## Department of Statistics

# Seminars

**Combined nonparametric tests**

Speaker: Asso. Prof. Stefano Bonnini

Affiliation: Department of Economics and Management, Center for Modelling Computing and Simulations, University of Ferrara (Italy)

When: Friday, 14 July 2017, 11:00 am to 12:00 pm

Where: 303-B07

In several application problems, the phenomena under study are multidimensional. Therefore, these phenomena are represented by multivariate variables. In multivariate inferential problems, such as tests of hypotheses for comparing two or more populations, where data are assumed to be determinations of random variables, standard parametric methods (e.g. likelihood ratio test, Hotelling T2 test, ...), when applicable, require stringent assumptions that make them non robust and often inappropriate.

The main limits of these methods are:

1) the assumed underlying distribution is not always plausible or cannot be tested (especially for small sample sizes);

2) the dependence structure (apart from the infrequent case of independent variables) must be formally defined and estimated. For example, in the case of normal multivariate distributions, it is necessary to estimate the covariance matrix or correlation matrix.

The proposed combined nonparametric test, is based on the breakdown of the problem into as many sub-problems as many variables, and on the application of a univariate permutation test for each subproblem. The combination of the permutation significance level functions of each test provides a unique test statistic (and a unique p-value) to solve the multivariate problem.

The test is therefore distribution-free and the dependence of partial tests doesn

**Couplings and how to use them: a random graph example**

Speaker: Dr. Jesse Goodman

Affiliation: University of Auckland

When: Wednesday, 14 June 2017, 3:00 pm to 4:00 pm

Where: 303S-561

Coupling two random objects means constructing them out of a shared source of randomness, in order to find out something interesting about one or both of them. This talk will describe (with not much prior knowledge assumed) some of the interesting things we can discover in this way: from classical extreme value theory, to some new results about random graphs, shortest distances and exploration processes.

**Classified Mixed Model Prediction**

Speaker: Professor J. Sunil Rao

Affiliation: University of Miami

When: Wednesday, 7 June 2017, 11:00 am to 12:00 pm

Where: 303S-561

Many practical problems are related to prediction, where the main interest is at subject (e.g., personalized medicine) or (small) sub-population (e.g., small community) level. In such cases, it is possible to make substantial gains in prediction accuracy by identifying a class that a new subject belongs to. This way, the new subject is potentially associated with a random effect corresponding to the same class in the training data, so that method of mixed model prediction can be used to make the best prediction. We propose a new method, called classified mixed model prediction (CMMP), to achieve this goal. We develop CMMP for both prediction of mixed effects and prediction of future observations, and consider different scenarios where there may or may not be a “match” of the new subject among the training-data subjects. Theoretical and empirical studies are carried out to study the properties of CMMP and its comparison with existing methods. In particular, we show that, even if the actual match does not exist between the class of the new observations and those of the training data, CMMP still helps in improving prediction accuracy. Some examples will be presented including making predictions from breast cancer genomic data samples. Additionally, some delineation of the extension to the unknown grouping structure problem will be provided. This is joint work with Jiming Jiang of UC-Davis, Jie Fan of the University of Miami and Thuan Nguyen of Oregon Health and Science University.

**Strategic bidding in a discrete accumulating priority queue**

Speaker: Raneetha Abeywickrama

Affiliation: University of Auckland

When: Wednesday, 12 April 2017, 3:00 pm to 4:00 pm

Where: 303-310, Room 310, Level 3, Uni building 303, The University of Auckland at 38 Princes Street, Auckland CBD

We consider a single server M/G/1 queue in which customers accumulate priority linearly while waiting. There are a number of priority classes, each of which accumulates priority at a different rate. Upon arrival, each customer pays to enter the queue without knowing the current state of the system. The rate at which they accumulate priority depends on the priority class they have entered. When the server becomes idle, the customer with the greatest accumulated priority is chosen for service. Accumulating priority queues have been proposed in healthcare settings since they permit priority to increase with time spent in the queue. In this talk, we focus on the existence of Nash equilibrium and stability of this model.

**Problems with predictive distribution**

Speaker: Murray Aitkin

Affiliation: University of Melbourne

When: Wednesday, 12 April 2017, 11:00 am to 12:00 pm

Where: 303-310, Room 310, Level 3, Uni building 303, The University of Auckland at 38 Princes Street, Auckland CBD

Many calls have been made for an increased emphasis on prediction in statistics teaching (see for example Harville 2014). Bayesian prediction has been increasingly popularised through the posterior predictive distribution. This talk raises questions about the interpretation of this distribution, and the need for posterior sampling procedures to provide the uncertainty assessment of predictions.

