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Uniformly most powerful confidence distributions are obtained for parameters in selected models of the exponential family. A conditioning on the selection event as well as on the sufficient statistics of nuisance parameters guarantees valid post-selection inference. Optimal confidence intervals are obtained directly from the confidence distribution without requiring an inversion of pivotal quantities. Simulations showcase that the method works also when all models are misspecified. ispartof: Journal Of Statistical Planning And Inference vol:222 issue:2023 pages:66-77 status: published

ispartof: Scandinavian Journal Of Statistics vol:50 issue:1 pages:358-382 status: accepted

We develop a high-dimensional graphical modeling approach for functional data where the number of functions exceeds the available sample size. This is accomplished by proposing a sparse estimator for a concentration matrix when identifying linear manifolds. As such, the procedure extends the ideas of the manifold representation for functional data to high-dimensional settings where the number of functions is larger than the sample size. By working in a penalized setting it enriches the functional data framework by estimating sparse undirected graphs that show how functional nodes connect to other functional nodes. The procedure allows multiple coarseness scales to be present in the data and proposes a simultaneous estimation of several related graphs. Its performance is illustrated using a real-life fMRI dataset and with simulated data.

The specific nature of credit loan data requires the use of mixture cure models within the class of survival analysis tools. The constructed models allow for com-peting risks such as early repayment and default, and for incorporating maturity, expressed as an unsusceptible part of the population. A novel further extension of such models incorporates unobserved heterogeneity within the risk groups. A hierar-chical expectation-maximization algorithm is derived to fit the models and standard errors are obtained. Simulations and a data analysis illustrate the applicability and benefits of these models, and in particular an improved event time estimation. ispartof: Econometrics and Statistics vol:22 pages:39-55 status: published

Quantile regression is a field with steadily growing importance in statistical modeling. It is a complementary method to linear regression, since computing a range of conditional quantile functions provides more accurate modeling of the stochastic relationship among variables, especially in the tails. We introduce a nonrestrictive and highly flexible nonparametric quantile regression approach based on C- and D-vine copulas. Vine copulas allow for separate modeling of marginal distributions and the dependence structure in the data and can be expressed through a graphical structure consisting of a sequence of linked trees. This way, we obtain a quantile regression model that overcomes typical issues of quantile regression such as quantile crossings or collinearity, the need for transformations and interactions of variables. Our approach incorporates a two-step ahead ordering of variables, by maximizing the conditional log-likelihood of the tree sequence, while taking into account the next two tree levels. We show that the nonparametric conditional quantile estimator is consistent. The performance of the proposed methods is evaluated in both low- and high-dimensional settings using simulated and real-world data. The results support the superior prediction ability of the proposed models.

A new method is proposed to estimate graphical models simultaneously from data obtained at different coarseness scales. Starting from a predefined scale the method offers the possibility to zoom in or out over scales on particular edges. The estimated graphs over the different scales have similar structures although their level of sparsity depends on the scale at which estimation takes place. The method makes it possible to evaluate the evolution of the graphs from the coarsest to the finest scale or vice versa. We select an optimal coarseness scale to be used for further analysis. Simulation studies and an application on functional magnetic resonance brain imaging data show the method's performance in practice. ispartof: Journal Of The Royal Statistical Society Series C-Applied Statistics vol:69 issue:1 pages:47-67 status: published

International audience; In functional data the interest is to find a global mean pattern, but also to capture the individual curve differences in phase and amplitude. This can be done conveniently by building in random effects on two levels: in the warping functions to account for individual phase variations; and in the linear structure to deal with individual amplitude variations. Via an appropriate choice of the warping function and B-spline approximations, estimation in the nonlinear mixed effects functional model is feasible, and does not require any prior knowledge on landmarks for the functional data. Sufficient and necessary conditions for identifiability of the flexible model are provided. A theoretical study is conducted: we establish asymptotic normality and consistency of the estimators of the registration and amplitude models, convergence of the iterative process, and consistency of the final estimator provided by the iterative process. The finite-sample performance of the proposed estimation procedure is investigated in a simulation study, which includes comparisons with existing methods. The added value of the developed method is further illustrated via the analysis of a real data example.

