Law of Large Numbers
A foundational theorem in probability theory, first rigorously proved by Jacob Bernoulli in the late 17th century. It states that as the number of independent repeated trials approaches infinity, the sample mean converges with probability 1 to the population expected value.
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The paper proves that the logarithmic factor appearing in previous risk bounds is not essential and can be completely eliminated, thereby improving the convergence rate to O(1/√N), consistent with the classical law of large numbers.
The O(1/√N) convergence rate cannot be further improved in the sense of rates, representing that risk estimation has reached the information-theoretically optimal rate.
Applying the law of large numbers requires iid and finite mean, while applying the central limit theorem additionally requires finite variance
According to the law of large numbers, the larger the sample size, the closer the frequency of an event's occurrence approaches its theoretical probability.
传统保险的精算模型建立在大数定律基础之上，通过观察大量同类事件的历史发生频率和损失分布推导未来风险概率，因此在前沿科技这种薄数据或零数据环境下失效
All Facts (5)
The paper proves that the logarithmic factor appearing in previous risk bounds is not essential and can be completely eliminated, thereby improving the convergence rate to O(1/√N), consistent with the classical law of large numbers.
50%UnverifiedThe O(1/√N) convergence rate cannot be further improved in the sense of rates, representing that risk estimation has reached the information-theoretically optimal rate.
50%UnverifiedApplying the law of large numbers requires iid and finite mean, while applying the central limit theorem additionally requires finite variance
50%UnverifiedAccording to the law of large numbers, the larger the sample size, the closer the frequency of an event's occurrence approaches its theoretical probability.
50%Unverified传统保险的精算模型建立在大数定律基础之上，通过观察大量同类事件的历史发生频率和损失分布推导未来风险概率，因此在前沿科技这种薄数据或零数据环境下失效
50%