redexes than usual and definitions are an important tool to allow for a more flexible typing system we show that this extension satisfies most of the original properties of the cube including church rosser subject reduction and strong normalisation

adaptive regression by mixing adaptation over different procedures is of practical importance different procedures perform well under different conditions in many practical situations it is rather hard to assess which conditions are approximately satisfied so as to identify the best procedure for the data at hand thus automatic adaptation over various scenarios is desirable a practically feasible method named adaptive regression by mixing arm is proposed to convexly combine general candidate regression procedures under mild conditions the resulting estimator is theoretically shown to perform optimally in rates of convergence without knowing which of the original procedures work the best simulations are conducted in several settings including comparing a parametric model with nonparametric alternatives comparing a neural network with a projection pursuit in multidimensional regression and combining bandwidths in kernel regression the results clearly support the theoretical property of arm the arm algorithm assigns we

semiparametric model averaging prediction for dichotomous response abstract model averaging has attracted abundant attentions in the past decades as it emerges as an impressive forecasting device in econometrics social sciences and medicine so far most developed model averaging methods focus only on either parametric models or nonparametric models with a continuous response in this paper we propose a semiparametric model averaging prediction smap method for a dichotomous response the idea is to approximate the unknown score function by a linear combination of one dimensional marginal score functions the weight parameters involved in the approximation are obtained by first smoothing the nonparametric marginal scores and then applying the parametric model averaging via a maximum likelihood estimation the proposed smap provides greater flexibility than parametric models while being more stable than a fully nonparametric approach theoretical properties are investigated in two practical scenarios i covariates are conditionally independent given the response and ii the conditional independence assumption does not hold in the first scenario we show that smap puts weight one to the true model and hence the model averaging estimators are consistent in the second scenario in which a true model may not exist smap is shown to be asymptotically optimal in the sense that its kullback leibler loss is asymptotically identical to that of the best but infeasible model averaging estimator empirical evidences from simulation studies and a real data analysis are presented to support and illustrate our methods

small sample degrees of freedom with multiple imputation an appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete data inferences into a final inference the repeated imputation inference rubin 1987 this inference is based on a t distribution and is derived from a bayesian paradigm under the assumption that the complete data degrees of freedom com are infinite but the number of imputations m is finite when com is small and there is only a modest proportion of missing data the calculated repeated imputation degrees of freedom m for the t reference distribution can be much larger than com which is clearly inappropriate following the bayesian paradigm we derive an adjusted degrees of freedom m with the following three properties for fixed m and estimated fraction of missing information m monotonically increases in com m is always less than or equal to com and m equals m when com is infinite a small simulation study demonstrates the superior frequentist performance when using m rather than m

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

model averaging by jackknife criterion in models with dependent data abstract the past decade witnessed a literature on model averaging by frequentist methods for the most part the asymptotic optimality of various existing frequentist model averaging estimators has been established under i i d errors recently hansen and racine hansen b e racine j 2012 jackknife model averaging journal of econometrics 167 38 46 developed a jackknife model averaging jma estimator which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors in this paper we broaden hansen and racine s scope of analysis to encompass models with i a non diagonal error covariance structure and ii lagged dependent variables thus allowing for dependent data we show that under these set ups the jma estimator is asymptotically optimal by a criterion equivalent to that used by hansen and racine a monte carlo study demonstrates the finite sample performance of the jma estimator in a variety of model settings

multivariate logit copula model with an application to dental data applications of copulas for multivariate continuous data abound but there are only a few that treat multivariate binary data in the present paper we model multivariate binary data based on copulas using mixtures of max infinitely divisible copulas introduced by joe and hu j multivar anal 1996 57 2 240 265 when applying copulas to binary data the marginal distributions also contribute to the dependence measures we propose the use of covariate information in the copula parameters to obtain a direct effect of a covariate on dependence to deal with model uncertainty due to selecting among several candidate models we use a model averaging technique we apply the model to data from the signal tandmobiel dental study and in particular to four binary responses that refer to caries experience in the mandibular and maxillary left and right molars we aim to model kendall s tau associations between them and examine how covariate information affects these associations we found that there are systematically larger associations between the two mandibular and the two maxillary molars using covariates to model these associations more closely we found that the systematic fluoride and age of the children affect the associations note that such relationships could not have been revealed by methods that focus on the marginal models copyright 2008 john wiley sons ltd

application of model selection criteria to some problems in multivariate analysis a review of model selection criteria is presented with a view toward showing their similarities it is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model selection criteria consideration is given to application of model selection criteria to some problems of multivariate analysis especially the clustering of variables factor analysis and more generally describing a complex of variables