© 2018 Elsevier B.V. The composite quantile estimator is a robust and efficient alternative to the least-squares estimator in linear models. However, it is computationally demanding when the number of quantiles is large. We consider a model-averaged quantile estimator as a computationally cheaper alternative. We derive its asymptotic properties in high-dimensional linear models and compare its performance to the composite quantile estimator in both low- and high-dimensional settings. We also assess the effect on efficiency of using equal weights, theoretically optimal weights, and estimated optimal weights for combining the different quantiles. None of the estimators dominates in all settings under consideration, thus leaving room for both model-averaged and composite estimators, both with equal and estimated optimal weights in practice. ispartof: Journal of Statistical Planning and Inference vol:200 issue:(2019) pages:32-46 status: published

Many scientific and engineering challenges -- ranging from pharmacokinetic drug dosage allocation and personalized medicine to marketing mix (4Ps) recommendations -- require an understanding of the unobserved heterogeneity in order to develop the best decision making-processes. In this paper, we develop a hypothesis test and the corresponding p-value for testing for the significance of the homogeneous structure in linear mixed models. A robust matching moment construction is used for creating a test that adapts to the size of the model sparsity. When unobserved heterogeneity at a cluster level is constant, we show that our test is both consistent and unbiased even when the dimension of the model is extremely high. Our theoretical results rely on a new family of adaptive sparse estimators of the fixed effects that do not require consistent estimation of the random effects. Moreover, our inference results do not require consistent model selection. We showcase that moment matching can be extended to nonlinear mixed effects models and to generalized linear mixed effects models. In numerical and real data experiments, we find that the developed method is extremely accurate, that it adapts to the size of the underlying model and is decidedly powerful in the presence of irrelevant covariates.

Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory identifies equivalence between model-averaged and composite quantile estimation. However, little to nothing is known about such equivalence between methods that encourage sparsity. This paper provides a toolbox to further study robustness in these settings and focuses on prediction. In particular, we study optimally weighted model-averaged as well as composite l1-regularized estimation. Optimal weights are determined by minimizing the asymptotic mean squared error. This approach incorporates the effects of regularization, without the assumption of perfect selection, as is often used in practice. Such weights are then optimal for prediction quality. Through an extensive simulation study, we show that no single method systematically outperforms others. We find, however, that model-averaged and composite quantile estimators often outperform least-squares methods, even in the case of Gaussian model noise. Real data application witnesses the method’s practical use through the reconstruction of compressed audio signals. ispartof: Electronic Journal Of Statistics vol:14 issue:2 pages:2551-2599 status: Published online

A data set from a Belgian telematics product aimed at young drivers is used to identify how car insurance premiums can be designed based on the telematics data collected by a black box installed in the vehicle. In traditional pricing models for car insurance, the premium depends on self-reported rating variables (e.g. age, postal code) which capture characteristics of the policy(holder) and the insured vehicle and are often only indirectly related to the accident risk. Using telematics technology enables tailor-made car insurance pricing based on the driving behavior of the policyholder. We develop a statistical modeling approach using generalized additive models and compositional predictors to quantify and interpret the effect of telematics variables on the expected claim frequency. We find that such variables increase the predictive power and render the use of gender as a rating variable redundant. ispartof: Journal of the Royal Statistical Society: Series C (Applied Statistics) vol:67, part 5 issue:5 pages:1275-1304 status: published

