Inference based on adaptive grid selection of probability transforms

Abstract

Probability transform-based inference, for example, characteristic function-based inference, is a good alternative to likelihood methods when the probability density function is unavailable or intractable. However, a set of grids needs to be determined to provide an effective estimator based on probability transforms. This paper is concerned with parametric inference based on adaptive selection of grids. By employing a closeness measure to evaluate the asymptotic variance of the transform-based estimator, we propose a statistical inference procedure, accompanied with adaptive grid selection. The selection algorithm aims for a small set of grids, and yet the resulting estimator can be highly efficient. Generally, the asymptotic variance is very close to that of the maximum likelihood estimator.

Keywords:

• adaptive grid selection
• asymptotic efficiency
• characteristic function
• empirical likelihood
• method of moments
• generalized method of moments
• generating moment function

Acknowledgments

We would like to thank the associate editor and two anonymous reviewers for their detailed reading of the paper and for helpful comments and suggestions which resulted in an improved version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the China Scholarship Council Foundation, the Shanghai Municipal Natural Science Foundation [grant number 13ZR1419100] and the Science Foundation of Shanghai Educational Committee [grant number 14YZ115].