Likelihood approximation by numerical integration on sparse grids

By Florian Heiss, Viktor Winschel. 2008

397 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d7061c84a759e1cef4739c0109ad63deefa331e4

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Citations in the corpus

A simple nonparametric approach to estimating the distribution of random coefficients in structural models (2016, neutral): “There are many ways to perform K -dimensional numerical integration, such as sparse grid quadrature (Heiss and Winschel, 2008).”
Non-intrusive reduced order modelling of the Navier-Stokes equations (2015, methodology): “This sparse grid method has been widely applied in various applications [26–28], including numerical integration [29], partial differential equations [30], economics [31,32], stochastic natural convection problems [33], sensitivity analysis [34], portfolio problems [35] and high dimensional interpol”
The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models (2011, methodology): “Some other recent sparse grid-based techniques for simulating the multivariate normal probabilities have also been proposed by Heiss and Winschel (2008), Huguenin et al. (2009), and Heiss (2010).”
ONLINE APPENDIX: Vertical Integration and Exclusivity in Platform and Two-Sided Markets (2013, positive): “…heterogeneity: consumers are divided among R groups indexed by i, each with price-sensitivity and gaming-preference coefficients (αpi , α γ i ) and initial population shares λi,t=0,ι=0 obtained via independent univariate Gauss-Hermite quadrature (c.f. Judd (1998); Heiss and Winschel (2007)).”
Best practices for differentiated products demand estimation with PyBLP (2020, methodology): “Numerical Integration Given extensive past work by Heiss and Winschel (2008), Judd and Skrainka (2011), Skrainka (2012b), and Freyberger (2015), it is not surprising that the choice of integration method has a striking effect.”
Regulation of Insurance with Adverse Selection and Switching Costs: Evidence from Medicare Part D (2015, methodology): “Since we don’t observe the individual-specific parameters of the utility function, I use a sparse grids method (Heiss and Winschel, 2008) to integrate out individual heterogeneity based on the observed distribution of demographics D and the estimates of the distributions of random coefficients.”
The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models (2014, methodology): “If the matrix is not positive-definite during a direction search at a given iteration, one can construct a “nearest” valid correlation matrix (for example, by replacing the negative eigenvalue components in the matrix with a small positive value, or by adding a sufficiently high positive value to th”