qle-package: Simulation-Based Quasi-Likelihood Estimation

In qle: Simulation-Based Quasi-Likelihood Estimation

Description

We provide a method for parameter estimation of parametric statistical models which can be at least simulated and where standard methods, such as maximum likelihood, least squares or Bayesian algorithms (including MCMC) are not applicable. We follow the quasi-likelihood theory [3] to estimate the unknown model parameter by finding a root of the so-called quasi-score estimating function. For an overview of our method and further in-depth examples please see the vignette.

Details

The basic idea is to transform the general parameter estimation problem into a global (black box) optimization problem (see [1]) with an expensive to evaluate objective function. This function can only be evaluated with substantial random errors due to the Monte Carlo simulation approach of the statistical model and the interpolation error of the involved approximating functions. The algorithm sequentially selects new evaluation points (which are the model parameters) for simulating the statistical model and aims on efficiently exploring the parameter space towards a root of the quasi-score vector as an estimate of the unknown model parameter by some weighted distance space-filling selection criteria of randomly generated candidate points.

The main estimation process can be started by the function qle where other functions like, for example, qscoring or searchMinimizer search for a root or a local and global minimizer (without sampling new candidates) of some monitor function to control the estimation procedure.

References

1. Baaske, M., Ballani, F., v.d. Boogaart,K.G. (2014). A quasi-likelihood approach to parameter estimation for simulatable statistical models. Image Analysis & Stereology, 33(2):107-119.

2. Chiles, J. P., Delfiner, P. (1999). Geostatistics: modelling spatial uncertainty. J. Wiley & Sons, New York.

3. Heyde, C. C. (1997). Quasi-likelihood and its applications: a general approach to optimal parameter estimation. Springer

4. Kleijnen, J. P. C. & Beers, W. C. M. v. (2004). Application-driven sequential designs for simulation experiments: Kriging metamodelling. Journal of the Operational Research Society, 55(8), 876-883

5. Mardia, K. V. (1996). Kriging and splines with derivative information. Biometrika, 83, 207-221

6. McFadden, D. (1989). A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration. Econometrica, 57(5), 995-1026.

7. Regis R. G., Shoemaker C. A. (2007). A stochastic radial basis function method for the global optimization of expensive functions. INFORMS Journal on Computing, 19(4), 497-509.

8. Wackernagel, H. (2003). Multivariate geostatistics. Springer, Berlin.

9. Zimmermann, D. L. (1989). Computationally efficient restricted maximum likelihood estimation of generalized covariance functions. Math. Geol.. 21, 655-672

10. Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman & Hall, New York.

qle documentation built on May 2, 2019, 9:55 a.m.