Naslov
Local asymptotic mixed normality of approximate maximum likelihood estimator of drift parameters in diffusion model

Autori
Lubura Strunjak, Snježana ; Huzak, Miljenko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
16th German Probability and Statistics Days - GPSD 2023

Mjesto i datum
Essen, Njemačka, 07.03.2023. - 10.03.2023

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
asymptotic mixed normality, ergodic diffusion, discrete observation, parameter estimation

Sažetak
Let X be a diffusion which satisfies a stochastic differential equation of the form: dXt=μ(Xt, θ)dt+σ0ν(Xt)dWt, , where drift parameter θ is unknown and diffusion coefficient parameter σ0 is known. We have discrete observations (X_ti, 0≤i≤n) along fixed time interval [0, T]. Let θ¯n be approximate maximum likelihood estimator of drift parameter obtained from discrete observations and let θ^ be maximum likelihood estimator obtained from continuous observations (Xt, 0≤t≤T) along fixed time interval [0, T]. We proved that θ¯n, when Δn=max1≤i≤n(t_i−t_{;i−1};) tends to zero, is locally asymptotic mixed normal, with covariance matrix which depends on MLE θ^ and on path (Xt, 0≤t≤T).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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