ENH: add inference for variance without normality assumptions #8293
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first version, mainly bonett for variance confidence interval using kurtosis
written while reading references in 8261
issues:
#8261 inference for variance
#8286 kurtosis and jarque-bera
#8289 inference for correlation (just references without details)
current plan
I just want to get the basic versions in mainly bonett, plain kurtosi-adjusted and traditional inference under normality assumptions.
There are too many options for additional variations of methods, e.g. for kurtosis small sample and bias corrections, and there is no obvious winner for those.
cases:
I would like to get some "score" versions (variance of test statistic base on null assumption), but there isn't much literature on it, confint requires derivation and needs to be verified by Monte Carlo.
Current versions and almost all the literature uses estimated variance in variance of test statistic, i.e. is wald-type.
However, exp transformation of variance ratio removes the variance from the variance of the test statistic. variance only enters through the kurtosis estimate.