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Consistency in Statistics: Consistency refers to the property that as you collect more and more data, the estimate θ̂ approaches the true parameter θ in probability. In other words, as your sample size increases, the estimate becomes more and more accurate, and it converges to the true value.

The consistency property can be formally expressed as follows:

If θ̂_n is an estimator of θ based on a sample of size n, then θ̂_n is said to be a consistent estimator of θ if, for any ε > 0:

          lim (n → ∞) P(|θ̂_n - θ| > ε) = 0 --------------------------------------------------- (3972a)

This means that the probability that the estimate θ̂_n differs from the true parameter θ by more than ε becomes negligible as the sample size (n) grows.

There are no specific equations for the consistency property, as it's a concept that deals with the behavior of estimators as the sample size increases rather than a specific mathematical formula.

If you have a different question or need clarification on a specific concept related to machine learning or statistics, please provide more context or details, and I'd be happy to assist further.

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