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

optimal designs for frequentist model averaging we consider the problem of designing experiments for estimating a target parameter in regression analysis when there is uncertainty about the parametric form of the regression function a new optimality criterion is proposed that chooses the experimental design to minimize the asymptotic mean squared error of the frequentist model averaging estimate necessary conditions for the optimal solution of a locally and bayesian optimal design problem are established the results are illustrated in several examples and it is demonstrated that bayesian optimal designs can yield a reduction of the mean squared error of the model averaging estimator by up to 45

strong normalization from weak normalization in typedλ calculi for some typed calculi it is easier to prove weak normalization than strong normalization techniques to infer the latter from the former have been invented over the last twenty years by nederpelt klop khasidashvili karr de groote and kfoury and wells however these techniques infer strong normalization of one notion of reduction from weak normalization of amore complicatednotion of reduction this paper presents a new technique to infer strong normalization of a notion of reduction in a typed calculus from weak normalization of thesamenotion of reduction the technique is demonstrated to work on some well known systems including second order calculus and the system of positive recursive types it gives hope for a positive answer to the barendregt geuvers conjecture stating that every pure type system which is weakly normalizing is also strongly normalizing the paper also analyzes the relationship between the techniques mentioned above and reviews in less detail other techniques for proving strong normalization

the exponential method of angled derivatives a hybrid numerical method is presented for a linear first order hyperbolic partial differential equation pde the nonhomogeneous one way advection reaction equation this pde is first reduced to an ordinary differential equation ode along a characteristic emanating backward in time from each mesh point these odes are then integrated numerically using exponential fitting to advance in time thus permitting wide disparities in size among the coefficients such temporal integration requires a spatial interpolation procedure dependent upon the slope of the local characteristic if the local courant number is less than one then the interpolation is afforded by the exponential angled derivative method while if greater than one then the exponential reflected angled derivative approximation is employed otherwise if the courant number is transitioning through one then the exponential box scheme is employed at the boundary parabolic tracing of the characteristics provides a comparable level of accuracy the net result is a three level explicit method which is second order accurate and unconditionally stable the efficacy of this exponential method of angled derivatives emad scheme for singular perturbation problems is demonstrated numerically

model selection for extended quasi likelihood models in small samples we develop a small sample criterion aicc for the selection of extended quasi likelihood models in contrast to the akaike information criterion aic aicc provides a more nearly unbiased estimator for the expected kullback leibler information consequently it often selects better models than aic in small samples for the logistic regression model monte carlo results show that aicc outperforms aic pregibon s 1979 data analytic methods for generalized linear models ph d thesis university of toronto cp and the cp selection criteria of hosmer et al 1989 biometrics 45 1265 1270 two examples are presented

combining linear regression models when and how model combining i e mixing methods have been proposed in recent years to deal with uncertainty in model selection even though advantages of model combining over model selection have been demonstrated in simulations and data examples it is still unclear to a large extent when model combining should be preferred in this work first we propose an instability measure to capture the uncertainty of model selection in estimation called perturbation instability in estimation pie based on perturbation of the sample we demonstrate that estimators from model selection can have large pie values and that model combining substantially reduces the instability for such cases second we propose a model combining method adaptive regression by mixing with model screening arms and derive a theoretical property in arms a screening step is taken to narrow down the list of candidate models before combining which not only saves computing time but also can improve estimation accuracy third we compare arms w