SCOPUS: ar.j, info:eu-repo/semantics/published

Ignoring the model selection step in inference after selection is harmful. This paper studies the asymptotic distribution of estimators after model selection using the Akaike information criterion. First, we consider the classical setting in which a true model exists and is included in the candidate set of models. We exploit the overselection property of this criterion in the construction of a selection region, and obtain the asymptotic distribution of estimators and linear combinations thereof conditional on the selected model. The limiting distribution depends on the set of competitive models and on the smallest overparameterized model. Second, we relax the assumption about the existence of a true model, and obtain uniform asymptotic results. We use simulation to study the resulting postselection distributions and to calculate confidence regions for the model parameters. We apply themethod to data. ispartof: Biometrika vol:105 issue:3 pages:645-664 status: published

The focused information criterion for model selection is constructed to select the model that best estimates a particular quantity of interest, the focus, in terms of mean squared error. We extend this focused selection process to the high-dimensional regression setting with potentially a larger number of parameters than the size of the sample. We distinguish two cases: (i) the case where the considered submodel is of low dimension and (ii) the case where it is of high dimension. In the former case, we obtain an alternative expression of the low-dimensional focused information criterion that can directly be applied. In the latter case, we use a desparsified estimator that allows us to derive the mean squared error of the focus estimator. We illustrate the performance of the high-dimensional focused information criterion with a numerical study and a real dataset.

We investigate the performance of various survival analysis techniques applied to ten actual credit data sets from Belgian and UK financial institutions. In the comparison we consider classical survival analysis techniques, namely the accelerated failure time models and Cox proportional hazards regression models, as well as Cox proportional hazards regression models with splines in the hazard function. Mixture cure models for single and multiple events were more recently introduced in the credit risk context. The performance of these models is evaluated using both a statistical evaluation and an economic approach through the use of annuity theory. It is found that spline-based methods and the single event mixture cure model perform well in the credit risk context.

Datasets encountered when examining deeper issues in ecology and evolution are often complex. This calls for careful strategies for both model building, model selection, and model averaging. Our paper aims at motivating, exhibiting, and further developing focused model selection criteria. In contexts involving precisely formulated interest parameters, these versions of FIC, the focused information criterion, typically lead to better final precision for the most salient estimates, confidence intervals, etc. as compared to estimators obtained from other selection methods. Our methods are illustrated with real case studies in ecology; one related to bird species abundance and another to the decline in body condition for the Antarctic minke whale. ispartof: Frontiers In Ecology And Evolution vol:7 pages:1-13 status: published

A new method is proposed to simultaneously estimate graphical models from data obtained at different coarseness scales. Starting from a predefined scale the method offers the possibility to zoom in or out over scales on particular edges. The estimated graphs over the different scales have similar structures although their sparsity level depends on the scale at which estimation takes place. The method makes it possible to evaluate the evolution of the graphs from the coarsest to the finest scale or vice-versa. We select an optimal coarseness scale to be used for further analysis. Simulation studies and the application on fMRI brain imaging data show the method's performance in practice.

A delay between the occurrence and the reporting of events often has practical implications such as for the amount of capital to hold for insurance companies, or for taking preventive actions in case of infectious diseases. The accurate estimation of the number of incurred but not (yet) reported events forms an essential part of properly dealing with this phenomenon. We review the current practice for analysing such data and we present a flexible regression framework to jointly estimate the occurrence and reporting of events. By linking this setting to an incomplete data problem, estimation is performed via an expectation-maximization algorithm. The resulting method is elegant, easy to understand and implement, and provides refined insights in the nowcasts. The proposed methodology is applied to a European general liability portfolio in insurance.

Mobile phone carriers in a saturated market must focus on customer retention to maintain profitability. This study investigates the incorporation of social network information into churn prediction models to improve accuracy, timeliness, and profitability. Traditional models are built using customer attributes, however these data are often incomplete for prepaid customers. Alternatively, call record graphs that are current and complete for all customers can be analysed. A procedure was developed to build the call graph and extract relevant features from it to be used in classification models. The scalability and applicability of this technique are demonstrated on a telecommunications data set containing 1.4 million customers and over 30 million calls each month. The models are evaluated based on ROC plots, lift curves, and expected profitability. The results show how using network features can improve performance over local features while retaining high interpretability and usability.

