- UNSW
- ...
- Our schools
- Mathematics & Statistics
- Engage with us
- Seminars
- 2013
- Accurate Approximations for Nonparametric Tests in Linear Models
- Home
- Our school
- Study with us
- Our research
-
Student life & resources
- Undergraduate
- Honours year
- Postgraduate coursework
-
Postgraduate research
- Info for new students
- Current research students
- Postgraduate conference
- Postgraduate events
- Postgraduate student awards
- Michael Tallis PhD Research Travel Award
- Information about research theses
- Past research students
- Resources
- Entry requirements
- PhD projects
- Obtaining funding
- Application & fee information
-
Student services
- Help for postgraduate students
- Thesis guidelines
- School assessment policies
- Computing information
- Mathematics Drop-in Centre
- Consultation
- Statistics Consultation Service
- Academic advice
- Enrolment variation
- Changing tutorials
- Illness or misadventure
- Application form for existing casual tutors
- ARC grants Head of School sign off
- Computing facilities
- Choosing your major
- Student societies
- Student noticeboard
- Casual tutors
- Engage with us
- News & events
- Contact
- Home
- Our school
- Study with us
- Our research
-
Student life & resources
Postgraduate research
- Info for new students
- Current research students
- Postgraduate conference
- Postgraduate events
- Postgraduate student awards
- Michael Tallis PhD Research Travel Award
- Information about research theses
- Past research students
- Resources
- Entry requirements
- PhD projects
- Obtaining funding
- Application & fee information
Student services
- Help for postgraduate students
- Thesis guidelines
- School assessment policies
- Computing information
- Mathematics Drop-in Centre
- Consultation
- Statistics Consultation Service
- Academic advice
- Enrolment variation
- Changing tutorials
- Illness or misadventure
- Application form for existing casual tutors
- ARC grants Head of School sign off
- Computing facilities
- Choosing your major
- Engage with us
- News & events
- Contact
Abstract:
In general nonparametric tests have been based on test statistics chosen to have good properties in related parametric problems. Bootstrap or asymptotic approximations for the distribution of the test statistics, or robust versions of them, are used to obtain p-values. We propose a likelihood like test statistic based on a tilted bootstrap. Approximations for the distribution of this test statistic can be made by Monte Carlo approximations to the bootstrap or by a general multivariate saddlepoint approximation which is accurate in the tails of the distribution. We will concentrate on robust multiple regression for both fixed and random independent variables, describing first the tilted bootstrap approach. Then we will consider a general result on saddlepoint approximations for certain statistics based on empirical exponential families and use this to give an approximation to the bootstrap distribution. Finally we will examine the numerical properties of the tests.