How does the delta method work?

When a random variable is approximately normal, applying a linear function to it results in another variable that is also approximately normal. This property makes the delta method an attractive choice for approximating the distribution of functions of normally distributed random variables.

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The univariate delta method is a statistical technique utilized to approximate the distribution of a function of a random variable. Its CORE concept lies in the belief that any function, within a sufficiently narrow range, can be closely approximated by a linear function derived from the first order Taylor series.

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Essentially, the delta method allows researchers to simplify complex functions by transforming them into linear expressions, making them easier to analyze and interpret. This method is particularly useful when dealing with random variables that exhibit non-linear behavior.