ウィッテイカー・ヘンダーソン平滑化法に関する諸論

広島大学(Hiroshima University)博士(経済学)Doctor of Economicsdoctora

Twenty years of P-splines

P-splines first appeared in the limelight twenty years ago. Since then they have become popular in applications and in theoretical work. The combination of a rich B-spline basis and a simple difference penalty lends itself well to a variety of generalizations, because it is based on regression. In effect, P-splines allow the building of a “backbone” for the “mixing and matching” of a variety of additive smooth structure components, while inviting all sorts of extensions: varying-coefficient effects, signal (functional) regressors, two-dimensional surfaces, non-normal responses, quantile (expectile) modelling, among others. Strong connections with mixed models and Bayesian analysis have been established. We give an overview of many of the central developments during the first two decades of P-splines.Peer Reviewe

Twenty years of P-splines

P-splines first appeared in the limelight twenty years ago. Since then they have become popular in applications and in theoretical work. The combination of a rich B-spline basis and a simple difference penalty lends itself well to a variety of generalizations, because it is based on regression. In effect, P-splines allow the building of a “backbone” for the “mixing and matching” of a variety of additive smooth structure components, while inviting all sorts of extensions: varying-coefficient effects, signal (functional) regressors, two-dimensional surfaces, non-normal responses, quantile (expectile) modelling, among others. Strong connections with mixed models and Bayesian analysis have been established. We give an overview of many of the central developments during the first two decades of P-splines

Quantifying Irrigated Winter Wheat LAI in Argentina Using Multiple Sentinel-1 Incidence Angles

Synthetic aperture radar (SAR) data provides an appealing opportunity for all-weather day or night Earth surface monitoring. The European constellation Sentinel-1 (S1) consisting of S1-A and S1-B satellites offers a suitable revisit time and spatial resolution for the observation of croplands from space. The C-band radar backscatter is sensitive to vegetation structure changes and phenology as well as soil moisture and roughness. It also varies depending on the local incidence angle (LIA) of the SAR acquisition’s geometry. The LIA backscatter dependency could therefore be exploited to improve the retrieval of the crop biophysical variables. The availability of S1 radar time-series data at distinct observation angles holds the feasibility to retrieve leaf area index (LAI) evolution considering spatiotemporal coverage of intensively cultivated areas. Accordingly, this research presents a workflow merging multi-date S1 smoothed data acquired at distinct LIA with a Gaussian processes regression (GPR) and a cross-validation (CV) strategy to estimate cropland LAI of irrigated winter wheat. The GPR-S1-LAI model was tested against in situ data of the 2020 winter wheat campaign in the irrigated valley of Colorador river, South of Buenos Aires Province, Argentina. We achieved adequate validation results for LAI with R2CV = 0.67 and RMSECV = 0.88 m2 m−2. The trained model was further applied to a series of S1 stacked images, generating temporal LAI maps that well reflect the crop growth cycle. The robustness of the retrieval workflow is supported by the associated uncertainties along with the obtained maps. We found that processing S1 smoothed imagery with distinct acquisition geometries permits accurate radar-based LAI modeling throughout large irrigated areas and in consequence can support agricultural management practices in cloud-prone agri-environments.EEA Hilario AscasubiFil: Caballero, Gabriel. Technological University of Uruguay (UTEC). Agri-Environmental Engineering; UruguayFil: Caballero, Gabriel. University of Valencia. Image Processing Laboratory (IPL); EspañaFil: Pezzola, Alejandro. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Hilario Ascasubi; ArgentinaFil: Winschel, Cristina Ines. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Hilario Ascasubi; ArgentinaFil: Casella, Alejandra. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Clima y Agua; ArgentinaFil: Sanchez Angonova, Paolo Andres. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Hilario Ascasubi; ArgentinaFil: Orden, Luciano. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Hilario Ascasubi; ArgentinaFil: Orden, Luciano. Universidad Miguel Hernández. Centro de Investigación e Innovación Agroalimentaria y Agroambiental. GIAAMA Reseach Group; EspañaFil: Berger, Katja. University of Valencia. Image Processing Laboratory (IPL); EspañaFil: Berger, Katja. Mantle Labs GmbH; AustriaFil: Verrelst, Jochem. University of Valencia. Image Processing Laboratory (IPL); EspañaFil: Delegido, Jesús. Universidad de Valencia. Image Processing Laboratory (IPL); Españ

Concentration inequalities for leave-one-out cross validation

In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds in a general framework. In particular, we provide concentration bounds beyond Lipschitz continuity assumptions on the loss or on the estimator. In order to obtain our results, we rely on random variables with distribution satisfying the logarithmic Sobolev inequality, providing us a relatively rich class of distributions. We illustrate our method by considering several interesting examples, including linear regression, kernel density estimation, and stabilized / truncated estimators such as stabilized kernel regression

Reconciling output gaps: Unobserved components model and Hodrick–Prescott filter

© 2017 Elsevier B.V. This paper reconciles two widely used trend–cycle decompositions of GDP that give markedly different estimates: the correlated unobserved components model yields output gaps that are small in amplitude, whereas the Hodrick–Prescott (HP) filter generates large and persistent cycles. By embedding the HP filter in an unobserved components model, we show that this difference arises due to differences in the way the stochastic trend is modeled. Moreover, the HP filter implies that the cyclical components are serially independent—an assumption that is decidedly rejected by the data. By relaxing this restrictive assumption, the augmented HP filter provides comparable model fit relative to the standard correlated unobserved components model