arXiv 21 Aug 2026 · Econometrics
arXiv:2608.21619 · PDF · Extracted main text
Rejection sampling requires a proposal that dominates the target by a known constant, generally unavailable for non-Gaussian state space models. We construct such a proposal for the latent state path, yielding independent exact smoothing draws and an unbiased likelihood estimator whose relative variance is at most $1/p-1$ per draw at acceptance probability $p$. The method covers scalar states with affine Gaussian dynamics and log-concave observation densities, including multivariate observations. Transition twisting makes the log target-to-proposal ratio separable, and tangent-line twists make each term nonpositive, producing an attained, sharp dominating constant. With a companding node placement, the accumulated envelope error is $O(T/G^2)$ for a sample of length $T$ with $G$ nodes per date, so $G\propto\sqrt{T}$ keeps acceptance bounded away from zero; for stochastic volatility, the required conditions hold almost surely. A simpler mode-centered grid shows the same scaling empirically. At $T=2{,}000$, acceptance is $75%$, versus roughly $10^{-16}$ for the Gaussian envelope.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Gilks and Wild (1992) Adaptive Rejection Sampling for Gibbs Sampling | 0.928 | 4 | 4 | 100% |
| 2 | Richard and Zhang (2007) Efficient High-Dimensional Importance Sampling | 0.928 | 4 | 3 | 100% |
| 3 | Bauwens and Veredas (2004) The Stochastic Conditional Duration Model: A Latent Variable Model for the Analysis of Financial Durations | 0.843 | 3 | 3 | 100% |
| 4 | McCausland (2012) The HESSIAN Method: Highly Efficient Simulation Smoothing, in a Nutshell | 0.737 | 3 | 2 | 100% |
| 5 | Chan and Jeliazkov (2009) Efficient Simulation and Integrated Likelihood Estimation in State Space Models self | 0.644 | 2 | 2 | 100% |
| 6 | Devroye (1986) Non-Uniform Random Variate Generation | 0.644 | 2 | 2 | 100% |
| 7 | Durbin and Koopman (1997) Monte Carlo Maximum Likelihood Estimation for Non-Gaussian State Space Models | 0.644 | 2 | 2 | 100% |
| 8 | Farmer (2021) The Discretization Filter: A Simple Way to Estimate Nonlinear State Space Models | 0.644 | 2 | 2 | 100% |
| 9 | Kim, Shephard, and Chib (1998) Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models | 0.644 | 2 | 2 | 100% |
| 10 | Koopman, Shephard, and Creal (2009) Testing the Assumptions Behind Importance Sampling | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 44 scored citations.