The Copula Information Criterion and Its Implications for the Maximum Pseudo-Likelihood Estimator

Abstract

Chapter 1. Introduction to the Thesis 1. From the ancients to 1640 2. The first limit theorem and the variable N ε 2.1. Improvements on the Bernoulli bound 2.2. Uniformity and the Vapnik-Chervonenkis inequalities 2.3. CLT-based approximations for the tail of N ε 2.4. Full circle: Calculating the quantiles of the limiting distribution 2.5. A new type of sequential confidence bands for the Nelson-Aalen estimator 3. Gorgias' revenge: Model selection and pragmatism 3.1. Two-stage model selection procedures 3.2. The way ahead: Non-asymptotic model-selection 3.3. A connection between the AIC and N ε 4. Non-standard alternative models: Regression with jumps Chapter 2. Paper 1: On the errors committed by sequences of estimator functionals Chapter 3. Paper 2: The Copula Information Criterion and its implications for the Maximum Pseudo Likelihood Estimator Chapter 4. Paper 3: The Copula Information Criteria Chapter 5. Paper 4: Estimation and Inference for Jump Regression Models 1 That is, the time between around 1750 to 1830, not the classical period of the ancients.

The Copula Information Criteria

“…Because c ° is invariant to monotone transformation of the marginals, empirical estimators of θ ° should share this invariance. This point is further discussed in Grønneberg (). The rank‐based MPLE defined in terms of the empirical copula shares this invariance and consistently estimates θ ° under various conditions (Genest et al ).…”

“…It is well‐known that the MPLE is not semiparametrically efficient in the sense of Bickel et al ). However, Grønneberg () argued that although the MPLE's lack of semiparametric efficiency in this sense is not a serious deficiency, its lack of a generally applicable AIC‐like criterion is. When the model‐selection problem is relevant, semiparametric efficiency—‐which is defined under the assumption of a correct model—does not seem as important as the invariance properties that the MPLE fulfils, as discussed near (.…”

“…This section summarizes a small‐scale simulation study that confirms the validity of the CIC formula. Some additional numerical illustrations are given in Grønneberg (). We will study simulated samples with standard normal marginals and a mixture copula with CDF λC F ( u , θ ) + (1 − λ ) C P ( u , θ ) with λ = 80 % .…”

Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence

“…We used a scoring via the AIC between the three component mixture CFG model versus the two component mixture CG model versus the two parameter OpC model. One could also use the Copula-InformationCriterion (CIC), see [13] for details.…”

Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence

“…We used a scoring via the AIC between the three component mixture CFG model versus the two component mixture CG model versus the two parameter OpC model. One could also use the Copula-Information-Criterion (CIC), see [13] for details. The results are presented for this comparison in Figure 2, which shows the differentials between AIC for CFG versus CG and CFG versus OpC for each of the high interest rate and the low interest rate currency baskets.…”