We present a focused selection method for social networks. The procedure is driven by a focus, the main quantity we want to estimate well. It represents the statistical translation of a research hypothesis into parameters of interest. Given a collection of models, the procedure estimates for each model the mean squared error of the estimator of the focus. The model with the smallest such value is selected. We present focused model selection for (i) exponential random graph models, (ii) network autocorrelation models and (iii) network regression models to investigate existing relations in social networks. Worked-out examples illustrate the methodology.

We develop a method for estimating brain networks from fMRI data sets that have not all been measured using the same set of brain regions. Some of the coarse scale regions have been split in smaller subregions. The proposed penalized estimation procedure selects undirected graphical models with similar structures that combine information from several subjects and several coarseness scales. Both within scale edges and between scale edges that identify possible connections between a large region and its subregions are estimated. Mixed scale data; Fused and Group lasso; Joint graphical lasso; l1 penalization, Sparsistency.

Variable selection methods and model selection approaches are valuable statistical tools that are indispensable for almost any statistical modeling question. This review first considers the use of information criteria for model selection. Such criteria provide an ordering of the considered models where the best model is selected. Different modeling goals might require different criteria to be used. Next, the effect of including a penalty in the estimation process is discussed. Third, nonparametric estimation is discussed; it contains several aspects of model choice, such as the choice of the estimator to use and the selection of tuning parameters. Fourth, model averaging approaches are reviewed in which estimators from different models are weighted to provide one final estimator. There are several ways to choose the weights, and most of them result in data-driven, hence random, weights. Challenges for inference after model selection and inference for model-averaged estimators are discussed.

This paper offers a theoretical explanation for the stylized fact that forecast combinations with estimated optimal weights often perform poorly in applications. The properties of the forecast combination are typically derived under the assumption that the weights are fixed, while in practice they need to be estimated. If the fact that the weights are random rather than fixed is taken into account during the optimality derivation, then the forecast combination will be biased (even when the original forecasts are unbiased) and its variance is larger than in the fixed-weights case. In particular, there is no guarantee that the ‘optimal’ forecast combination will be better than the equal-weights case or even improve on the original forecasts. We provide the underlying theory, some special cases, and a numerical illustration. publisher: Elsevier articletitle: The forecast combination puzzle: A simple theoretical explanation journaltitle: International Journal of Forecasting articlelink: http://dx.doi.org/10.1016/j.ijforecast.2015.12.005 content_type: article copyright: Crown Copyright © 2016 Published by Elsevier B.V. on behalf of International Institute of Forecasters. All rights reserved. ispartof: International Journal of Forecasting vol:32 issue:3 pages:754-762 status: published

Ignoring the model selection step in inference after selection is harmful. This paper studies the asymptotic distribution of estimators after model selection using the Akaike information criterion. First, we consider the classical setting in which a true model exists and is included in the candidate set of models. We exploit the overselection property of this criterion in the construction of a selection region, and obtain the asymptotic distribution of estimators and linear combinations thereof conditional on the selected model. The limiting distribution depends on the set of competitive models and on the smallest overparameterized model. Second, we relax the assumption about the existence of a true model, and obtain uniform asymptotic results. We use simulation to study the resulting postselection distributions and to calculate confidence regions for the model parameters. We apply the method to data.

