Probability and Statistics

Coordinator:
Célia Maria Pinto Nunes

Group
Clara Margarida Pisco Viseu
Dário Jorge da Conceição Ferreira
Helena Maria Simões Ferreira
Luísa Maria Jota Pereira Amaral
Sandra Maria Bargão Saraiva Ferreira


Collaborators: 
Ana Paula André Martins Fernandes
Cecília Maria Fernandes Fonseca
Gilberto Capistrano Cunha de Andrade 
Jorge Manuel dos Reis Gama



The main objective of PS group is to make contributions on specific Probability and Statistical issues, namely: 

• Conduct stochastic modeling in time and space to obtain random fields with finite dimension distributions having asymptotic independent tails. The asymptotic and pre-asymptotic dependence will be evaluated and summarized through coefficients that generalize known results for stochastic processes.
• Quantify clustering propensity of high values in a random filed through coefficients whose values present a variability adequate for the needs of the users of these models.
• Construct estimators for the coefficients that summarize extremal dependence and study their properties.
• Apply the constructed models, coefficients and estimators to real regional data, of geographic, climatic and economical nature;
• Extend the theory of F- tests with random sample sizes to mixed effects models, namely obtain the statistics and their distributions and develop techniques for calculating critical values;
• Apply this technique on a cancer patients database and other types of pathologies to demonstrate the advantages of using our approach instead of the usual F- tests;
• Develop the theory of Linear Regression under the assumption of random sample sizes;
• Develop numerical and algebraic procedures to improve the inference in orthogonal and non-orthogonal linear models, in terms of accuracy and ease of calculation.


AWARDS

Mexia, J.T., Nunes, C., Ferreira, D., Ferreira, S.S. and Moreira, E. (2011).
Orthogonal fixed effects ANOVA with random sample sizes.
The WSEAS Award the prize of the Best Paper of the 5th International Conference on Applied Mathematics, Simulation, Modelling (ASM '11), Corfu Island, Greece, July, 14-16.
http://www.wseas.us./reports/2011/corfu2011.htm
http://www.wseas.us/reports/2011/best2011.htm#july-2011-b



Publications

2013 

Ferreira, M., Ferreira, H. (2013). Extremes of multivariate ARMAX processes. Test, 22 (4), 606-627. 

Ferreira, D., Ferreira, S.S. and Nunes, C. Inducing pivot variables and non-centrality parameters in elliptical distributions. 11th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. ,Volume 1558, pp. 833-836 (2013).

Ferreira, D., Ferreira, S. S., Nunes, C., Fonseca, M. and Mexia, J. T. (2013). Chisquared and Related Inducing Pivot Variables: An Application to Orthogonal Mixed Models. Communications in Statistics – Theory and Methods.  DOI:10.1080/03610926.2013.770532 

Ferreira, S.S., Ferreira, D., Nunes, C. and Mexia, J. T. (2013). Estimation of variance components in linear mixed models with commutative orthogonal block structure. Revista Colombiana de Estadistica. Vol 36(2), pp. 261- 271.

Nunes, C., Oliveira, M. M. and Mexia, J. T. (2013). Application domains for the Delta method. Statistics. Vol. 47(2), pp. 317-328. DOI:10.1080/02331888.2011.605892

Nunes, C., Ferreira, D., Ferreira, S. and Mexia, J.T.(2013). Generalized F tests in models with random perturbations: the truncated Normal case. Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics, 307-315, Springer.

Nunes, C., Capistrano, G., Ferreira, D. and Ferreira, S.S. (2013). ANOVA with Random Sample Sizes: An Application to a Brazilian Database on Cancer Registries. 11th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc., Volume 1558, pp. 825-828 (2013).

Nunes, C., Ferreira, D., Ferreira, S.S. and Mexia, J. T. (2013). Fixed effects ANOVA: An extension to samples with random size. J. Stat. Comput. Simul. DOI: 10.1080/00949655.2013.791293

Pereira, L. (2013) On the maximum and minimum of a stationary random field. Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics, 337-345, Springer.

Pereira, L. (2013). Asymptotic location of largest values of a stationary random field. Communications in Statistics – Theory and Methods, 42 (24), 4513-4524. 

Sebastião, J.R., Martins, A.P., Pereira, L. e Ferreira, H. (2013). Estimating the upcrossings index. Test, 22 (4), 549-579.

Viseu, C., Pereira, L., Martins, A. P., Ferreira, H. (2013) Dependence of multivariate extremes. Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics, 463-471, Springer. 