Harville, D.A. (2014). The need for more emphasis on prediction: a "non-denominational" model-based approach (with discussion). The American Statistician 68 (2), 71-92.

http://www.ms.unimelb.edu.au/~maitkin@unimelb/

**Case--control logistic regression is more complicated than you think.**

Speaker: Prof. Thomas Lumley

Affiliation: University of Auckland

When: Wednesday, 5 April 2017, 11:00 am to 12:00 pm

Where: 303S-561

It is a truth universally acknowledged that logistic regression gives consistent and fully efficient estimates of the regression parameter under case-control sampling, so we can often ignore the distinction between retrospective and prospective sampling in epidemiology. I will talk about two issues that are more complicated than this. First, the behaviour of pseudo-r^2 statistics under case-control sampling: most of these are not consistently estimated. Second, the question of when and why unweighted logistic regression is much more efficient than survey-weighted logistic regression: the traditional answers of 'always' and 'because of variation in weights' are wrong.

**Statistical computing in a (more) static environment**

Speaker: Ross Ihaka & Brendan McArdle

Affiliation: Department of Statistics, University of Auckland

When: Wednesday, 29 March 2017, 6:00 pm to 7:30 pm

Where: -

6pm NZT - Foyer area, Ground floor, of Building 302, 23 Symonds Street. Refreshments will be available here before each lecture at 6pm.

6.30pm NZT - Lectures commence at 6.30pm (to 7.30pm), Wednesdays, MLT1 Lecture Theatre, Ground Floor, Building 303, 38 Princes Street.

Or

Live Stream to a screen from 630pm NZT onwards

https://www.stat.auckland.ac.nz/en/about/news-and-events-5/events/events-2017/03/ihaka-ross-ihaka.html

Or join a local group screening in your city.(Auckland, Brisbane, Christchurch, Sydney, Wellington...)

**Estimation of a High-Dimensional Covariance Matrix**

Speaker: Xiangjie Xue

Affiliation: Uni of Auckland

When: Wednesday, 29 March 2017, 3:00 pm to 4:00 pm

Where: 303-310, Room 310, Level 3, Uni building 303, The University of Auckland at 38 Princes Street, Auckland CBD

The estimation of covariance or precision (inverse covariance) matrices plays a prominent role in multivariate analysis. The usual estimator, the sample covariance matrix, is known to be unstable and ill-conditioned in high-dimensional setting. In the past two decades, various methods have been developed to give a stable and well-conditioned estimator and they have their own advantages and disadvantages. For example, thresholding methods carry almost no computational burden but their estimators can not guarantee to be positive-definite. In this talk, we will review some of the most popular methods and describe a new method to estimate the correlation matrix using the empirical Bayes method. To our best knowledge, we have not yet found any method in the literature using the empirical Bayes method to estimate correlation matrices to date. We use the fact that the elements in the sample correlation matrix can be approximated by the same one-parameter normal distribution with unknown means, along with the non-parametric maximum likelihood estimation proposed by Wang (2007) to give a new estimator of the correlation matrix. Preliminary simulation results show that the new estimator has some advantages over various thresholding methods in estimating sparse covariance matrices.

**The Use of Accuracy Indicators in Survey Data Analysis to Compensate for Measurement Error**

Speaker: Prof. Skinner,CJ

Affiliation: The London School of Economics and Politics Science

When: Monday, 27 March 2017, 11:00 am to 12:00 pm

Where: 303-310,Room 310, Level 3, Uni building 303, The University of Auckland at 38 Princes Street, Auckland CBD

There is growing interest among survey methodologists in collecting and using auxiliary variables related to the data quality, often called 'paradata'. I shall talk about binary paradata related to measurement error in a survey variable, indicating whether the variable is measured with error. This may be used in the design of the survey instrument. Here, the talk focusses on its use in survey data analysis to correct estimation for the potential biasing effects of measurement error.

http://www.lse.ac.uk/RESEARCHANDEXPERTISE/EXPERTS/profile.aspx?KeyValue=c.j.skinner%40lse.ac.uk

**Interactive visualisation and fast computation of the solution path for convex clustering and biclustering**

Speaker: Dr Genevera Allen, Dobelman Family Junior Chair

Affiliation: Departments of Statistics and Electrical and Computer Engineering, Rice University

When: Wednesday, 22 March 2017, 6:00 pm to 7:30 pm

Where: -

6pm NZT - Foyer area, Ground floor, of Building 302, 23 Symonds Street. Refreshments will be available here before each lecture at 6pm.

6.30pm NZT - Lectures commence at 6.30pm (to 7.30pm), Wednesdays, MLT1 Lecture Theatre, Ground Floor, Building 303, 38 Princes Street.

Or

Live Stream to a screen from 630pm NZT onwards

https://www.stat.auckland.ac.nz/en/about/news-and-events-5/events/events-2017/03/ihaka-genevera-allen.html

Or join a local group screening in your city.(Auckland, Brisbane, Christchurch, Sydney, Wellington...)