Multivariate mixtures of Erlang distributions form a versatile, yet analytically tractable, class of distributions making them suitable for multivariate density estimation. We present a flexible and effective fitting procedure for multivariate mixtures of Erlangs, which iteratively uses the EM algorithm, by introducing a computationally efficient initialization and adjustment strategy for the shape parameter vectors. We furthermore extend the EM algorithm for multivariate mixtures of Erlangs to be able to deal with randomly censored and fixed truncated data. The effectiveness of the proposed algorithm is demonstrated on simulated as well as real data sets. ispartof: Lifetime Data Analysis vol:22 issue:3 pages:429-455 ispartof: location:United States status: published

The focused information criterion for model selection is constructed to select the model that best estimates a particular quantity of interest, the focus, in terms of mean squared error. We extend this focused selection process to the high-dimensional regression setting with potentially a larger number of parameters than the size of the sample. We distinguish two cases: (i) the case where the considered submodel is of low-dimension and (ii) the case where it is of high-dimension. In the former case, we obtain an alternative expression of the low-dimensional focused information criterion that can directly be applied. In the latter case we use a desparsified estimator that allows us to derive the mean squared error of the focus estimator. We illustrate the performance of the high-dimensional focused information criterion with a numerical study and a real dataset.

This article defines and studies a depth for multivariate functional data. By the multivariate nature and by including a weight function, it acknowledges important characteristics of functional data, namely differences in the amount of local amplitude, shape, and phase variation. We study both population and finite sample versions. The multivariate sample of curves may include warping functions, derivatives, and integrals of the original curves for a better overall representation of the functional data via the depth. We present a simulation study and data examples that confirm the good performance of this depth function. Supplementary materials for this article are available online.

The prediction of the time of default in a credit risk setting via survival analysis needs to take a high censoring rate into account. This rate is due to the fact that default does not occur for the majority of debtors. Mixture cure models allow the part of the loan population that is unsusceptible to default to be modelled, distinct from time of default for the susceptible population. In this paper, we extend the mixture cure model to include time-varying covariates. We illustrate the method via simulations and by incorporating macro-economic factors as predictors for an actual bank data set. ispartof: Journal of Business and Economic Statistics vol:37 issue:1 pages:40-53 status: published

A data set from a Belgian telematics product aimed at young drivers is used to identify how car insurance premiums can be designed based on the telematics data collected by a black box installed in the vehicle. In traditional pricing models for car insurance, the premium depends on self-reported rating variables (e.g. age, postal code) which capture characteristics of the policy(holder) and the insured vehicle and are often only indirectly related to the accident risk. Using telematics technology enables tailor-made car insurance pricing based on the driving behavior of the policyholder. We develop a statistical modeling approach using generalized additive models and compositional predictors to quantify and interpret the effect of telematics variables on the expected claim frequency. We find that such variables increase the predictive power and render the use of gender as a discriminating rating variable redundant.

We study partially linear single-index models where both model parts may contain high-dimensional variables. While the single-index part is of fixed dimension, the dimension of the linear part is allowed to grow with the sample size. Due to the addition of penalty terms to the loss function in order to provide sparse estimators, such as obtained by lasso or SCAD, the construction of confidence intervals for the model parameters is not as straightforward as in the classical low-dimensional data framework. By adding a correction term to the penalized estimator a desparsified estimator is obtained for which asymptotic normality is proven. We study the construction of confidence intervals and hypothesis tests for such models. The simulation results show that the method performs well for high-dimensional single-index models. publisher: Elsevier articletitle: Confidence intervals for high-dimensional partially linear single-index models journaltitle: Journal of Multivariate Analysis articlelink: http://dx.doi.org/10.1016/j.jmva.2016.03.007 content_type: article copyright: © 2016 Elsevier Inc. All rights reserved. ispartof: Journal of Multivariate Analysis vol:149 pages:13-29 status: published

Functional data that are not perfectly aligned in the sense of not showing peaks and valleys at the precise same locations possess phase variation. This is commonly addressed by preprocessing the data via a warping procedure. As opposed to treating phase variation as a nuisance effect, it is advantageous to recognize it as a possible important source of information for clustering. It is illustrated how results from a multiresolution warping procedure can be used for clustering. This approach allows us to address detailed questions to find local clusters that differ in phase, or clusters that differ in amplitude, or both simultaneously.

