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Brombin, Chiara (2009) A nonparametric permutation approach to statistical shape analysis. [Tesi di dottorato]

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Abstract (inglese)

The statistical community has shown an increased interest in shape analysis in the last decade, in particular with reference to the development of robust inferential statistical methods.
In this Ph.D. thesis we present an extension of NonParametric Combination (NPC) methodology (Pesarin, 2001) to shape analysis. At first we review inferential methods known in the shape analysis literature, highlighting some drawbacks of using Hotelling's T^2 test statistic. Then, focussing on the two independent sample case, through an exhaustive comparative simulation study, we evaluate the behaviour of traditional tests along with nonparametric permutation tests using also Multiple Aspect (MA) procedures and domain combinations.
The case of heterogeneous and dependent variation at each landmark is also investigated, along with the effects of superimposition on the power of NPC tests.
Permutation tests have been evaluated also in the particular case in which the number of variables is larger than the cardinality of permutation sample space. We have performed a simulation study to evaluate the power of multivariate NPC tests, showing that the power for the proposed tests increases when increasing the number of the processed variables provided that the noncentrality parameter increases, even when the number of covariates is larger than the permutation sample space.
These preliminary results allowed us to extend the notion of finite-sample consistency for permutation tests combination-based to the shape analysis field.
Sufficient conditions are given in order that the rejection rate converges to one, for fixed sample sizes at any attainable alpha-value, when the number of variables diverges, provided that the noncentrality induced by test statistics also diverges.
On the basis of these findings, we emphasize that the proposed tests provide efficient solutions to multivariate small sample problems, like those encountered in the shape analysis field.
Along with simulation studies, we present two applications to real data sets concerning Mediterranean monk seal skulls and aortic valve morphology.

Abstract (italiano)

Nell'ultimo decennio la comunità statistica ha mostrato un crescente interesse per i problemi di shape analysis, con particolare riferimento allo sviluppo di tecniche inferenziali robuste. In questa tesi di dottorato presentiamo un'estensione della metodologia NPC per la combinazione non parametrica di test di permutazione dipendenti (Pesarin, 2001) nell'ambito della shape analysis.
Inizialmente si introduce una revisione dei metodi inferenziali noti in letteratura, evidenziando alcune problematiche legate all'uso della statistica test T^2 di Hotelling.
Focalizzandoci poi sul caso di due campioni indipendenti, tramite un esauriente studio di simulazione, abbiamo confrontato il comportamento, in termini di potenza, dei test parametrici tradizionali con quello dei test non parametrici proposti. Sono state utilizzate anche procedure di tipo multi aspetto (MA) e combinazioni per domini.
E’ stato anche esaminato il caso in cui i landmark sono correlati tra loro. Inoltre è stato valutato l'impatto della superimposizione sulla potenza dei test NPC.
I test di permutazione sono stati valutati in potenza e sotto H_0 nel caso in cui il numero di variabili processate è superiore alla cardinalità dello spazio di permutazione. Abbiamo inoltre effettuato uno studio di simulazione per valutare la potenza dei test multivariati NPC, evidenziando che la potenza di questi test cresce al crescere del numero di variabili processate, qualora apportino un aumento della non centralità, anche quando il numero di variabili è superiore alla cardinalità dello spazio di permutazione. Questi risultati preliminari ci hanno consentito di estendere la nozione di finite-sample consistency per i test NPC nell'ambito della shape analysis.
Vengono fornite condizioni sufficienti tali per cui la potenza del test converge a uno, per ampiezze campionarie fissate ad ogni livello raggiungibile alpha, quando il numero di variabili diverge, posto che diverga anche la non centralità indotta dall'aumento del numero di variabili.
Sulla base dei risultati ottenuti, possiamo affermare che i test NPC forniscono soluzioni efficienti per i problemi multivariati di shape analysis in presenza di bassa numerosità campionarie, problemi del resto frequenti nell'ambito della shape analysis. Oltre agli studi di simulazione, vengono presentati due casi studio, uno relativo allo studio della forma del cranio della foca monaca del Mediterraneo e l'altro relativo alla morfologia della valvola aortica.

