رهیافتی برای تعیین آماره های ناوردای بیشین

نویسنده
دانشگاه کاشان
چکیده
اصول ناوردایی، یکی از راه های خلاصه کردن اطلاعات نمونه است و توسط این اصول از قواعد تصمیم ناوردا یا هم وردا بهره گرفته می شود. در این مقاله ابتدا روش های یافتن تابع ناوردای بیشین معرفی می شود. به عنوان یک روش جدید به کمک توابع هم وردا، آماره ناوردای بیشین ساخته می شود. سپس به کمک چند تابع هم وردا، آماره ناوردای بیشین به دست می آید. در حالتی که گروه به طور یکتا انتقالی عمل کند، توابع هم وردا به براوردگر تبدیل خواهند شد که در شاخه های آماری می توان از آن استفاده کرد. در پایان نشان داده می شود در حالتی که عمل گروه به طور یکتا انتقالی نیست ولی یک زیر گروه نرمال با این خاصیت دارد نیز می توان آماره ناوردای بیشین را محاسبه کرد.
کلیدواژه‌ها

عنوان مقاله English

An Approach to Deriving Maximal Invariant Statistics

نویسنده English

Mehdi Shams
University of Kashan
چکیده English

Invariance principles is one of the ways to summarize sample information and by these principles invariance or equivariance decision rules are used. In this paper, first, the methods for finding the maximal invariant function are introduced. As a new method, maximal invariant statistics are constructed using equivariant functions. Then, using several equivariant functions, the maximal invariant statistic is obtained. If the group acts uniquely transitively, the equivariant functions will be converted into estimators that can be used in statistical branches. Finally, it is shown that in the case that the group action is not uniquely transitive but a normal subgroup has this property, the maximal invariant statistic can also be calculated.

کلیدواژه‌ها English

maximal invariant statistic‎
‎equivariant estimator‎
‎stability subgroup‎
‎normal subgroup‎
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