The quest for a good estimator of a certain focus or target is present regardless of the dimensionality of the data. Obtaining such a good estimator with low mean squared error (MSE), or a prediction with low prediction error often proceeds via a variable selection or model selection search. Estimators can also be averaged to enlarge the space of possible estimators in an attempt to further lower the MSE. While these methods are being studied mostly for unpenalized estimation methods in situations with the number of variables much smaller than the sample size, this article concentrates on the additional difficulties and challenges when applying focused model selection for squared error loss with penalized estimation, for example, in a context of high-dimensional data.

We obtain the asymptotic distribution of score and restricted likelihood ratio statistics for testing whether variance components are equal to zero in linear mixed models with a fixed and finite number of random effects. The main new innovation of this paper is in deriving the components of the distribution, which are not chi-squared. The proposed test statistics are used for lack-of-fit testing using wavelets, where the finest scale wavelet coefficients are allowed to have a different variance than the other wavelet coefficients in the mixed effect wavelet model. We study the power of a wavelet-based test for a hypothesised parametric model within a mixed model framework in a simulation study.

Variable selection is fundamental in high-dimensional statistical modelling, including non-and semiparametric regression. However, little work has been done for variable selection in a partially linear model (PLM). We propose and study a unified approach via double penalized least squares, retaining good features of both variable selection and model estimation in the framework of PLM. The proposed method is distinguished from others in that the penalty functions combine the l1 penalty coming from wavelet thresholding in the non-parametric component with the l1 penalty from the lasso in the parametric component. Simulations are used to investigate the performances of the proposed estimator in various settings, illustrating its effectiveness for simultaneous variable selection as well as estimation.

We derive explicit formulae for estimation in logistic regression models where some of the covariates are missing. Our approach allows for modeling the distribution of the missing covariates either as a multivariate normal or multivariate t-distribution. A main advantage of this method is that it is fast and does not require the use of iterative procedures. A model selection method is derived which allows to choose amongst these distributions. In addition we consider versions of AIC that are based on the EM algorithm and on multiple imputation methods that have a wide applicability to model selection in likelihood models in general. ispartof: Statistical Modelling vol:11 issue:2 pages:69-93 status: published

Standard variable selection procedures, primarily developed for the construction of outcome prediction models, are routinely applied when assessing exposure effects in observational studies. We argue that this tradition is sub-optimal and prone to yield bias in exposure effect estimators as well as their corresponding uncertainty estimators. We weigh the pros and cons of confounder-selection procedures and propose a procedure directly targeting the quality of the exposure effect estimator. We further demonstrate that certain strategies for inferring causal effects have the desirable features (a) of producing (approximately) valid confidence intervals, even when the confounder-selection process is ignored, and (b) of being robust against certain forms of misspecification of the association of confounders with both exposure and outcome.

Nonparametric tests for the null hypothesis that a function has a prescribed form are developed and applied to data sets with missing observations. Omnibus nonparametric tests such as the order selection tests, do not need to specify a particular alternative parametric form, and have power against a large range of alternatives. More specifically, likelihood-based order selection tests are defined that can be used for multiply imputed data when the data are missing-at-random. A simulation study and data analysis illustrate the performance of the tests. In addition, an Akaike information criterion for model selection is presented that can be used with multiply imputed datasets.

Summary Warping is an approach to the reduction and analysis of phase variability in functional observations, by applying a smooth bijection to the function argument. We propose a natural representation of warping functions in terms of a new type of elementary functions named ‘warping component functions’, or ‘warplets’, which are combined into the warping function by composition. The inverse warping function is trivial and explicit to obtain. A sequential Bayesian estimation strategy is introduced which fits a series of models and transfers the posterior of the previous fit into the prior of the next fit. Model selection is based on a warping analogue to wavelet thresholding, combined with Bayesian inference.