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Tipo di EPrint:Tesi di dottorato
Relatore:Salmaso, Luigi
Correlatore:Pesarin, Fortunato
Dottorato (corsi e scuole):Ciclo 21 > Scuole per il 21simo ciclo > SCIENZE STATISTICHE
Data di deposito della tesi:29 Gennaio 2009
Anno di Pubblicazione:2009
Parole chiave (italiano / inglese):Finite-sample consistency, NPC methodology, Shape analysis
Settori scientifico-disciplinari MIUR:Area 13 - Scienze economiche e statistiche > SECS-S/01 Statistica
Struttura di riferimento:Dipartimenti > Dipartimento di Scienze Statistiche
Codice ID:1683
Depositato il:29 Gen 2009
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Chiara Brombin - Curriculum Vitae Cerca con Google

Personal information Cerca con Google

Address: Department of Statistics, University of Padova, Cerca con Google

Via Cesare Battisti 241-243 - 35121 Padova (Italy) Cerca con Google

Phone: +39 049 827 4174 Cerca con Google

E-Mail: chiara.brombin@unipd.it Cerca con Google

Education Cerca con Google

University Cerca con Google

From January 2006 until present (expected completion by December Cerca con Google

2008): Cerca con Google

enrolled at the Doctoral School in Statistical Sciences, at the Department Cerca con Google

of Statistical Sciences, University of Padua, Italy. Actually I'm working Cerca con Google

on nonparametric methods for statistical shape analysis, under the supervision Cerca con Google

of Prof. Luigi Salmaso. Cerca con Google

June 2005: Cerca con Google

Laurea Degree (four years) in Statistics, at the Faculty of Statistical Sciences, Cerca con Google

University of Padova, Italy. Thesis on \Multivariate analysis with Cerca con Google

paired observations and missing values", advisors: Prof. F. Pesarin and Cerca con Google

Prof. G. A. Fava. Cerca con Google

Secondary school Cerca con Google

July 2000: Cerca con Google

Secondary School Diploma in Classical Studies, at Liceo G.B. Ferrari, Cerca con Google

Este (Padova) Italy. Cerca con Google

Study periods abroad Cerca con Google

From March 2008 to June 2008: Cerca con Google

Visiting Ph.D. student at the Department of Ecology and Evolution, Cerca con Google

State University of New York, Stony Brook, NY. Advisor: Prof. F. J. Cerca con Google

Rohlf. Cerca con Google

From April 2007 to June 2007: Cerca con Google

Visiting Ph.D. student at the Department of Anthropology, EVAN (European Cerca con Google

Virtual Anthropology Network) Centre, Vienna, Austria. Advisor: Cerca con Google

Prof. Stanislav Katina. Cerca con Google

Conferences and Presentations Cerca con Google

24-29 Agosto 2008 Cerca con Google

Porto-Portogallo Cerca con Google

COMPSTAT2008, International Conference on Computational Statistics, Cerca con Google

talk titled \Searching for powerful tests in shape analysis". Cerca con Google

23-24 May 2008 Cerca con Google

Penn State's University Park campus, State College, Pennsylvania Cerca con Google

Nonparametric Statistics and Mixture Models: Past, Present, and Fu- Cerca con Google

ture, poster presentation \The Hotelling's T2 permutation counterpart in Cerca con Google

shape analysis". Cerca con Google

19-22 September 2007 Cerca con Google

Palermo Cerca con Google

IV Congresso Nazionale SISMEC, poster presentation\Nonparametric Cerca con Google

methods in observational studies for testing for association in bladder Cerca con Google

cancer". Cerca con Google

8-11 July 2007 Cerca con Google

Vienna Cerca con Google

MCP 2007 Conference, talk \Adjusting stepwise p-values in generalized Cerca con Google

linear models". Cerca con Google

8-11 May 2007 Cerca con Google

Rolduc (Kerkrade, The Netherlands) Cerca con Google

First IBS Channel Network Conference (International Biometric Soci- Cerca con Google