2012 

Campos, R., Dias, G., Jorge, A. and Nunes, C. (2012). Enriching Temporal Query Understanding through Date Identification: How to Tag Implicit Temporal Queries? In Proceedings of the 2nd International Temporal Web Analytics Workshop (TWAW 2012) associated to 21th International World Wide Web Conference (WWW2012) Lyon, France, 17 April. ISBN 978-1-4503-1188-5, pp 41 – 48. ACM - DL

Campos, R., Dias, G., Jorge, A. and Nunes, C. (2012). GTE: A Distributional Second-Order Co-Occurrence Approach to Improve the Identification of Top Relevant Dates in Web Snippets. In Proceedings of the 21st ACM International Conference on Information and Knowledge Management (CIKM 2012) Maui, Hawaii, October 29 - November 02. ISBN 978 -1- 4503 -1156 -4, pp. 2035 – 2039. DBLP. ACM - DL.

Campos, R., Jorge, A., Dias, G. and Nunes, C. (2012). Disambiguating Implicit Temporal Queries by Clustering Top Relevant Dates in Web Snippets. In IEEE Main Conference Proceedings of The 2012 IEEE/WIC/ACM International Conference on Web Intelligence Macau, China, 04 - 07 December, IEEE Computer Society Press. DBLP. ACM - DL. 

Costa AM1, Marinho DA, Rocha H, Silva AJ, Barbosa TM, Ferreira SS, Martins M. (2012) Deep and shallow water effects on developing preschoolers' aquatic skills Journal of Human Kinetics, ;32:211-9. doi: 10.2478/v10078-012-0037-1.

Ferreira, H., Ferreira, M. (2012). On extremal dependence: some contributions. Test, 21, 566-583.

Ferreira, H., Ferreira, M. (2012). Tail dependence between order statistics. JMVA 105(1), 176-192.

Ferreira, H., Ferreira, M. (2012). Fragility index of block tailed vectors, Journal of Statistical Planning and Inference, 142 (7), 1837-1848.

Ferreira, H. and Pereira, L. (2012) Point processes of exceedances by random fields. Journal of Statistical Planning and Inference 142, pp. 773-779.

Ferreira, H. (2012) Multivariate maxima of moving multivariate maxima, Statistics and Probability Letters, 82, 1489-1496.

Ferreira, D., Ferreira, S.S., Nunes, C., Ramos, L. and Mexia, J. T. (2012). Approximate normality of low degree polynomials in normal independent variables. Far East J. Math. Sci. (FJMS). Vol. 68(2), 287 – 296.

Ferreira, S., Ferreira, D., Nunes, C. and Mexia, J. T. (2012). Estimation and crossing for models with commutative orthogonal block structure. Advances and Applications in Statistical Sciences. Vol. 7, Issue 2, pp. 23-34. ISSN 0974-6811

Ferreira, D., Ferreira, S.S. and Nunes, C. (2012). Confidence regions for variance components using inducing pivot variables. 10th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. Vol. 1479, 1682-1685(2012); doi: 10.1063/1.4756493

Ferreira, S.S., Ferreira, D. and Nunes, C. (2012). Linear and Quadratic Sufficiency and Commutativity. 10th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. Vol. 1479, 1694-1697(2012); doi: 10.1063/1.4756496

Nunes, C., Ferreira, D., Ferreira, S. and Mexia, J. T. (2012). F tests with a rare pathology. J. Appl. Stat.Vol. 39(3), pp. 551-561. DOI:10.1080/02664763.2011.603293

Nunes, C., Ferreira, D., Ferreira, S. and Mexia, J.T. (2012). Control of the truncation errors for generalized F distributions. J. Stat. Comput. Simul.Vol. 82 (2), pp. 165-171. DOI:10.1080/00949655.2011.631924

Nunes, C., Ferreira, D., Ferreira, S. and Mexia, J.T. (2012) Generalized F distributions with random non-centrality parameters: The convolution of Gamma and Beta variables. Far East J. Math. Sci. (FJMS). Vol. 62(1), pp. 1-14.

Nunes, C., Ferreira, D., Ferreira, S.S., Oliveira, M.M. and Mexia, J.T. (2012). One-way Random Effects ANOVA: An Extension to Samples with Random Size. 10th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. Vol. 1479, 1678-1681(2012); doi: 10.1063/1.4756492 

 
2011

Ferreira, S., Ferreira, D., Nunes, C. and Mexia, J. T. (2011). Discriminant Analysis and Decision Theory. Far East J. Math. Sci. (FJMS). Vol 51(1), 69-79. 

Ferreira, H. (2011) Dependence between two multivariate extremes Statistics and Probability Letters, 81 (5), 586–591. 

