Bent Nielsen's research while affiliated with University of Oxford and other places

... According to [24], "An outlying observation (outlier) appears to deviate from other members of the sample in which it occurs and should be identified and removed" [24,25]. To find outliers in this study, the box plot method described by Tukey (1977) was applied [26][27][28]. The interquartile distance (Q3 − Q1), which is equivalent to 1.5 times the box's height, is typically used to calculate whiskers. ...

... However, this approach requires selecting an appropriate cut-off value, effectively becoming another model selection problem. More principled methods include forward search (Riani et al., 2009;Atkinson et al., 2010) and a normality test (Berenguer-Rico et al., 2023). We will delve further into both in Section 2. ...

... The inability to generate a model that assigns variation in linear effects of age, period, and cohort is termed "the identification problem" [24]. Throughout the past six decades, efforts to generate models of age, period, and cohort effects have focused on various aspects of the underlying data generating process, including non-linear variation [25,26], variance and covariance matrix constraints [27,28], mechanisms [29], multi-level nesting [30,31], and other approaches [32,33]. Each provides one way to further visualize data, but inevitably requires assumptions that will privilege some aspect of the model and result in influence on study results (e.g., true period effects will be modeled as cohort effects, or vice versa, etc.). ...

... As implied by the name, a common feature of such models is that the mean of cumulative paid claims until the next development period is assumed to be a multiplication of the development factor (DF) and the most recent cumulative claim. Over the past several decades, various parametric models have been developed as stochastic extensions of the classic CL method (e.g., Wright, 1990;Mack & Venter, 2000;England & Verrall, 2002;Wüthrich & Merz, 2008;Kuang et al., 2015;Kuang & Nielsen, 2020;Gao et al., 2021). Many of these extensions are based on a generalized linear model (GLM) framework with a Poisson family distribution. ...

... For instance, the hypothesis that all α parameters are known corresponds the hypothesis of known values of relative ultimates. This may be of interest in an Bornhuetter-Ferguson context, see Elpidorou et al. (2019). This is analysed by restricted least squares which also leads to t and F statistics. ...

... The vector auto-regressive (VAR) model, proposed by Nobel Prize winner Sims in 1980, is widely used to analyze the interactive relationships between multiple variables [52], [53]. It constructs a model by taking each endogenous variable as a function of the lag value of all endogenous variables in the system, thereby extending the univariate auto-regressive model to the vector auto-regressive model composed of multiple time series [54]. The general mathematical expression is as follows: ...

... In addition there is a lot of literature on Chebychev's estimation, dealing with the computational aspects of these estimators using linear programming and numerical analysis (Appa and Smith, 1973;Sielken Jr and Hartley, 1973;Hand and Sposito, 1980;Armstrong and Kung, 1980;Sklar and Armstrong, 1982). Recent statistical studies of the Chebyshev estimator include (Castillo et al., 2009;Knight, 2020;Berenguer-Rico et al., 2019;Du et al., 2019). Of note Du et al. (2019), present a high-dimensional problem in composite fuselage assembly where a regularized Chebyshev estimator is a natural choice (i.e. the ∞ loss seems more natural in this problem compared to other standard loss functions such as the 2 and 1 losses). ...

... Berenguer-Rico, Johansen, and Nielsen [1] (BJN) considers the problem under a slightly different set of Assumptions. JN Assumption 4.1 has three parts. ...

... there is also literature on specification testing in this setting (e.g. Wang and Phillips, 2012;Dong, Gao, Tjøstheim, and Yin, 2017;Wang, Wu, and Zhu, 2018;Berenguer-Rico and Nielsen, 2020). Notable variants have used f to model transitions between regimes with distinct linear cointegrating relations (Saikkonen and Choi, 2004;Gonzalo and Pitarakis, 2006), or allowed it to take the 'functional coefficient' form β(w t )x t (Cai, Li, and Park, 2009;Xiao, 2009;Sun, Cai, and Li, 2013). ...

... Johansen's likelihood ratio test allows to test the null of rank R (i.e., of m = N − R common trends), where R is user-chosen, versus the alternative of rank greater than R (i.e., less than N − R common trends). However, whilst the limiting distribution under the null is well-known, if the true rank is lower than R, then the limiting distribution is different (see Bernstein and Nielsen, 2019). ...