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stepwise-GLM ndings?". Cerca con Google

Collaborations Cerca con Google

Prof. Ferronato G., MD Peretta R. and MD Galzignato P. F., Dept. of Cerca con Google

Medical and Surgical Specialties, University of Padova, Italy. Cerca con Google

Prof. Floreani A., Dept. of Surgical and Gastroenterological Science, Cerca con Google

University of Padova, Italy. Cerca con Google

Prof. B. Mozzanega, Dept. of Gynaecology and Human Reproduction Cerca con Google

Sciences, University of Padova, Italy. Cerca con Google

Prof. B. Cozzi, Dept. of Experimental Veterinary Science, University of Cerca con Google

Padova, Italy. Cerca con Google

Prof. P. F. Bassi, Dept. of Urology, Sacro Cuore Catholic University Cerca con Google

Hospital \A. Gemelli", Roma, Italy. Cerca con Google

Teaching experiences Cerca con Google

From November 2007 to January 2008: Cerca con Google

Descriptive Statistics at the Department of Statistical Sciences, University Cerca con Google

of Padova (Dott. B. Scarpa) Cerca con Google

From November 2006 to January 2007: Cerca con Google

Descriptive Statistics at the Department of Statistical Sciences, University Cerca con Google

of Padova (Prof. F. Pesarin) Cerca con Google

Publications Cerca con Google

Brombin C. and Salmaso L. (2008) Multi-aspect permutation tests in Cerca con Google

shape analysis with small sample size. Submitted to Computational Cerca con Google

Statistics and Data Analysis. Cerca con Google

Brombin C., Pesarin F. and Salmaso L. (2008) Dealing with multivariate Cerca con Google

data and small sample sizes: an application to shape analysis as a particular Cerca con Google

case. Submitted to the Annals of Applied Statistics (a Festschrift Cerca con Google

in the Lecture Notes-Monograph Series of the Institute of Mathematical Cerca con Google

Statistics (LNMS) from the Nonparametric Statistics and Mixture Models Cerca con Google

Conference). Cerca con Google

Brombin C. and Salmaso L. (2008) Searching for Powerful Tests in Shape Cerca con Google

Analysis. Proceedings of COMPSTAT2008, International Conference on Cerca con Google

Computational Statistics, Vol. II, Contributed Papers, 3-10, P. Brito Cerca con Google

(Editor) Physica-Verlag: A Springer Company. Cerca con Google

Caroli D., Variola A., Ferrara F., Rizzotto E. R., Baldo V., Salmaso L., Cerca con Google

Chiaramonte M., Brombin C. and Floreani A. (2008) The early diagnosis Cerca con Google

improves survival in primary biliary cirrhosis: A 35-year follow-up in a Cerca con Google

single centre. Digestive and Liver Disease, 40, A119. Cerca con Google

Arboretti R., Brombin C., Pellizzari P., Salmaso L., Mozzanega B. (2008) Cerca con Google

Nonparametric methods applied to nuchal translucency and foetal macrosomia. Cerca con Google

JP Journal of Biostatistics, 2, 19-36. This paper is available online Cerca con Google

at \http://www.pphmj.com", JP Journal of Biostatistics. Vai! Cerca con Google

Finos L., Brombin C., Salmaso L. (2008) Adjusting stepwise p-values in Cerca con Google

generalized linear models. Submitted to Communications in Statistics: Cerca con Google

Theory and Methods. Cerca con Google

Guarda-Nardini L., Stifano M., Brombin C., Salmaso L., Manfredini D. Cerca con Google

(2007) A one-year case series of arthrocentesis with hyaluronic acid injections Cerca con Google

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