Ferreira, H. (2011) Dependence between two multivariate extremes Statistics and Probability Letters, 81 (5), 586–591. 

Ferreira, H. and Pereira, L. (2011) Generalized logistic model and its orthant tail dependence Kybernetika, 47 (5), 732-739.

Mexia, J. T., Nunes, C. and Oliveira, M.M. (2011). Multivariate application domains for the Delta method. 9th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. Vol. 1389, 1486-1489 (2011); doi: 10.1063/1.3637906

Mexia, J.T., Nunes, C., Ferreira, D., Ferreira, S.S. and Moreira, E. (2011). Orthogonal fixed effects ANOVA with random sample sizes. Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling (ASM'11), Corfu, Greece, 2011, 84-90. ISBN: 978-1-61804-016-9. 

Morgado MP1, Morgado SR, Mendes LC, Pereira LJ, Castelo-Branco M. (2011) Pharmacist interventions to enhance blood pressure control and adherence to antihypertensive therapy: Review and meta-analysis American Journal of Health-System Pharmacy, 68(3):241-53. doi: 10.2146/ajhp090656


2010

Nunes, C., Ferreira, D., Ferreira, S. S. and Mexia, J. T. (2010). F tests with random sample sizes. 8th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. Vol. 1281, 1241-1244 (2010); doi: 10.1063/1.3497911

Ferreira, D., Ferreira, S. S., Nunes, C. and Mexia, J. T. (2010). Maximum likelihood estimation methods for variance components in linear non-orthogonal small size design models. 8th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. 1281, 1233-1236 (2010); doi: 10.1063/1.3497905

Ferreira, S. S., Ferreira, D., Nunes, C. and Mexia, J. T. (2010). Crossing Segregated Commutative Orthogonal Block Structure. 8th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. 1281, 1229-1232 (2010); doi: 10.1063/1.3497904

Ferreira, S., Ferreira, D., Nunes, C. and Mexia, J.T. (2010). Nesting segregated mixed models. J. Stat. Theory and Pract. Vol. 4(2), 233-242.

Ferreira, D; Ferreira, S; Moreira, E. and Mexia, J.T. (2010). Exact Estimators for Normal Linear Models. Far East Journal of Theoretical Statistics Vol. 31 No 1, 33-48. 

Manuel Morgado, Sandra Rolo, Luísa Pereira, Miguel Castelo Branco. Blood pressure control and antihypertensive pharmacotherapy patterns in a hipertensive population of Eastern Central Region of Portugal BMC Health Services Research (2010), 10:349.M. 

Pereira, L. (2010) On the extremal behavior of a nonstationary normal random field Journal of Statistical Planning and Inference, 140 (11), 3567–3576.

Sebastião, J. R., Martins, A.P., Pereira, L., Ferreira, H. et al. (2010) Clustering of upcrossings of high values Journal of Statistical Planning and Inference, 140 (4), 1003–1012. 


2009

Nunes, C., Ferreira, S. and Ferreira, D. (2009). Generalized F tests in models with random perturbations: the Gamma case. Discuss. Math. Probab. Stat. Vol. 29(2), pp. 185-198

Ferreira, D., Ferreira, S., Nunes, C. and Mexia, J. T. (2009). Adjustment of normal mixed models through triple minimization. In: InterStat - Statistics on the Internet. http://interstat.statjournals.net/. Index for September 2009

Ferrão, M.E., Goldstein, H. (2009). Adjusting for measurement error in the Value Added Model: evidence from Portugal. Quality and Quantity – International Journal of Methodology, 43, p.951-963.

Ferrão, M.E. (2009). Sensitivity of Value-Added Model Specifications: measuring socio-economic status. Revista de Educación, 348, p.137-152.

Ferreira, S. S.; Ferreira, D; Moreira, E. and Mexia, J.T. (2009). Inference for L Orthogonal Models. Journal of Interdisciplinary Mathematics. Vol 12, No 6, 815—824. ISSN 0972-0502 

Pereira, L. (2009) The asymptotic location of the maximum of a stationary random field, Statistics and Probability Letters, 79 (20), 2166–2169. 


2008

Ferreira, S.; Ferreira, D. and Mexia, J.T. (2008). Double Tier Cross Nesting Design Models . Journal of Interdisciplinary Mathematics, 11 (2), 275-289.

Ferreira, D; Ferreira, S; Ramos, L and Mexia, J.T. (2008) Normal approximation to the product of a Non Central Chi-Square by an Independent Normal Variable. Aplimat - Journal of Applied Mathematics, I (2), 185-192.

