• Corpus ID: 3560513

Parametric inference for stochastic differential equations: a smooth and match approach

@article{Gugushvili2011ParametricIF,
  title={Parametric inference for stochastic differential equations: a smooth and match approach},
  author={Shota Gugushvili and Peter Spreij},
  journal={arXiv: Statistics Theory},
  year={2011}
}
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first step, which is referred to as a smoothing step, we smooth the data and construct a nonparametric estimator of the invariant density of the process. In the second step, which is referred to as a matching step, we exploit a characterisation of the invariant… 
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References

SHOWING 1-10 OF 60 REFERENCES
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically…
Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process
We consider a one‐dimensional diffusion process X, with ergodic property, with drift b(x, θ) and diffusion coefficient a(x, θ) depending on an unknown parameter θ that may be multidimensional. We are…
A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions
CHAPTER 4 – Estimating Functions for Discretely Sampled Diffusion-Type Models
Nonparametric estimation of scalar diffusions based on low frequency data
We study the problem of estimating the coefficients of a diffusion (X t , t ≥ 0); the estimation is based on discrete data X n Δ, n = 0, 1,..., N. The sampling frequency Δ -1 is constant, and…
Penalized nonparametric mean square estimation of the coefficients of diffusion processes
We consider a one-dimensional diffusion process (Xt) which is observed at n + 1 discrete times with regular sampling interval ∆. Assuming that (Xt) is strictly stationary, we propose nonparametric…
Statistical Inference for Ergodic Diffusion Processes
Lévy Processes” (eight papers), “III. Empirical Processes” (four papers), and “IV. Stochastic Differential Equations” (four papers). Here are some comments about the individual papers: In I.2 (paper…
Malliavin calculus, geometric mixing, and expansion of diffusion functionals
Abstract. Under geometric mixing condition, we presented asymptotic expansion of the distribution of an additive functional of a Markov or an ε-Markov process with finite autoregression including…
Evaluation of the maximum-likelihood estimator where the likelihood equation has multiple roots.
TLDR
In effect, it is shown that the iteration processes usually applied in practice are justifiable, in large samples at least', in a subsequent paper, Kale (1962) makes a similar study for the multi-parameter case.
Parameter estimation and bias correction for diffusion processes
...
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