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I am working on an academic paper proposing a new estimator for a population mean. It works quite well in simulations across various superpopulation models (linear, quadratic, and strictly nonlinear). However, it is very very involved, and I'm worried that a pursuit of the asymptotic variance/bias will not be fruitful. Yet every paper I have included in my literature review has a section purely devoted to asymptotic results. Granted the proposed estimators there are not as complicated.

My question is this: is it frowned upon for me to focus on numerical approximations of the variance and bias instead? I am just honestly concerned of not being able to derive the asymptotics due to their complications.

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  • $\begingroup$ Is the estimator so complicated you cannot apply the delta method to estimate variance? $\endgroup$
    – Aaron Hendrickson
    Commented Mar 20, 2023 at 19:52
  • $\begingroup$ @AaronHendrickson I may be mistaken, but to use the delta method, doesn't that require the CLT and the variance of the estimator? $\endgroup$
    – JerBear
    Commented Mar 20, 2023 at 19:55
  • $\begingroup$ Delta method needs the variance of the random variable used in the estimator and the derivative of the estimator to compute asymptotic variance. $\endgroup$
    – Aaron Hendrickson
    Commented Mar 20, 2023 at 19:59
  • $\begingroup$ @AaronHendrickson The proposed estimator uses medians and random variables in both the numerator and the denominator :/ Am just not sure how to find that variance without using some sort of approximation. $\endgroup$
    – JerBear
    Commented Mar 20, 2023 at 20:01

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