Ferreira, S., Moreira, E. e Mexia, J.T. (2008). Orthogonal Almost Balanced Models. Aplimat - Journal of Applied Mathematics, I (2), 193-198. 

Ivette Gomes, Lígia Rodrigues, Björn Vandewalle & Clara Viseu (2008) A heuristic adaptive choice of the threshold for bias-corrected Hill estimators Journal of Statistical Computation and Simulation, 78 (2), 133-150 

Martins, A.P., Ferreira, H., Pereira, L. (2008) Multidimensional outlier-proneness of dependent data and the extremal index Statistical Methodology, 72–82.

Nunes, C., Santos, C. and Mexia, J. T. (2008). Relevant statistics for models with commutative orthogonal block structure and unbiased estimator for variance components. Journal of Interdisciplinary Mathematics. Vol.11, No. 4, pp. 553-564. 

Pereira, L. and Ferreira, H. (2008) How to compute the extremal index of stationary random fields Statistics and Probability Letters, 78 (11), 1301–1304.

Pinto, I., Nunes, C. and Mexia, J.T. (2008). Analysis of a with-covariates model for the Environmental Indexes. Biometrical Letters. Vol. 45(2), pp. 9-22.

Nunes, C., Pinto, I. and Mexia, J.T. (2008). Generalized F tests and selective generalized F tests for orthogonal associated mixed models. Discuss. Math. Probab. Stat. Vol. 28(2), pp. 229-246.

Campos, R., Dias, G., Nunes, C. and Nonchev, B. (2008). Clustering of Web Page Search Results: A Full Text Based Approach. International Journal of Computing and Information Science (IJCIS). International Association for Computer and Information Science. Vol. 9 (4), pp. 29-40.

2007

Ferreira, S., Ferreira, D. e Mexia, J.T. (2007). Cross Additivity in Models with Cross Nesting . Journal of Statistical Theory and Practice, 1(3-4), 377-392.

Fernandes, C., Ramos, P., Ferreira, S. e Mexia, J.T. (2007). Variance components estimation in generalized orthogonal models. Discuss. Math. Probab. Stat. 27, 99-115.

Jesus, V., Ferreira, S.S. e Mexia, J.T. (2007). Joint Estimation for Normal Orthogonal Mixed Models. Discussiones Mathematicae - Probability and Statistics, 27, 5-13.

Ferrão, M. E., Nunes, C. and Braumann, C. A. (2007). Estatística: Ciência Interdisciplinar. Actas do XIV Congresso Anual da Sociedade Portuguesa de Estatística. ISBN 978-972-8890-12-4

2006

Nunes C., Pinto, I. and Mexia J.T. (2006). F and Selective F tests with balanced cross-nesting and associated models. Discuss. Math. Probab. Stat. Vol. 26(2), 193-205

Nunes, C. and Mexia, J. T. (2006). Non-central generalized F distributions. Discuss. Math. Probab. Stat. Vol. 26(1), 47-61

Ferreira, D., Saraiva, S. e Mexia, J.T. (2006). Cross Additivity-An Application. Discuss. Math. Probab. Stat. 26, 207-219.

Dias, G., Nunes C., Cordeiro J.P., Moraliyski, R. Marcelino, I., Mukelov Raycho, Campos R., Santos, C., Alves, E., Conde, Bruno and Nonchev B. (2006). Language Independent Methodologies to Tackle Multilinguality. In Readings in Multilinguality. Selected Papers from Young Researchers in BIS-21++. Galia Angelova, Kiril Simov, Milena Slavcheva (Editors). Incoma Ltd. Shoumen, Bulgaria

2005

Dias, G., Alves, E. and Nunes, C. (2005). Topic Segmentation: How much can we do by counting words and sequences of words. Pliska Stud. Math. Bulgar. Vol. 17, pp. 39-70.

Ferreira, D., Mexia, J. T. e Saraiva, S. F. (2005). Stable hypothesis for Mixed Models with balanced cross-nesting. Discuss. Math. Probab. Stat. 25, 241-249.

Ferreira, D. e Mexia, J. T. (2005). Confidence intervals for the variance components in a grapevine experiment. Biometrical Letters. 42(2), 113-131.

2004

Nunes, C. and Mexia, J. T. (2004). Selective generalized F tests. Discuss. Math. Probab. Stat. Vol. 24(2), pp. 281-288

2003

Nunes, C. and Mexia, J. T. (2003). Selective F tests for sub-normal models. Discuss. Math. Probab. Stat.Vol. 23(2), pp. 167-174

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