Talk:Asymptotic theory (statistics)
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Dr. Anatolyev's comment on this article
Dr. Anatolyev has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
It reads: "In practical applications, asymptotic theory is applied by treating the asymptotic results as approximately valid for finite sample sizes as well. Such approach is often criticized for not having any mathematical grounds behind it, yet it is used ubiquitously anyway" This is inaccurate. The asymptotic theory exists for the purpose of entertaining these approximations. In this light, it is strange to hear the very purpose is is criticized and that there is no mathematical ground.
Inaccuracy 2: It reads: "At the same time for finite n it is impossible to claim anything about the distribution of X¯n... if the distributions of individual Xi’s is unknown." This is not true -- some things can be claimed. For example, its expectation exactly equals population mean; its variance is the population variance divided by n, etc., so it is not true that it is "impossible to claim anything".
Inaccuracy 3: It reads: "For panel data, it is commonly assumed that one dimension in the data (T) remains fixed, whereas the other dimension grows: T = const, n → ∞." This is only partly true -- what is described is the case of SHORT panels, but also there are LONG panels where both T → ∞ and n → ∞.
Inaccuracy 4: It reads: "There are models where the dimension of the parameter space Θn slowly expands with n, reflecting the fact that the more observations a statistician has, the more he is tempted to introduce additional parameters in the model. An example of this is the weak instruments asymptotic." There is inaccuracy here in saying "slowly expands" because there are setups when it expands quite fast, even with rate n. Also, there is a mistake here: an example for the described approach is NOT "weak instruments asymptotic" but rather "many instrument asymptotics". The weak instruments asymptotics is a good example of the "drifting parameter asymptotics", see below.
Incompleteness 1: The description of “alternative” asymptotic approaches is very incomplete. There are missing a few important cases of "dimensionality asymptotics" and "drifting parameter asymptotics". A rather modern overview can be found in the last chapter of the following book: Stanislav Anatolyev and Nikolay Gospodinov. Methods for Estimation and Inference in Modern Econometrics. CRC Press, Taylor & Francis. June 06, 2011. ISBN: 9781439838242, ISBN 10: 1439838240
Incompleteness 2: While "kernel density estimation and kernel regression additional parameter — the bandwidth" is mentioned, this should be extended to other non-parametric methods and smoothing parameters, respectively.
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
We believe Dr. Anatolyev has expertise on the topic of this article, since he has published relevant scholarly research:
- Reference : Stanislav Anatolyev, 2009. "Inference in Regression Models with Many Regressors," Working Papers w0125, Center for Economic and Financial Research (CEFIR).