Receiver operating characteristic (ROC) curves are widely used in medical decision making. It was recognized in the last decade that only a specific region of the ROC curve is of clinical interest, which can be summarized by the partial area under the ROC curve (partial AUC). Early statistical methods for evaluating partial AUC assume that the data are from a specified underlying distribution. Nonparametric estimators of the partial AUC emerged recently, but there are theoretical issues to be addressed. In this dissertation, we propose two new nonparametric statistics, partially integrated ROC and partially integrated weighted ROC, for estimating partial AUC. We show that our partially integrated ROC statistic is a consistent estimator of the partial AUC, and derive its asymptotic distribution which is distribution free under the null hypothesis. In the partially integrated ROC statistic, when the ROC curve crosses the Uniform distribution function (CDF) and if the partial area evaluated contains the crossing point, or when there are multiple crossing, the partially integrated ROC statistic might not perform well. To address this issue, we propose the partially integrated weighted ROC statistic. This statistic evaluates the partially weighted AUC, where larger weight is given when the ROC curve is above the Uniform CDF and smaller weight is given when the ROC curve is below the Uniform CDF. We show that our partially integrated weighted ROC statistic is a consistent estimator of the partially weighted AUC. We derive its asymptotic distribution which is distribution free under the null hypothesis. We propose to apply our two nonparametric statistics to functional category analysis in microarray experiments. We define the functional category analysis to be the statistical identification of over-represented functional gene categories in a microarray experiment based on differential gene expression. We compare our statistics with existing methods for the functional category analysis both via simulation study and application to a real microarray data, and demonstrate that our two statistics are effective for identifying over-represented functional gene categories. We also emphasize the essential role of the empirical distribution function plots and the ROC curves in the functional category analysis.

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Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-02T14:51:29Z No. of bitstreams: 1 flaviacarvalhofaria.pdf: 1606221 bytes, checksum: 51227a764c6f1f3ec1b3b2f9dde179b3 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-02T13:12:47Z (GMT) No. of bitstreams: 1 flaviacarvalhofaria.pdf: 1606221 bytes, checksum: 51227a764c6f1f3ec1b3b2f9dde179b3 (MD5) / Made available in DSpace on 2016-07-02T13:12:47Z (GMT). No. of bitstreams: 1 flaviacarvalhofaria.pdf: 1606221 bytes, checksum: 51227a764c6f1f3ec1b3b2f9dde179b3 (MD5) Previous issue date: 2012-08-17 / A tese investiga os aspectos do pronome possessivo relevantes para sua aquisição no português brasileiro (PB) e se desenvolve dentro de uma perspectiva psicolinguística da aqui-sição da língua materna. Assume-se, de acordo com o Programa Minimalista (Chomsky, 1995 e obras posteriores) uma gramática universal (GU) inata correspondente ao estado inicial da aquisição da linguagem e a concepção de uma língua I (interna) composta por um sistema computacional e um léxico. Assume-se, também, modelos de processamento que explique como a criança adquire esse léxico: o Bootstrapping Fonológico (Morgan & Demuth, 1996; Christophe et al., 1997), que considera que, antes de adquirir um léxico, a criança faz uso de habilidades perceptuais para segmentar informações do input em unidades linguísticas, e o Bootstrapping Sintático (Gleitman, 1990; 1994), segundo o qual a criança usa dados da estru-tura sintática para deduzir o significado das palavras. Dessa forma, pode-se dizer que a crian-ça em processo de aquisição do PB identifica o possessivo através de uma análise perceptual do fluxo da fala e, uma vez disponível no léxico, o sistema computacional opera sobre seus traços formais, relacionando-o numa estrutura hierárquica correspondente a uma expressão linguística. Tais itens são identificados na interface fônica através de um tratamento estatístico da fala recebida no input e seus traços semânticos/formais são adquiridos via processamento na interface semântica. O possessivo, apesar de se tratar de um elemento de comportamento complexo, surge relativamente cedo na produção inicial da criança, se comparado a outros itens determinantes. Em PB, tal elemento apresenta variação semântica de acordo com as pos-sibilidades de posicionamento na sentença, o que motivou uma proposta de divisão categorial dos pronomes possessivos em dois tipos: pronomes possessivos antepostos ao nome são de-terminantes e, portanto, considerados itens funcionais, enquanto os pospostos são adjetivos e, nesta tese, considerados itens semifuncionais. A fim de verificar a importância, para a aquisi-ção do pronome possessivo, de aspectos (i) fonológicos, como sua forma fônica, (ii) semânti-cos, como a relevância do traço de posse e (iii) sintáticos, como posicionamento na sentença, foram realizados três experimentos cujos resultados sugerem que a criança aos 11 meses de idade é sensível à forma fônica do pronome possessivo e, aos 3 anos e meio, é sensível ao seu traço de posse, assim como ao posicionamento destequando anteposto em SN adjetivado. / This thesis investigates relevant aspects of the acquisition of the possessive pronounsby Brazilian children in a psycholinguistic view of language acquisition. According to Minimalism Program (Chomsky, 1995 and subsequent works) an innate Universal Gram-mar (UG) corresponding to the initial state of language acquisition and the conception of I-language (internal) - that consists of a lexicon and a computational system – are assumed. We also assume Phonological Bootstrapping Model (Morgan & Demuth, 1996; Christophe et al., 1997), that explains how children acquire the lexicon using perceptual abilities to segment the input data into linguistic units, and Syntactic Bootstrapping Model (Gleitman, 1990; 1994). According to this model, children use information from syntactic structure to deduce the meaning of the words. We hypothesized that children acquiring BP identify the possessive pronouns through perceptual analysis of speech and, once they are available in the lexicon, the computational system operates on their formal features correlating them into a hierarchical structure as a linguistic expression. The possessives are identified in the phonologi-cal interface by a statistical analysis of speech and the semantic features are acquired via pro-cessing in the semantic interface. Despite the possessive behavior being considered complex, this pronouns appear before other functional items in children early production. Because pos-sessive pronoun semantic value changes according to its position in a sentence, we propose a categorical division of it into two types: functional and semi-functional items. Three experi-ments were conducted in order to verify phonological, semantic and syntactic aspects of pos-sessive pronouns learning. The results suggest that children at 11 months are sensitive to their phonetic forms, at 3 ½ years are sensitive to their semantic possession features as well as to their syntactic position in DP.