Asymptotics

Lindsey, J K

doi:10.1093/oso/9780198523598.003.0005

Chapter

5 Asymptotics

Get access

https://doi.org/10.1093/oso/9780198523598.003.0005

Pages

185–232

Published:

May 1996

Abstract

If exact analytic results for the likelihood function of some model are difficult to obtain or are complex to calculate, it is often useful to have available approximations. Indeed, this was precisely what we did for the likelihood function of continuous distributions in Section 3.2.1, for the approximate likelihood based on the standard error in Section 3.5.2, for model selection in Section 3.6.1, and for profile likelihoods in Section 3.6.3. Numerical approximations are very important in statistics. Some of the common techniques, with which the reader should be familiar, are outlined in Appendix D. In this chapter, we shall be concerned with deriving some of the more commonly used analytic approximations. Often n independent observations are made, in a random sample, assuming the same parametric statistical model. In such situations, it may be interesting to study what would happen if we could imagine observing a much larger sample or perhaps the whole theoretically infinite population. Many statisticians go further and claim that maximum likelihood estimation is premised on the viewpoint according to which the data collection process can accrue information in a way that can lead, in the limit, to all parameters in a given model becoming known. As we saw in Chapter 1, this, in fact, makes little sense from a modelling perspective, except perhaps when production and measurement error models are involved. However, it is the major assumption underlying the original derivation of many of the classical results to be exposed in this chapter.

You do not currently have access to this chapter.

Sign in with email/username & password
Get email alerts
Save searches
Purchase content
Activate your purchase/trial code
Add your ORCID iD

Get help with access

Institutional access

Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:

IP based access

Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.

Sign in through your institution

Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institutionâ€™s website and Oxford Academic.

Click Sign in through your institution.
Select your institution from the list provided, which will take you to your institution's website to sign in.
When on the institution site, please use the credentials provided by your institution. Do not use an Oxford Academic personal account.
Following successful sign in, you will be returned to Oxford Academic.

If your institution is not listed or you cannot sign in to your institutionâ€™s website, please contact your librarian or administrator.

Sign in with a library card

Enter your library card number to sign in. If you cannot sign in, please contact your librarian.

Society Members

Society member access to a journal is achieved in one of the following ways:

Sign in through society site

Many societies offer single sign-on between the society website and Oxford Academic. If you see â€˜Sign in through society siteâ€™ in the sign in pane within a journal:

Click Sign in through society site.
When on the society site, please use the credentials provided by that society. Do not use an Oxford Academic personal account.
Following successful sign in, you will be returned to Oxford Academic.

If you do not have a society account or have forgotten your username or password, please contact your society.

Sign in using a personal account

Some societies use Oxford Academic personal accounts to provide access to their members. See below.

Personal account

A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.

Some societies use Oxford Academic personal accounts to provide access to their members.

Viewing your signed in accounts

Click the account icon in the top right to:

View your signed in personal account and access account management features.
View the institutional accounts that are providing access.

Signed in but can't access content

Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.

Institutional account management

For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.

Metrics

Total Views 2

1 Pageviews

1 PDF Downloads

Since 9/1/2024

Month:	Total Views:
September 2024	2

Contents

5 Asymptotics

Abstract

Email alerts

Contents

5 Asymptotics

Abstract

Sign in

Personal account

Institutional access

Institutional account management

Get help with access

Institutional access

IP based access

Sign in through your institution

Sign in with a library card

Society Members

Sign in through society site

Sign in using a personal account

Personal account

Viewing your signed in accounts

Signed in but can't access content

Institutional account management

Purchase

Email alerts

This Feature Is Available To Subscribers Only