the method of angled derivatives a hybrid numerical method is presented for a linear first order hyperbolic partial differential equation pde the nonhomogeneous one way advection equation the unifying thread is the reduction of the pde to an ordinary differential equation ode along a characteristic emanating backward in time from each mesh point these odes are then integrated numerically to advance in time such integration requires an interpolation procedure dependent upon the slope of the local characteristic if the local courant number is less than one then the interpolation is afforded by the angled derivative method while if greater than one then a reflected angled derivative approximation is introduced otherwise if the courant number is transitioning through one then the box scheme is employed at the boundary parabolic tracing of the characteristics provides a comparable level of accuracy the net result is a compact nondissipative three level explicit method which is second order accurate and unconditionally stable the efficacy of this method of angled derivatives mad scheme for both constant and variable coefficient problems with or without inhomogeneities is demonstrated numerically

a useful l notation abstract in this article we introduce a notation that is useful for many concepts of the calculus the new notation is a simple translation of the classical one yet it provides many nice advantages first we show that definitions such as compatibility the heart of a term and redexes become simpler in item notation second we show that with this item notation reduction can be generalised in a nice way we find a relation which extends which is church rosser and strongly normalising this reduction relation may be the way to new reduction strategies in classical notation it is much harder to present this generalised reduction in a convincing manner third we show that the item notation enables one to represent in a very simple way the canonical type a of a term a in context this canonical type plays the role of a preference type and can be used to split a b into the two parts a and a b this means that the question is a typable with a type b is divided into two questions is a typable and is b in the class of types of a it turns out that calculating this preference type of a in item notation is a straightforward operation one just goes through a from left to right performing very trivial steps on the items till the end variable or heart of a is reached fourth we can with this item notation find the parts of a term t relevant for a variable occurrence x in terms of binding typing and substitution again this part of t t x is very easy to find in item notation just take the part of t to the left of x and remove all unmatched parentheses fifth we reflect on the status of variables and show that indeed it is easy to study this status in item notation finally we show that for a substitution calculus a la de bruijn with open terms it is simpler to describe normal forms using item notation there are further advantages of item notation that are studied elsewhere for example in 9 we show that explicit substitution is easily built in item notation and that global and local strategies of substitution can be accommodated in 10 we show that with item notation one can give a unified approach to type theory an implementation of this item notation with most of the concepts discussed in this paper can be found in 15

stability of multivariable fractional polynomial models with selection of variables and transformations a bootstrap investigation sauerbrei and royston have recently described an algorithm based on fractional polynomials for the simultaneous selection of variables and of suitable transformations for continuous predictors in a multivariable regression setting they illustrated the approach by analyses of two breast cancer data sets here we extend their work by considering how to assess possible instability in such multivariable fractional polynomial models we first apply the algorithm repeatedly in many bootstrap replicates we then use log linear models to investigate dependencies among the inclusion fractions for each predictor and among the simplified classes of fractional polynomial function chosen in the bootstrap samples to further evaluate the results we define measures of instability based on a decomposition of the variability of the bootstrap selected functions in relation to a reference function from the original model for each data set we are able to identify large reasonably stable subsets of the bootstrap replications in which the functional forms of the predictors appear fairly stable despite the considerable flexibility of the family of fractional polynomials and the consequent risk of overfitting when several variables are considered we conclude that the multivariable selection algorithm can find stable models

optimal model averaging estimation for generalized linear models and generalized linear mixed effects models abstractconsidering model averaging estimation in generalized linear models we propose a weight choice criterion based on the kullback leibler kl loss with a penalty term this criterion is different from that for continuous observations in principle but reduces to the mallows criterion in the situation we prove that the corresponding model averaging estimator is asymptotically optimal under certain assumptions we further extend our concern to the generalized linear mixed effects model framework and establish associated theory numerical experiments illustrate that the proposed method is promising

estimation of the adjusted cause specific cumulative probability using flexible regression models for the cause specific hazards in competing risks setting we account for death according to a specific cause and the quantities of interest are usually the cause specific hazards cshs and the cause specific cumulative probabilities a cause specific cumulative probability can be obtained with a combination of the cshs or via the subdistribution hazard here we modeled the csh with flexible hazard based regression models using b splines for the baseline hazard and time dependent td effects we derived the variance of the cause specific cumulative probabilities at the population level using the multivariate delta method and showed how we could easily quantify the impact of a covariate on the cumulative probability scale using covariate adjusted cause specific cumulative probabilities and their difference we conducted a simulation study to evaluate the performance of this approach in its ability to estimate the cumulative probabilities using different functions for the cause specific log baseline hazard and with or without a td effect in the scenario with td effect we tested both well specified and misspecified models we showed that the flexible regression models perform nearly as well as the nonparametric method if we allow enough flexibility for the baseline hazards moreover neglecting the td effect hardly affects the cumulative probabilities estimates of the whole population but impacts them in the various subgroups we illustrated our approach using data from people diagnosed with monoclonal gammopathy of undetermined significance and provided the r code to derive those quantities as an extension of the r package mexhaz

