Statistik und Datenwissenschaften

A collection of functional quantiles offers a comprehensive portrayal of an individual's distinct physical activity patterns, characterizing the distributions of activity at specific time points over a defined duration. However, the potential to present such a collection as a unified, complete activity surface for each individual remains unexplored in current literature. In this paper, we rectify this shortcoming by proposing functional quantile surface estimation (FQSE), a methodology designed to calculate fully parameterized activity surfaces at the participant level. We embed practical and theoretical requirements by imposing constraints that guarantee non-negativity and non-crossing properties in the direction of the quantile order, respectively. We achieve this by employing a dimensionality reduction algorithm that enforces non-negativity throughout and incorporates a parametric spline-based score structure that is monotonic across different quantile levels. We assess the proposed methodology in terms of the precision and stability of the estimated quantile surfaces. Our findings indicate that our estimations are not only more rational but also more accurate compared to alternative approaches.

Ordinal data are quite common in applied statistics. Although some model selection and regularization techniques for categorical predictors and ordinal response models have been developed over the past few years, less work has been done concerning ordinal-on-ordinal regression. Motivated by survey datasets on food products consisting of Likert-type items, we propose a strategy for smoothing and selection of ordinally scaled predictors in the cumulative logit model. First, the original group lasso is modified by use of difference penalties on neighbouring dummy coefficients, thus taking into account the predictors' ordinal structure. Second, a fused lasso type penalty is presented for fusion of predictor categories and factor selection. The performance of both approaches is evaluated in simulation studies, while our primary case study is a survey on the willingness to pay for luxury food products.