On one property of martingales with conditionally Gaussian increments and its application in the theory of nonasymptotic inference V. V. Konev
Material type:
ArticleSubject(s): мартингалы | гауссовские случайные величины | дискретное время | авторегрессионные модели первого порядкаGenre/Form: статьи в журналах Online resources: Click here to access online
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Doklady mathematics Vol. 94, № 3. P. 676-680Abstract: A transformation of a discrete-time martingale with conditionally Gaussian increments into a sequence of i.i.d. standard Gaussian random variables is proposed as based on a sequence of stopping times constructed using the quadratic variation. It is shown that sequential estimators for the parameters in AR(1) and generalized first-order autoregressive models have a nonasymptotic normal distribution.
Библиогр.: с. 680
A transformation of a discrete-time martingale with conditionally Gaussian increments into a sequence of i.i.d. standard Gaussian random variables is proposed as based on a sequence of stopping times constructed using the quadratic variation. It is shown that sequential estimators for the parameters in AR(1) and generalized first-order autoregressive models have a nonasymptotic normal distribution.
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