generalized multiple contrast tests in dose response studies in the process of developing drugs proof of concept studies can be helpful in determining whether there is any evidence of a dose response relationship a global test for this purpose that has gained popularity is a component of the multiple comparisons procedure with modeling techniques mcp mod which involves the specification of a candidate set of several plausible dose response models for each model a test is performed for significance of an optimally chosen contrast among the sample means an overall p value is obtained from the distribution of the maximum of the contrast statistics this is equivalent to basing the test on the minimum of the p values arising from these contrast statistics and hence can be viewed as a method for combining dependent p values we generalize this idea to the use of different statistics for combining the dependent p values such as fisher s combination method or the inverse normal combination method simulation studies show that the generalized multiple contrast tests gmcts based on the fisher and inverse normal methods are generally more powerful than the mcp mod procedure based on the minimum of the p values except for cases where the true dose response model is in a sense near the extremes of the candidate set of dose response models the proposed gmcts can also be used for model selection and dosage selection by employing a closed testing procedure

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

on the bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty we consider the estimation of the size of a closed population often of interest for wild animal populations using a capture recapture study the estimate of the total population size can be very sensitive to the choice of model used to fit to the data we consider a bayesian approach in which we consider all eight plausible models initially described by otis et al 1978 wildlife monographs 62 1 135 within a single framework including models containing an individual heterogeneity component we show how we are able to obtain a model averaged estimate of the total population incorporating both parameter and model uncertainty to illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known before considering a real example relating to a population of dolphins off northeast scotland

estimation and accuracy after model selection classical statistical theory ignores model selection in assessing estimation accuracy here we consider bootstrap methods for computing standard errors and confidence intervals that take model selection into account the methodology involves bagging also known as bootstrap smoothing to tame the erratic discontinuities of selection based estimators a useful new formula for the accuracy of bagging then provides standard errors for the smoothed estimators two examples nonparametric and parametric are carried through in detail a regression model where the choice of degree linear quadratic cubic is determined by the cp criterion and a lasso based estimation problem

a note on the fourier series model for analysing line transect data the fourier series model offers a powerful procedure for the estimation of animal population density from line transect data the estimate is reliable over a wide range of detection functions in contrast analytic confidence intervals yield at best 90 confidence for nominal 95 intervals three solutions one using monte carlo techniques another making direct use of replicate lines and the third based on the jackknife method are discussed and compared

a mallows type model averaging estimator for the varying coefficient partially linear model in the last decade significant theoretical advances have been made in the area of frequentist model averaging fma however the majority of this work has emphasized parametric model setups this

monte carlo confidence intervals des intervalles de confiance non parametriques obtenus par la methode de monte carlo sont utiles quand les intervalles obtenus par les methodes analytiques sont indisponibles ou ne correspondent pas au niveau nominal on fournit des formules permettant de generer un intervalle de niveau donne et de quantifier la variation due a la methode de monte carlo

model selection an integral part of inference we argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data we consider different philosophies for achieving this goal and suggest strategies for data analysis we illustrate our methods through three examples the first is a poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates the second is a line transect data set for which different models yield substantially different estimates of abundance the third is a simulated example in which truth is known

the analysis of data from 2 2 cross over trials with baseline measurements an account is given of the analysis of data from 2 x 2 cross over trials which include baseline measurements we show that most of the previously proposed methods can be incorporated into a general framework of least squares estimation with a simple linear model a simple analysis based on ordinary least squares estimators is described which can be used with either two sample t tests and confidence intervals or with the corresponding non parametric procedures it is shown how the use of generalized least squares estimators is equivalent to the use of covariance adjustment these methods require no assumptions about the covariance structure of the measurements from each subject the results of assessing the covariance structure present in examples of data from a number of trials are summarized these results suggest that previously proposed simple covariance structures are unlikely to be appropriate in general

