استقلال آماره هم‌وردای بسنده و آماره ناوردا تحت گروه‌های توپولوژیکی

نویسنده
دانشگاه کاشان
چکیده
در علم آمار وجود استقلال بین آمارهها از اهمیت ویژهای برخوردار است. بدون محاسبه توزیع توﺃم دو آماره، با داشتن شرایط لازم از جمله بسنده کامل بودن یک آمار و کمکی بودن آماره دیگر، وجود این استقلال ثابت می‌شود. در این مقاله تعمیم‌های این موضوع و همچنین حالت‌های به‌طور شمارا کامل بودن و ‌بیزی مورد بررسی قرار خواهند گرفت. در پایان، تحت عمل گروه‌های توپولوژیکی این حقیقت تعمیم داده شده و استقلال یک تابع ناوردا و هم‌وردای بسنده ثابت می‌شود.
کلیدواژه‌ها

عنوان مقاله English

Independence of sufficient equivariant statistics and invariant statistics under topological groups

نویسنده English

Mehdi Shams
University of Kashan
چکیده English

In statistics, the existence of independence between statistics is of particular importance.

Without calculating the joint distribution of two statistics, the existence of this independence is proven by meeting the necessary conditions,

including the sufficient completeness of one statistic and the ancillarity of the other.

In this paper, generalizations of this issue, as well as the cases of countably completeness and Bayesian framework , will be examined.

Finally, under the action of topological groups,

this fact is generalized and the independence of a sufficiently equivariant and invariant function is proven.

کلیدواژه‌ها English

Group action
countably completeness
pairwise sufficiency
Bayesian perspective
invariance
equivariance
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