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In this dissertation, we investigate four distinct and interrelated problems for high-dimensional inference of mean vectors in multi-groups. The first problem concerned is the profile analysis of high dimensional repeated measures. We introduce new test statistics and derive its asymptotic distribution under normality for equal as well as unequal covariance cases. Our derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. We also derive consistent and unbiased estimators of the asymptotic variances for equal and unequal covariance cases respectively. The second problem considered is the accurate inference for high-dimensional repeated measures in factorial designs as well as any comparisons among the cell means. We derive asymptotic expansion for the null distributions and the quantiles of a suitable test statistic under normality. We also derive the estimator of parameters contained in the approximate distribution with second-order consistency. The most important contribution is high accuracy of the methods, in the sense that p-values are accurate up to the second order in sample size as well as in dimension. The third problem pertains to the high-dimensional inference under non-normality. We relax the commonly imposed dependence conditions which has become a standard assumption in high dimensional inference. With the relaxed conditions, the scope of applicability of the results broadens. The fourth problem investigated pertains to a fully nonparametric rank-based comparison of high-dimensional populations. To develop the theory in this context, we prove a novel result for studying the asymptotic behavior of quadratic forms in ranks. The simulation studies provide evidence that our methods perform reasonably well in the high-dimensional situation. Real data from Electroencephalograph (EEG) study of alcoholic and control subjects is analyzed to illustrate the application of the results.

An experimental research study using a mixed-method analysis to was conducted to examine educational video game effects on mathematics achievement and motivation between sexes. This study examined sex difference in a 7th grade mathematics (Mathematics 2/Mathematics 2 Advanced) classroom (n=60) learning algebra. Attributes and barriers relating to educational video game play, preference, and setting characteristics were explored. To examine achievement and motivation outcomes, a repeated-measure (SPSS v14) test was used. The analysis included ethnographic results from both student and teacher interview and observation sessions for data triangulation. Results revealed a statistically significant academic mathematics achievement score increase (F =21.8, df =1, 54, < .05). Although, mathematics class motivation scores did not present significance (F =.79, df =1, 47, p > .05), both sexes posted similar data outcomes with regard to mathematics class motivation after using an educational video game as treatment during an eighteen-week term in conjunction with receiving in-class instruction. Additionally, there was an increase in male variability in standard deviation score (SDmotivationpre=8.76, SDmotivation post=11.70) for mathematics class motivation. Lastly, self-reported differences between the sexes for this limited sample, with regard to game design likes and dislikes and observed female game play tendencies, were also investigated. The data presented customization as a unified, but most requested, game design need between the sexes. Between sex differences were found only to be superficial other than a female delay in game acceptance with regard to time and game play comfort.

Utilizando a teoria de função de estimação linear ótima (Crowder, 1987), propomos equações de estimação generalizadas para modelos de regressão beta (Ferrari e Cribari-Neto, 2004) com medidas repetidas. Além disso, apresentamos equações de estimação generalizadas para modelos de regressão simplex baseadas nas propostas de Song e Tan (2000) e Song et al. (2004) e equações de estimação generalizadas para modelos lineares generalizados com medidas repetidas baseadas nas propostas de Artes e Jorgensen (2000) e Liang e Zeger (1986). Todas essas equações de estimação são desenvolvidas sob os enfoques da modelagem da média com homogeneidade da dispersão e da modelagem conjunta da média e da dispersão com intuito de incorporar ao modelo uma possível heterogeneidade da dispersão. Como técnicas de diagnóstico, desenvolvemos uma generalização de algumas medidas de diagnóstico quando abordamos quaisquer equações de estimação definidas tanto para modelagem do parâmetro de posição considerando a homogeneidade do parâmetro de dispersão como para modelagem conjunta dos parâmetros de posição e dispersão. Entre essas medidas, destacamos a proposta da influência local (Cook, 1986) desenvolvida para equações de estimação. Essa medida teve um bom desempenho, em simulações, para destacar corretamente pontos influentes. Por fim, realizamos aplicações a conjuntos de dados reais. / Based on the concept of optimum linear estimating equation (Crowder, 1987), we develop generalized estimating equation (GEE) to analyze longitudinal data considering marginal beta regression models (Ferrari and Cribari-Neto, 2004). The GEEs are also presented to marginal simplex models for longitudinal continuous proportional data proposed by Song and Tan (2000) and Song et al. (2004) and to generalized linear models for longitudinal data based on the proposes of Artes and J$\\phi$rgensen (2000) and Liang and Zeger (1986). All of them are developed focusing the assumption of homogeneous dispersion and with varying dispersion. For the diagnostic techniques, we generalize some diagnostic measures for estimating equations to model the position parameter considering an homogeneous dispersion parameter and for joint modelling of position and dispersion parameters to take in account a possible heterogeneous dispersion. Among these measures, we point out the local influence (Cook, 1986) developed to estimating equations. This measure can correctly show influential observations in simulation study. Finally, the theory is applied to real data sets.

