Tatyana Krivobokova

Fast Adaptive Penalized Splines

This article proposes a numerically simple method for locally adaptive smoothing. The heterogeneous regression function is modeled as a penalized spline with a varying smoothing parameter modeled as another penalized spline. This is formulated as a hierarchical mixed model, with spline coefficients following zero mean normal distribution with a smooth variance structure. The major contribution of this article is to use the Laplace approximation of the marginal likelihood for estimation. This method is numerically simple and fast. The idea is extended to spatial and non-normal response smoothing.

A Note on Penalized Spline Smoothing With Correlated Errors

We investigate the behavior of data-driven smoothing parameters for penalized spline regression in the presence of correlated data. It has been shown for other smoothing methods that mean squared error minimizers, such as (generalized) cross-validation or the Akaike information criterion, are extremely sensitive to misspecifications of the correlation structure resulting in over- or (under-)fitting the data. In contrast to this, we show that a maximum likelihood–based choice of the smoothing parameter is more robust and that for a moderately misspecified correlation structure over- or (under-)fitting does not occur. This is demonstrated in simulations and data examples and is supported by theoretical investigations.

Simultaneous Confidence Bands for Penalized Spline Estimators

In this article we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (a) as a standard (fixed effect) nonparametric model, (b) using the mixed-model framework with the spline coefficients as random effects, and (c) a full Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared with Bayesian simultaneous confidence bands from a frequentist perspective. We show that the mixed-model formulation of penalized splines can help obtain, at least approximately, confidence bands with either Bayesian or frequentist properties. Simulations and data analysis support the proposed methods. The R package ConfBands accompanies the article.

Evaluating the learning effectiveness of using simulations in software project management education: results from a twice replicated experiment

Abstract The increasing demand for software project managers in industry requires strategies for the development of management-related knowledge and skills of the current and future software workforce. Although several educational approaches help to develop the necessary skills in a university setting, few empirical studies are currently available to characterise and compare their effects. This paper presents the results of a twice replicated experiment that evaluates the learning effectiveness of using a process simulation model for educating computer science students in software project management. While the experimental group applied a System Dynamics simulation model, the control group used the well-known COCOMO model as a predictive tool for project planning. The results of each empirical study indicate that students using the simulation model gain a better understanding about typical behaviour patterns of software development projects. The combination of the results from the initial experiment and the two replications with meta-analysis techniques corroborates this finding. Additional analysis shows that the observed effect can mainly be attributed to the use of the simulation model in combination with a web-based role-play scenario. This finding is strongly supported by information gathered from the debriefing questionnaires of subjects in the experimental group. They consistently rated the simulation-based role-play scenario as a very useful approach for learning about issues in software project management.

The Estimation of Threshold Models in Price Transmission Analysis

The threshold vector error correction model is a popular tool for the analysis of spatial price transmission and market integration. In the literature, the profi le likelihood estimator is the preferred choice for estimating this model. Yet, in certain settings this estimator performs poorly. In particular, if the true thresholds are such that one or more regimes contain only a small number of observations, if unknown model parameters are numerous or if parameters diff er little between regimes, the profi le likelihood estimator displays large bias and variance. Such settings are likely when studying price transmission. For simpler, but related threshold models Greb et al. (2011) have developed an alternative estimator, the regularized Bayesian estimator, which does not exhibit these weaknesses. We explore the properties of this estimator for threshold vector error correction models. Simulation results show that it outperforms the profi le likelihood estimator, especially in situations in which the pro file likelihood estimator fails. Two empirical applications - a reassessment of the the seminal paper by Goodwin and Piggott (2001), and an analysis of price transmission between German and Spanish markets for pork - demonstrate the relevance of the new approach for spatial price transmission analysis.

Partial Least-Squares Functional Mode Analysis: Application to the Membrane Proteins AQP1, Aqy1, and CLC-ec1

We introduce an approach based on the recently introduced functional mode analysis to identify collective modes of internal dynamics that maximally correlate to an external order parameter of functional interest. Input structural data can be either experimentally determined structure ensembles or simulated ensembles, such as molecular dynamics trajectories. Partial least-squares regression is shown to yield a robust solution to the multidimensional optimization problem, with a minimal and controllable risk of overfitting, as shown by extensive cross-validation. Several examples illustrate that the partial least-squares-based functional mode analysis successfully reveals the collective dynamics underlying the fluctuations in selected functional order parameters. Applications to T4 lysozyme, the Trp-cage, the aquaporin channels Aqy1 and hAQP1, and the CLC-ec1 chloride antiporter are presented in which the active site geometry, the hydrophobic solvent-accessible surface, channel gating dynamics, water permeability (p(f)), and a dihedral angle are defined as functional order parameters. The Aqy1 case reveals a gating mechanism that connects the inner channel gating residues with the protein surface, thereby providing an explanation of how the membrane may affect the channel. hAQP1 shows how the p(f) correlates with structural changes around the aromatic/arginine region of the pore. The CLC-ec1 application shows how local motions of the gating Glu(148) couple to a collective motion that affects ion affinity in the pore.

Filtering Time Series with Penalized Splines

The decomposition and filtering of time series is an important issue in economics and econometrics and related fields. Even though there are numerous competing methods on the market, in applications one often meets one of the few favorites, like the Hodrick-Prescott filter or the bandpass filter.In this paper, we suggest to employ penalized splines fitting for detrending. The approach allows to take correlation of the residuals into account and provides a data driven setting of the smoothing parameter, none of which the classical filters allow. We show the simplicity of the penalized spline filter using the open source software R and demonstrate differences and features with numerous data examples.

Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition

This article proposes a simple and fast approach to build simultaneous confidence bands and perform specification tests for smooth curves in additive models. The method allows for handling of spatially heterogeneous functions and its derivatives as well as heteroscedasticity in the data. It is applied to study the determinants of chronic undernutrition of Kenyan children, with a particular focus on the highly nonlinear age pattern in undernutrition. Model estimation using the mixed model representation of penalized splines in combination with simultaneous probability calculations based on the volume-of-tube formula enable the simultaneous inference directly, that is, without resampling methods. Finite sample properties of simultaneous confidence bands and specification tests are investigated in simulations. To facilitate and enhance its application, the method has been implemented in the R package AdaptFitOS.

Regularized Bayesian estimation of generalized threshold regression models.

Estimation of threshold parameters in (generalized) threshold regression models is typically performed by maximizing the corresponding pro file likelihood function. Also, certain Bayesian techniques based on non-informative priors are developed and widely used. This article draws attention to settings (not rare in practice) in which these standard estimators either perform poorly or even fail. In particular, if estimation of the regression coeffcients is associated with high uncertainty, the pro file likelihood for the threshold parameters and thus the corresponding estimator can be highly aff ected. We suggest an alternative estimation method employing the empirical Bayes paradigm, which allows to circumvent defi ciencies of standard estimators. The new estimator is completely data-driven and induces little additional numerical e ffort compared with the old one. Simulation results show that our estimator outperforms commonly used estimators and produces excellent results even if the latter show poor performance. The practical relevance of our approach is illustrated by a real-data example; we follow up the anlysis of cross-country growth behavior detailed in Hansen (2000).

Adaptive Empirical Bayesian Smoothing Splines

In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the model. The selected order and smoothing parameter are used to construct adaptive credible sets with good frequentist coverage for the underlying regression function. We use these credible sets as a proxy to show the superior performance of adaptive empirical Bayesian smoothing splines compared to frequentist smoothing splines.