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Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard for standard decision trees. But most existing methods for fitting linear model trees are time consuming and therefore not scalable to large data sets. In addition, they are more prone to overfitting and extrapolation issues than standard regression trees. In this paper we introduce PILOT, a new algorithm for linear model trees that is fast, regularized, stable and interpretable. PILOT trains in a greedy fashion like classic regression trees, but incorporates an L2 boosting approach and a model selection rule for fitting linear models in the nodes. The abbreviation PILOT stands for PIecewise Linear Organic Tree, where 'organic' refers to the fact that no pruning is carried out. PILOT has the same low time and space complexity as CART without its pruning. An empirical study indicates that PILOT tends to outperform standard decision trees and other linear model trees on a variety of data sets. Moreover, we prove its consistency in an additive model setting under weak assumptions. When the data is generated by a linear model, the convergence rate is polynomial. [ABSTRACT FROM AUTHOR]

In this study, we investigated the relationship between age and performance in professional road cycling. We considered 1864 male riders present in the yearly top 500 ranking of ProCyclingStats (PCS) since 1993 until 2021 with more than 700 PCS Points. We applied a data-driven approach for finding natural clusters of the rider's speciality (General Classification, One Day, Sprinter or All-Rounder). For each cluster, we divided the riders into the top 50% and bottom 50% based on their total number of PCS points. The athlete's yearly performance was defined as the average number of points collected per race. Age-performance models were constructed using polynomial regression and we obtained that the top 50% of the riders in each cluster have a statistically significant (p < 0.05) higher peak performance age. Considering the best 50% of the riders, general classification riders peak at an older age than the other rider types (p < 0.05). For those top riders, we found ages of peak performance of 26.3, 26.5, 26.2 and 27.5 years for sprinters, all-rounders, one day specialists and general classification riders, respectively. Our findings can be used for scouting purposes, assisting coaches in designing long-term training programmes and benchmarking the athletes' performance development. [ABSTRACT FROM AUTHOR]

In this paper, a multivariate constrained robust M‐regression method is developed to estimate shaping coefficients for electricity forward prices. An important benefit of the new method is that model arbitrage can be ruled out at an elementary level, as all shaping coefficients are treated simultaneously. Moreover, the new method is robust to outliers, such that the provided results are stable and not sensitive to isolated sparks or dips in the market. An efficient algorithm is presented to estimate all shaping coefficients at a low computational cost. To illustrate its good performance, the method is applied to German electricity prices. [ABSTRACT FROM AUTHOR]

The seemingly unrelated regression (SUR) model is a generalization of a linear regression model consisting of more than one equation, where the error terms of these equations are contemporaneously correlated. The standard feasible generalized linear squares (FGLS) estimator is efficient as it takes into account the covariance structure of the errors, but it is also very sensitive to outliers. The robust SUR estimator of Bilodeau and Duchesne (Canadian Journal of Statistics, 28:277-288, 2000) can accommodate outliers, but it is hard to compute. First, we propose a fast algorithm, FastSUR, for its computation and show its good performance in a simulation study. We then provide diagnostics for outlier detection and illustrate them on a real dataset from economics. Next, we apply our FastSUR algorithm in the framework of stochastic loss reserving for general insurance. We focus on the general multivariate chain ladder (GMCL) model that employs SUR to estimate its parameters. Consequently, this multivariate stochastic reserving method takes into account the contemporaneous correlations among run-off triangles and allows structural connections between these triangles. We plug in our FastSUR algorithm into the GMCL model to obtain a robust version. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016 [ABSTRACT FROM AUTHOR]

The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) do not need to be equal to the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue, we propose a robust alternative that estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to automatically flag the claims with a significantly large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data. [ABSTRACT FROM AUTHOR]

Abstract: A new method to estimate case specific prediction uncertainty for univariate trilinear partial least squares (tri-PLS1) regression is introduced. This method is, from a theoretical point of view, the most exact finite sample approximation to true prediction uncertainty that has been reported up till now. Using the new method, different error sources can be propagated, which is an advantage that cannot be offered by data driven approaches such as the bootstrap. In a concise example, it is illustrated how the method can be applied. In the Appendix, efficient algorithms are presented to compute the estimates required. [Copyright &y& Elsevier]