On the Validity of Edgeworth and Saddlepoint Approximations
In the classical theory of Edgeworth expansion for the sample mean, it is typically assumed that the sampling distribution is either lattice valued or is sufficiently smooth to satisfy Cramér's regularity condition. However, applications of Edgeworth expansions to problems involving the bootstrap require regularity conditions which fail into the poorly understood grey area between these two cases. In the past, a limited amount of theory has been developed to take care of this problem, but it is restricted to the special case of the "classical" bootstrap, where the resample size is equal to the sample size and the resampling probabilities are all identical, In the present paper we extend this theory by developing Edgeworth expansions for general discrete distributions where the number of atoms is either fixed or increasing with sample size at an arbitrary rate. Implications of this result for the Lugannani-Rice tail area approximation are discussed, and it is established that this approximation is a large deviation formula in the present context. Our results shed light on much older work about the validity of Edgeworth expansions in the absence of Cramer's condition, despite being motivated by very recent developments in bootstrap theory, for example, to contexts where the sample size and resample size are different or where the resampling probabilities are unequal.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 51 (1994)
Issue (Month): 1 (October)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:51:y:1994:i:1:p:121-138. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.