Statistica Neerlandica

doi: 10.1111/stan.12269pmid: N/A

Chang, Chih‐Hao; Wong, Kam‐Fai; Lim, Wei‐Yee

doi: 10.1111/stan.12268pmid: N/A

This paper considers a continuous three‐phase polynomial regression model with two threshold points for dependent data with heteroscedasticity. We assume the model is polynomial of order zero in the middle regime, and is polynomial of higher orders elsewhere. We denote this model by ℳ2$$ {\mathcal{M}}_2 $$, which includes models with one or no threshold points, denoted by ℳ1$$ {\mathcal{M}}_1 $$ and ℳ0$$ {\mathcal{M}}_0 $$, respectively, as special cases. We provide an ordered iterative least squares (OiLS) method when estimating ℳ2$$ {\mathcal{M}}_2 $$ and establish the consistency of the OiLS estimators under mild conditions. When the underlying model is ℳ1$$ {\mathcal{M}}_1 $$ and is (d0−1)$$ \left({d}_0-1\right) $$th‐order differentiable but not d0$$ {d}_0 $$th‐order differentiable at the threshold point, we further show the Op(N−1/(d0+2))$$ {O}_p\left({N}^{-1/\left({d}_0+2\right)}\right) $$ convergence rate of the OiLS estimators, which can be faster than the Op(N−1/(2d0))$$ {O}_p\left({N}^{-1/\left(2{d}_0\right)}\right) $$ convergence rate given in Feder when d0≥3$$ {d}_0\ge 3 $$. We also apply a model‐selection procedure for selecting ℳκ$$ {\mathcal{M}}_{\kappa } $$; κ=0,1,2$$ \kappa =0,1,2 $$. When the underlying model exists, we establish the selection consistency under the aforementioned conditions. Finally, we conduct simulation experiments to demonstrate the finite‐sample performance of our asymptotic results.

Campisi, Giovanni; La Rocca, Luca; Muzzioli, Silvia

doi: 10.1111/stan.12273pmid: N/A

It is a matter of common observation that investors value substantial gains but are averse to heavy losses. Obvious as it may sound, this translates into an interesting preference for right‐skewed return distributions, whose right tails are heavier than their left tails. Skewness is thus not only a way to describe the shape of a distribution, but also a tool for risk measurement. We review the statistical literature on skewness and provide a comprehensive framework for its assessment. Then, we present a new measure of skewness, based on the decomposition of variance in its upward and downward components. We argue that this measure fills a gap in the literature and show in a simulation study that it strikes a good balance between robustness and sensitivity.

Zhou, Jing; Claeskens, Gerda

doi: 10.1111/stan.12274pmid: N/A

Hypothesis testing is challenging due to the test statistic's complicated asymptotic distribution when it is based on a regularized estimator in high dimensions. We propose a robust testing framework for ℓ1$$ {\ell}_1 $$‐regularized M‐estimators to cope with non‐Gaussian distributed regression errors, using the robust approximate message passing algorithm. The proposed framework enjoys an automatically built‐in bias correction and is applicable with general convex nondifferentiable loss functions which also allows inference when the focus is a conditional quantile instead of the mean of the response. The estimator compares numerically well with the debiased and desparsified approaches while using the least squares loss function. The use of the Huber loss function demonstrates that the proposed construction provides stable confidence intervals under different regression error distributions.

Fang, Longxiang; Balakrishnan, Narayanaswamy; Huang, Wenyu; Zhang, Shuai

doi: 10.1111/stan.12275pmid: N/A

In this paper, we discuss stochastic comparison of the largest order statistics arising from two sets of dependent distribution‐free random variables with respect to multivariate chain majorization, where the dependency structure can be defined by Archimedean copulas. When a distribution‐free model with possibly two parameter vectors has its matrix of parameters changing to another matrix of parameters in a certain mathematical sense, we obtain the first sample maxima is larger than the second sample maxima with respect to the usual stochastic order, based on certain conditions. Applications of our results for scale proportional reverse hazards model, exponentiated gamma distribution, Gompertz–Makeham distribution, and location‐scale model, are also given. Meanwhile, we provide two numerical examples to illustrate the results established here.

Ben Elouefi, Rim; Saâdaoui, Foued

doi: 10.1111/stan.12276pmid: N/A

The stratified logrank test can be used to compare survival distributions of several groups of patients, while adjusting for the effect of some discrete variable that may be predictive of the survival outcome. In practice, it can happen that this discrete variable is missing for some patients. An inverse‐probability‐weighted version of the stratified logrank statistic is introduced to tackle this issue. Its asymptotic distribution is derived under the null hypothesis of equality of the survival distributions. A simulation study is conducted to assess behavior of the proposed test statistic in finite samples. An analysis of a medical dataset illustrates the methodology.