Cette thèse concerne l’étude de grandes déviations précises pour deux statistiques de test:le coefficient de corrélation empirique de Pearson et la statistique de Moran.Les deux premiers chapitres sont consacrés à des rappels sur les grandes déviations précises et sur la méthode de Laplace qui seront utilisés par la suite. Par la suite, nous étudions les grandes déviations précises pour des coefficients de Pearson empiriques qui sont définis par:$r_n=\sum_{i=1}^n(X_i-\bar X_n)(Y_i-\bar Y_n)/\sqrt{\sum_{i=1}(X_i-\bar X_n)^2 \sum_{i=1}(Y_i-\bar Y_n)^2}$ ou, quand les espérances sont connues, $\tilde r_n=\sum_{i=1}^n(X_i-\mathbb E(X))(Y_i-\mathbb E(Y))/\sqrt{\sum_{i=1}(X_i-\mathbb E(X))^2 \sum_{i=1}(Y_i-\mathbb E(Y))^2} \, .$. Notre cadre est celui d’échantillons (Xi, Yi) ayant une distribution sphérique ou une distribution gaussienne. Dans chaque cas, le schéma de preuve suit celui de Bercu et al.Par la suite, nous considérons la statistique de Moran $T_n=\frac{1}{n}\sum_{k=1}^n\log\frac{X_i}{\bar X_n}+\gamma \, ,$o\`u $\gamma$, où γ est la constante d’ Euler. Enfin l’appendice est consacré aux preuves de résultats techniques. / This thesis focuses on the study of Sharp large deviations (SLD) for two test statistics:the Pearson’s empirical correlation coefficient and the Moran statistic.The two first chapters aim to recall general results on SLD principles and Laplace’s methodsused in the sequel. Then we study the SLD of empirical Pearson coefficients, name $r_n=\sum_{i=1}^n(X_i-\bar X_n)(Y_i-\bar Y_n)/\sqrt{\sum_{i=1}(X_i-\bar X_n)^2 \sum_{i=1}(Y_i-\bar Y_n)^2}$ and when the meansare known,$\tilde r_n=\sum_{i=1}^n(X_i-\mathbb E(X))(Y_i-\mathbb E(Y))/\sqrt{\sum_{i=1}(X_i-\mathbb E(X))^2 \sum_{i=1}(Y_i-\mathbb E(Y))^2} \, .$ .Our framework takes place in two cases of random sample (Xi, Yi): spherical distributionand Gaussian distribution. In each case, we follow the scheme of Bercu et al. Next, westate SLD for the Moran statistic $T_n=\frac{1}{n}\sum_{k=1}^n\log\frac{X_i}{\bar X_n}+\gamma \, ,$o\`u $\gamma$ , where γ is the Euler constant.Finally the appendix is devoted to some technical results.

