Asymptotic efficiency of the two-stage estimation method for copula-based models

By Harry Joe. 2005

672 citations recorded by the source corpus.

For multivariate copula-based models for which maximum likelihood is computationally difficult, a two-stage estimation procedure has been proposed previously; the first stage involves maximum likelihood from univariate margins, and the second stage involves maximum likelihood of the dependence parameters with the univariate parameters held fixed from the first stage. Using the theory of inference functions, a partitioned matrix in a form amenable to analysis is obtained for the asymptotic covariance matrix of the two-stage estimator. The asymptotic relative efficiency of the two-stage estimation procedure compared with maximum likelihood estimation is studied. Analysis of the limiting cases of the independence copula and Frechet upper bound help to determine common patterns in the efficiency as the dependence in the model increases. For the Frechet upper bound, the two-stage estimation procedure can sometimes be equivalent to maximum likelihood estimation for the univariate parameters. Numerical results are shown for some models, including multivariate ordinal probit and bivariate extreme value distributions, to indicate the typical level of asymptotic efficiency for discrete and continuous data.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b1e2d3a9683b32d2c8f24f950d9d16edaddcde94

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Citations in the corpus

Copula Methods for Forecasting Multivariate Time Series (2013, background): “However, simulation studies in Joe (2005) and Patton (2006b) indicate that this loss is not great in many cases.”
Bivariate Flood Frequency Analysis with Historical Information Based on Copula (2013, result): “Similar comparisons have also been made by Joe (1997, 2005) and the derived conclusions are: (a) the ML estimation is much more time-consuming than IFM method; (b) the IFM method allows one to do inference and modeling starting with univariate and lower-dimensional margins; (c) there is some…”
Simulated Method of Moments Estimation for Copula-Based Multivariate Models (2013, neutral): “Dependence measures like Spearman’s rank correlation, quantile dependence, and Kendall’s tau are functions only of the copula (see, e.g., Joe 1997; Nelsen 2006).”
Selection of Vine Copulas (2013, methodology): “The latter method is called inference functions for margins (IFM) by [38, 37].”
Maximum likelihood estimation of mixed C-vines with application to exchange rates (2012, methodology): “The parametric transformation was suggested by Joe (2005), while a rank based transformation was used by Genest et al. (1995).”
Composite likelihood estimation in multivariate data analysis (2005, methodology): “In a similar way, the limits for the independence boundary are obtained for the method of inference function for margins (Joe 2005).”
Pair-Copula Constructions for Financial Applications: A Review (2016, methodology): “Hence, the parameters of a given PCC may be estimated using any multivariate copula estimator, such as the inference function for margins (IFM) method [1,32] or the maximum pseudo likelihood (MPL) estimator [33,34].”
Copula-Based Models of Systemic Risk in U.S. Agriculture: Implications for Crop Insurance and Reinsurance Contracts (2015, background): “Joe (2005) provides additional details on the distinction and efficiency differences between full maximum likelihood and the IFM estimator.”
Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask (2007, background): “Joe 2005 quantifies the asymptotic efficiency of the approach in different circumstances.”
Bayesian model selection for D‐vine pair‐copula constructions (2011, methodology): “The statistical properties of such two step estimation procedures are investigated by Joe (2005) for a known standardized residual distribution and by Chen and Fan (2006) for unknown standardized residual distribution, respectively.”
Construction of asymmetric multivariate copulas (2008, methodology): “The asymptotic behaviour of two-stage estimation procedures is studied in [13].”
Goodness-of-fit tests for copulas: A review and a power study (2006, background): “(1996) or Jouini and Clemen (1996). Let K denote the (univariate) distribution function of V .”
Birnbaum‐Saunders distribution: A review of models, analysis, and applications (2018, methodology): “[107] Joe, H. (2005), “Asymptotic efficiency of the two-stage estimation method for copula-based models”, Journal of Multivariate Analysis, vol. 94, 401 - 419.”