forecasting with factor augmented regression a frequentist model averaging approach abstract this paper considers forecast combination with factor augmented regression in this framework a large number of forecasting models are available varying by the choice of factors and the number of lags we investigate forecast combination across models using weights that minimize the mallows and the leave h out cross validation criteria the unobserved factor regressors are estimated by principle components of a large panel with n predictors over t periods with these generated regressors we show that the mallows and leave h out cross validation criteria are asymptotically unbiased estimators of the one step ahead and multi step ahead mean squared forecast errors respectively provided that n t however the paper does not establish any optimality properties for the methods in contrast to well known results in the literature this result suggests that the generated regressor issue can be ignored for forecast combination without restrictions on the relation between n and t simulations show that the mallows model averaging and leave h out cross validation averaging methods yield lower mean squared forecast errors than alternative model selection and averaging methods such as aic bic cross validation and bayesian model averaging we apply the proposed methods to the us macroeconomic data set in stock and watson 2012 and find that they compare favorably to many popular shrinkage type forecasting methods

lower bounds and aggregation in density estimation in this paper we prove the optimality of an aggregation procedure we prove lower bounds for aggregation of model selection type of m density estimators for the kullback leibler divergence kl the hellinger s distance and the l1 distance the lower bound with respect to the kl distance can be achieved by the on line type estimate suggested among others by yang 2000a combining these results we state that log m n is an optimal rate of aggregation in the sense of tsybakov 2003 where n is the sample size

sparsity oriented importance learning for high dimensional linear regression abstractwith now well recognized nonnegligible model selection uncertainty data analysts should no longer be satisfied with the output of a single final model from a model selection process regar

is there an optimal forecast combination abstract we consider several geometric approaches for combining forecasts in large samples a simple eigenvector approach a mean corrected eigenvector and trimmed eigenvector approach we give conditions where geometric approach yields identical result as the regression approach we also consider a mean and scale corrected simple average of all predictive models for finite sample and give conditions where simple average is an optimal combination monte carlos are conducted to compare the finite sample performance of these and some popular forecast combination and information combination methods and to shed light on the issues of forecast combination vs information combination we also try to shed light on whether there exists an optimal forecast combination method by comparing various forecast combination methods to predict us real output growth rate and excess equity premium

proof of concept and dose estimation with binary responses under model uncertainty this article suggests a unified framework for testing proof of concept poc and estimating a target dose for the benefit of a more comprehensive robust and powerful analysis in phase ii or similar clinical trials from a pre specified set of candidate models we choose the ones that best describe the observed dose response to decide which models if any significantly pick up a dose effect we construct the permutation distribution of the minimum p value over the candidate set this allows us to find critical values and multiplicity adjusted p values that control the familywise error rate of declaring any spurious effect in the candidate set as significant model averaging is then used to estimate a target dose popular single or multiple contrast tests for poc such as the cochran armitage dunnett or williams tests are only optimal for specific dose response shapes and do not provide target dose estimates with confidence limits a thorough evaluation and comparison of our approach to these tests reveal that its power is as good or better in detecting a dose response under various shapes with many more additional benefits it incorporates model uncertainty in poc decisions and target dose estimation yields confidence intervals for target dose estimates and extends to more complicated data structures we illustrate our method with the analysis of a phase ii clinical trial

double observer line transect methods levels of independence double observer line transect methods are becoming increasingly widespread especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain the resulting data supplement conventional distance sampling data with two sample mark recapture data like conventional mark recapture data these have inherent problems for estimating abundance in the presence of heterogeneity unlike conventional mark recapture methods line transect methods use knowledge of the distribution of a covariate which affects detection probability namely distance from the transect line in inference this knowledge can be used to diagnose unmodeled heterogeneity in the mark recapture component of the data by modeling the covariance in detection probabilities with distance we show how the estimation problem can be formulated in terms of different levels of independence at one extreme full independence is assumed as in the petersen estimator which does not use distance data at the other extreme independence only occurs in the limit as detection probability tends to one between the two extremes there is a range of models including those currently in common use which have intermediate levels of independence we show how this framework can be used to provide more reliable analysis of double observer line transect data we test the methods by simulation and by analysis of a dataset for which true abundance is known we illustrate the approach through analysis of minke whale sightings data from the north sea and adjacent waters

