# 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

- Mathematics
- 2010

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

- Mathematics
- 2000

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

- Mathematics
- 2005

Nonparametric estimation of scalar diffusions based on low frequency data

- Mathematics
- 2004

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

- Mathematics
- 2007

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

- Mathematics
- 2006

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

- Mathematics
- 2000

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.

- MathematicsBiometrika
- 1966

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.