Abstract
We develop a nonnegative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The sample PLR converges to the unknown population PLR under mild conditions. The methodology allows for additional shape restrictions, as we illustrate with two empirical applications. The first develops a PLR for the unknown transition density of a jump-diffusion process, while the second extracts a positive density directly from option prices. In both cases, we show the importance of implementing the non-negativity restriction.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 482-493 |
| Number of pages | 12 |
| Journal | Journal of Business and Economic Statistics |
| Volume | 43 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2025 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Statistics, Probability and Uncertainty
Keywords
- Likelihood ratio
- Positive polynomial
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