weighted envelope estimation to handle variability in model selection summaryenvelope methodology can provide substantial efficiency gains in multivariate statistical problems but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains current envelope methodology does not account for the added variance that can result from this selection in this article we circumvent dimension selection volatility through the development of a weighted envelope estimator theoretical justification is given for our estimator and the validity of the residual bootstrap for estimating its asymptotic variance is established a simulation study and real data analysis illustrate the utility of our weighted envelope estimator

jackknife model averaging for quantile regressions abstract in this paper we consider model averaging for quantile regressions qr when all models under investigation are potentially misspecified and the number of parameters is diverging with the sample size to allow for the dependence between the error terms and regressors in the qr models we propose a jackknife model averaging jma estimator which selects the weights by minimizing a leave one out cross validation criterion function and demonstrate its asymptotic optimality in terms of minimizing the out of sample final prediction error we conduct simulations to demonstrate the finite sample performance of our estimator and compare it with other model selection and averaging methods we apply our jma method to forecast quantiles of excess stock returns and wages

estimating marginal properties of quantitative real time pcr data using nonlinear mixed models summary a unified modeling framework based on a set of nonlinear mixed models is proposed for flexible modeling of gene expression in real time pcr experiments focus is on estimating the marginal or population based derived parameters cycle thresholds and but retaining the conditional mixed model structure to adequately reflect the experimental design additionally the calculation of model average estimates allows incorporation of the model selection uncertainty the methodology is applied for estimating the differential expression of a phosphate transporter gene ospt6 in rice in comparison to a reference gene at several states after phosphate resupply in a small simulation study the performance of the proposed method is evaluated and compared to a standard method

improved power in crossover designs through linear combinations of baselines in a crossover design in the absence of any carryover effect including period specific baselines as covariates in an analysis of covariance is known to increase the precision of the estimated treatment effect the extent of the efficiency gain is a function of the joint covariance structure of the baselines and post treatment responses as well as the metric used to incorporate the baselines into the analysis here we show how the underlying covariance structure can be leveraged to find an optimal linear combination of baselines so as to minimize the theoretical variance of the analysis of covariance based estimated treatment effect our work is relevant to complete designs with up to four periods specifically the 2 2 3 3 and 4 4 given that the optimal linear combination of baselines is a function of the covariance structure which in practice is unknown we propose an adaptive method here the covariance structure is chosen using information criterion to guide the choice of the linear combination of baselines evaluation of the proposed approach suggests that the type i error rate is maintained moreover relative to previously published methods sizeable gains in power are possible with this method results from a 2 2 trial exploring renal function and a 3 3 trial with heart rate as the outcome are used to illustrate the methods copyright 2016 john wiley sons ltd

optimal model assessment selection and combination central to statistical theory and application is statistical modeling which typically involves choosing a single model or combining a number of models of different sizes and from different sources whereas model selection seeks a single best modeling procedure model combination combines the strength of different modeling procedures in this article we look at several key issues and argue that model assessment is the key to model selection and combination most important we introduce a general technique of optimal model assessment based on data perturbation thus yielding optimal selection in particular model selection and combination from a frequentist perspective we advocate model combination over a selected subset of modeling procedures because it controls bias while reducing variability hence yielding better performance in terms of the accuracy of estimation and prediction to realize the potential of model combination we develop methodologies for determining the optimal tuning parameter such

optimal and efficient crossover designs when subject effects are random most studies on optimal crossover designs are based on models that assume subject effects to be fixed effects in this article we identify and study optimal and efficient designs for a model with random subject effects with the number of periods not exceeding the number of treatments we find that totally balanced designs are universally optimal for treatment effects in a large subclass of competing designs however in the entire class of designs totally balanced designs are in general not optimal and their efficiency depends on the ratio of the subject effects variance and the error variance we develop tools to study the efficiency of totally balanced designs and to identify designs with higher efficiency

