Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, e.g. from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns proper handling of censorings. So far, all existing factorial analyses for survival data were developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods in factorial survival analyses under quite general dependent censoring regimes. This will be accomplished by combining existing results for factorial survival analyses with techniques developed for survival copula models. As a result, we will present an appealing F-test that exhibits sound performance in our simulation study. The new methods are illustrated in a real data analysis. We implement the proposed method in an R function surv.factorial(.) in the R package compound.Cox.
本報告では，セミ競合リスクのもとでの2変量生存時間コピュラモデルの推定方式を議論する．EMアルゴリズムを用いた推定アルゴリズムを構成し，生存関数の推定やハザード比の推定に応用する．いくつかのシミュレーション実験を行い，推定アルゴリズムの性能を調べる．またこの推定アルゴリズムに基づく漸近的な議論も行う．
臨床試験や動物実験で得られる生存時間データから治療効果を推定・検定するために要因実験計画法を採用することがある．生存時間は，打ち切りデータであることや非正規なデータであるため，通常の正規分布に基づく分散分析が適用できない．近年，独立打ち切りの仮定の下，ペアワイズ効果に基づく要因実験解析法が開発された（Dobler and Pauly 2020)．しかしながら，独立打ち切りの仮定が満足されない場合，この手法はバイアスのある結果を与える．本講演では，コピュラモデルを用いて，このペアワイズ効果に基づく要因実験法を修正し，従属打ち切りの下でも適用可能にすること考える．我々の提案手法は，コピュラを正しく特定できれば，バイアスの無い治療効果の推定・検定が可能になる．
We study the large sample properties of sparse M-estimators in the presence of pseudo-observations. Our framework covers a broad class of semi-parametric copula models, for which the marginal distributions are unknown and replaced by their empirical counterparts. It is well known that the latter modification significantly alters the limiting laws compared to usual M-estimation. We establish the consistency and the asymptotic normality of our sparse penalized M-estimator and we prove the asymptotic oracle property with pseudo-observations, possibly in the case when the number of parameters is diverging. Our framework allows to manage copula-based loss functions that are potentially unbounded. Additionally, we state the weak limit of multivariate rank statistics for an arbitrary dimension and the weak convergence of empirical copula processes indexed by maps. We apply our inference method to Canonical Maximum Likelihood losses with Gaussian copulas, mixtures of copulas or conditional copulas. The theoretical results are illustrated by two numerical experiments.
Capital allocation is a procedure for calculating the contribution of each source of risk to the aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation, under which the allocated capital captures the diversification benefit of the marginal risk as a component of the overall risk. This study concentrates on the Expected Shortfall (ES) as a regulatory standard, which has replaced Value-at-Risk (VaR), and focuses on the gradient allocations of ES, known as ES contributions. Within the framework of the comparative backtest, we compare a variety of models, including copula-GARCH models, for forecasting dynamic ES contributions. For robust forecasting evaluation against the choice of scoring function, we develop a Murphy diagram for ES contributions, a graphical tool to check whether one forecast dominates another under a class of scoring functions. Leveraging the recent concept of elicitability, we also propose a novel semiparametric model for forecasting dynamic ES contributions based on a compositional regression model and any forecasting model of VaR and ES of the total loss. In our empirical analysis, we demonstrate that a comparative backtest reveals distinct advantages of various advanced models when forecasting ES contributions.
Capturing the dynamic tail dependence of global stock markets is crucial for financial risk management. In recent research, dynamic skew t copula which is composed of generalized hyperbolic skew t distribution (It is called GHDySktC.) is used because it is very flexible to capture not only dynamic linear dependence but also tail dependence. On the other hand, the tail dependence of GHDySktC tends to be expressed conservatively which means CVaR of GHDySktC tends to be conservative. In this research, we propose another dynamic skew t copula which is composed of Azzalini and Capitanio (2003)’s skew t distribution (It is called ACDySktC.), and we compare the tail dependence of two skew t copulas with normal copula and t copula. In the empirical analysis, we estimate the dynamic tail dependence of global stock markets using these four copulas, and we compare them by AIC. We also consider the characteristics of the dynamic tail dependence. In addition to this in-sample analysis, We conduct CVaR backtesting (out-of-sample analysis) and compare them in terms of the accuracy of CVaR of equal weight portfolio and risk parity portfolio.