| Title |
Tolydaus laiko diskrečiųjų martingalų statistinių modelių asimptotinis įvertinimas / |
| Translation of Title |
Asymptotic estimation for statistical models of continuous-time discrete martingales. |
| Authors |
Kanišauskas, Vaidotas ; Kanišauskienė, Karolina |
| DOI |
10.15388/LMD.2024.37772 |
| Full Text |
|
| Is Part of |
Lietuvos matematikos rinkinys. Lietuvos matematikų draugijos darbai. Ser. B.. Vilnius : Vilniaus universiteto leidykla. 2024, t. 65, p. 22-33.. ISSN 0132-2818. eISSN 2335-898X |
| Keywords [eng] |
continuous-time discrete local martingale ; local asymptotic normality ; compensator ; differentiation in normed spaces |
| Abstract [eng] |
The paper deals with statistical experiments of the continuous-time discrete local martingales, including models of all types of point processes. The process of local density of the discrete local martingales is expressed by a stochastic exponent of the stochastic integral according to the compensated point measure. General conditions convenient for testing are determined to assure continuous validity of the maximum probability and Bayesian estimators, as well as the continuous asymptotic normality and the asymptotic minimaxity in each compact of the parametric set. The research applies the optimum Fréchet differentiation of random and parametric functions based on the probability in normed spaces in terms of a continuous compensator. It is demonstrated how the basic conditions become much simpler in the case of the renewal process with the continuous compensator. |
| Published |
Vilnius : Vilniaus universiteto leidykla |
| Type |
Journal article |
| Language |
Lithuanian |
| Publication date |
2024 |
| CC license |
|