unified maximum likelihood estimates for closed capture recapture models using mixtures summary agresti 1994 biometrics50 494 500 and norris and pollock 1996a biometrics52 639 649 suggested using methods of finite mixtures to partition the animals in a closed capture recapture experiment into two or more groups with relatively homogeneous capture probabilities this enabled them to fit the models mh mbh norris and pollock and mth agresti of otis et al 1978 wildlife monographs62 1 135 in this article finite mixture partitions of animals and or samples are used to give a unified linear logistic framework for fitting all eight models of otis et al by maximum likelihood likelihood ratio tests are available for model comparisons for many data sets a simple dichotomy of animals is enough to substantially correct for heterogeneity induced bias in the estimation of population size although there is the option of fitting more than two groups if the data warrant it

optimal crossover designs in a model with self and mixed carryover effects we consider a variant of the usual model for crossover designs with carryover effects instead of assuming that the carryover effect of a treatment is the same regardless of the treatment in the next period the model assumes that the carryover effect of a treatment on itself is different from the carryover effect on other treatments for the traditional model optimal designs tend to have pairs of consecutive identical treatments for the model considered here they tend to avoid such pairs practitioners have long expressed reservations about designs that exhibit such pairs and about the traditional model the new model provides an attractive alternative that leads to appealing optimal designs

handling of baseline measurements in the analysis of crossover trials different analytic approaches for modeling baseline data in crossover trials were compared based on the efficiency in estimating treatment effects jointly modeling baseline and post baseline data is recommended to best utilize baseline data it results in the most significant gain in efficiency when data are strongly correlated within the same period but weakly correlated between different periods its performance remains comparable to the best of various other modeling methods under small within period correlation or large between period correlation we also examined the use of baseline data in modeling carryover effect we noted that to model carryover effect in crossover trial generally would lead to a much less efficient estimator and much more sensitive inference copyright 2012 john wiley sons ltd

least squares model averaging by mallows criterion abstract this paper is in response to a recent paper by hansen 2007 who proposed an optimal model average estimator with weights selected by minimizing a mallows criterion the main contribution of hansen s paper is a demonstration that the mallows criterion is asymptotically equivalent to the squared error so the model average estimator that minimizes the mallows criterion also minimizes the squared error in large samples we are concerned with two assumptions that accompany hansen s approach the first is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors often there is no clear basis for the ordering and the approach does not permit non nested models which are more realistic from a practical viewpoint second for the optimality result to hold the model weights are required to lie within a special discrete set in fact hansen noted both difficulties and called for extensions of the proof techniques we provide an alternative proof which shows that the result on the optimality of the mallows criterion in fact holds for continuous model weights and under a non nested set up that allows any linear combination of regressors in the approximating models that make up the model average estimator these results provide a stronger theoretical basis for the use of the mallows criterion in model averaging by strengthening existing findings

robust forecast combinations abstract forecast outliers commonly occur in economic financial and other areas of forecasting applications in the literature of forecast combinations there have been only a few studies exploring how to deal with outliers in this work we propose two robust combining methods based on the after algorithm yang 2004a our approach utilizes robust loss functions in order to reduce the influence of outliers oracle inequalities for certain versions of these methods are obtained which show that the combined forecasts automatically perform as well as the best individual among the pool of original forecasts systematic simulations and data examples show that the robust methods outperform the after algorithm when outliers are likely to occur and perform on par with after when there are no outliers comparison of the robust afters with some commonly used combining methods also shows their potential advantages

unimodal regression using bernstein schoenberg splines and penalties summary research in the field of nonparametric shape constrained regression has been intensive however only few publications explicitly deal with unimodality although there is need for such methods in applications for example in dose response analysis in this article we propose unimodal spline regression methods that make use of bernstein schoenberg splines and their shape preservation property to achieve unimodal and smooth solutions we use penalized splines and extend the penalized spline approach toward penalizing against general parametric functions instead of using just difference penalties for tuning parameter selection under a unimodality constraint a restricted maximum likelihood and an alternative bayesian approach for unimodal regression are developed we compare the proposed methodologies to other common approaches in a simulation study and apply it to a dose response data set all results suggest that the unimodality constraint or the combination of unimodality and a penalty can substantially improve estimation of the functional relationship