Utilizando a teoria de função de estimação linear ótima (Crowder, 1987), propomos equações de estimação generalizadas para modelos de regressão beta (Ferrari e Cribari-Neto, 2004) com medidas repetidas. Além disso, apresentamos equações de estimação generalizadas para modelos de regressão simplex baseadas nas propostas de Song e Tan (2000) e Song et al. (2004) e equações de estimação generalizadas para modelos lineares generalizados com medidas repetidas baseadas nas propostas de Artes e Jorgensen (2000) e Liang e Zeger (1986). Todas essas equações de estimação são desenvolvidas sob os enfoques da modelagem da média com homogeneidade da dispersão e da modelagem conjunta da média e da dispersão com intuito de incorporar ao modelo uma possível heterogeneidade da dispersão. Como técnicas de diagnóstico, desenvolvemos uma generalização de algumas medidas de diagnóstico quando abordamos quaisquer equações de estimação definidas tanto para modelagem do parâmetro de posição considerando a homogeneidade do parâmetro de dispersão como para modelagem conjunta dos parâmetros de posição e dispersão. Entre essas medidas, destacamos a proposta da influência local (Cook, 1986) desenvolvida para equações de estimação. Essa medida teve um bom desempenho, em simulações, para destacar corretamente pontos influentes. Por fim, realizamos aplicações a conjuntos de dados reais. / Based on the concept of optimum linear estimating equation (Crowder, 1987), we develop generalized estimating equation (GEE) to analyze longitudinal data considering marginal beta regression models (Ferrari and Cribari-Neto, 2004). The GEEs are also presented to marginal simplex models for longitudinal continuous proportional data proposed by Song and Tan (2000) and Song et al. (2004) and to generalized linear models for longitudinal data based on the proposes of Artes and J$\\phi$rgensen (2000) and Liang and Zeger (1986). All of them are developed focusing the assumption of homogeneous dispersion and with varying dispersion. For the diagnostic techniques, we generalize some diagnostic measures for estimating equations to model the position parameter considering an homogeneous dispersion parameter and for joint modelling of position and dispersion parameters to take in account a possible heterogeneous dispersion. Among these measures, we point out the local influence (Cook, 1986) developed to estimating equations. This measure can correctly show influential observations in simulation study. Finally, the theory is applied to real data sets.

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Baserat på Self-Determination Theory (SDT) och en randomiserad kontrollstudiedesign undersöktes effekten av autonomistödjande textmeddelanden i jämförelse med neutrala meddelanden eller inga meddelanden på deltagarnas behovstillfredsställelse, motivation, och aktivitetsnivå. Digital kvantitativ datainsamling användes där webbenkäterna skickades ut tre gånger till deltagarna, innan, under samt efter intervention. Totalt 107 frivilliga män och kvinnor svarade vid baslinjemätningen och delades sedan in i tre olika grupper, inaktiv kontrollgrupp (n = 45), aktiv kontrollgrupp (n = 29) samt interventionsgrupp (n = 33). Interventionen ägde rum i samband med en stegtävling. Textmeddelandena skickades ut till deltagarna i aktiva kontrollgruppen och interventionsgruppen två gånger varje vecka under åtta veckor, via en digital plattform. Det förelåg inga signifikanta skillnader mellan grupperna vid baslinjemätningen. En tvåvägs-ANOVA (repeated measure) visade att interventionen hade en signifikant effekt på upplevelsen av tillhörighet under interventionen. Dock förelåg inga andra signifikanta interventionseffekter. Det sammanlagda resultatet antyder således att den digitala interventionen, det vill säga att tillhandahålla deltagarna med autonomistödjande textmeddelanden, inte har någon bestående effekt på deltagarnas behovstillfredsställelse, motivation eller aktivitetsnivå. / Based on Self-Determination Theory (SDT) and a randomized controlled trial design, the effect of autonomy-supportive text messages was examined in comparison with neutral messages or no messages regarding the participants basic psychological needs, motivation and activity level. Digital quantitative data collection was used, and the web surveys were sent out three times to participants, pre, during and post intervention. A total of 107 male and female volunteers responded to the baseline measurement and were then divided into three different groups, inactive control group (n = 45), active control group (n = 29) and intervention group (n = 33). The intervention took place in relation to a step contest. Text messages were sent to the participant’s in the active control group and intervention group twice a week for a total of eight weeks, via a digital platform. There were no significant differences between the groups in the baseline measurement. A two-way ANOVA (repeated measure) showed that the intervention had a significant effect on the experience of relatedness during the intervention. However, there were no other significant intervention effects. The results suggest that the digital intervention, to provide participants with autonomy supportive text messages, does not have a lasting effect on need satisfaction, motivation or activity level.