This degree project aims to explore the subject of forecasting, which is an ongoing and much alive debate within economics and finance. Within the forecasting field the available research is vast and even if restricted to real estate, which is the main focus of this paper, the available material is comprehensive. A large fraction of published research concerning the subject of real estate forecasting consists of post mortem studies, with econometric models trying to replicate historical trends with the help of available micro and macro data. This branch within the field of forecasting seems to advance and progress with help of refined econometric models. This paper, on the other hand, rather examines the fundamentals behind forecasting and why forecasting can be a difficult task in general. This is shown with an examination of the accuracy of 160 unique forecasts within the field of real estate. To evaluate the accuracy and predictability from different perspectives we state three main null hypotheses: 1. Correct forecasts and the direction of the predictions are independent variables. 2. Correct forecasts and the examined consultants are independent variables. 3. Correct forecasts and the examined cities are independent variables. 4 The observed frequencies for Hypothesis 1 indicate that upward predictions seem to be easier to predict than downward predictions. This is however not supported by the statistical tests. The observed frequencies for Hypothesis 2 clearly indicate that one consultant is a superior forecaster than compared to the other consultants. The statistical tests confirm this. The observed frequencies for Hypothesis 3 indicate no signs of dependence for the variables. The statistical tests confirm this. / Detta examensarbete ämnar att utforska ämnesområdet kring prognoser och prognosmakande, vilket är en högst levande debatt inom ekonomi och finans. Inom detta område är tillgänglig forskning mycket omfattande och även om materialet begränsas till fastighetsmarknaden, som är huvudspåret i denna uppsats, är mängden information ansenlig. En stor andel av publicerad forskning som berör prognoser av fastighetsmarkanden består ofta av studier av typen "post mortem", där man med ekonometriska modeller försöker efterlikna tidigare historiska trender med hjälp av tillgänglig mikro- eller makrodata. Denna gren av forskningen tycks vinna mark och fortsätter att utvecklas med hjälp av allt mer avancerade ekonometriska modeller. Denna studie fokuserar däremot snarare på de fundamentala elementen av prognosmakande och varför detta ibland kan vara en problematisk uppgift. Detta visas med hjälp av en undersökning gällande utfallet och träffsäkerheten av 160 unika prognoser på fastighetsmarknaden. 7 För att utvärdera träffsäkerheten hos prognoserna sätts tre olika nollhypoteser upp: 1. Korrekt prognos och riktning av prognos är oberoende variabler. 2. Korrekt prognos och konsult är oberoende variabler. 3. Korrekt prognos och undersökta städer är oberoende variabler. De observerade frekvenserna för Hypotes 1 indikerar att uppåtgående prognoser är enklare att förutspå än övriga prognoser. Detta kan dock inte stödjas av de statistiska testerna. De observerade frekvenserna för Hypotes 2 indikerar tydligt att en konsult är en överlägsen prognosmakare än övriga konsulter. Detta stöds av de statistiska testerna. De observerade frekvenserna för Hypotes 3 indikerar inget samband av beroende mellan variablerna. Detta kan dock inte stödjas av de statistiska testerna.

This is a study where the purpose is to investigate the risk-adjusted return and the correlation between the two investments, the stock market and the condominium market. In addition to this, it was analyzed how the two investments performed during the financial crisis and the covid-19 crisis. Study is carried out to get answers to the eternal question of which of these two investments is considered the most suitable for both short-term or long-term investment goals where financial conditions are taken into account. The study conducted various tests such as Pearson correlation test, volatility and regression models. The Sharpe ratio was used to measure the risk-adjusted return. These are carefully selected to see what returns the two investments give at different risks, as well as how the investments correlate with each other during crises and conditions of economic growth. The conclusion reached by this study is that the investor should diversify and invest in both investments. This is because their risk versus return profile becomes more even by investing in both investments. When one investment does worse, the other investment will, according to the study's various tests, make the return and risk profile more stable. Despite the high correlation between the investments, diversification is useful in case of possible future economic crises. / Detta är en studie där syftet är att undersöka den riskjusterade avkastningen samt korrelationen  mellan de två investeringarna aktiemarknaden och bostadsrättsmarknaden. Utöver detta analyserades hur de två investeringarna presterade under finanskrisen och covid-19-krisen.  Studie är genomförd för att få svar på den eviga frågan om vilken av dessa två investeringar som anses vara lämpligast för både kortsiktiga eller långsiktiga investeringsmål där ekonomiska förhållanden tas i akt.  Studien genomförde olika tester som Pearson korrelationstest, volatilitet och regressionsmodeller. Sharpekvoten användes  för att mäta den riskjusterade avkastningen. Dessa är noga utvalda för att se vad de två investeringarna ger för avkastning vid olika risker, samt hur investeringarna korrelerar med varandra under kriser och förhållanden vid ekonomisk tillväxt. Slutsatsen som denna studie kom fram till är att investeraren bör diversifiera sig och investera i båda investeringarna. Detta på grund av att deras riskprofil kontra avkastning blir mer jämnare genom att investera i båda investeringarna. När den ena investeringen går sämre kommer den andra investeringen som enligt studiens olika tester att göra att avkastningen och riskprofilen blir mer stabil. Trots den höga korrelationen mellan investeringarna så är diversifiering användbar vid eventuella framtida ekonomiska kriser.

Les modèles linéaires généralisés (GLMs) constituent l’une des classes de modèles les plus populaires en statistique. Cette classe contient une grande variété de modèles de régression fréquemment utilisés, tels que la régression linéaire normale, la régression logistique et les gamma GLMs. Dans les GLMs, la distribution de la variable de réponse définit une famille exponentielle. Un désavantage de ces modèles est qu’ils ne sont pas robustes par rapport aux valeurs aberrantes. Pour les modèles comme la régression linéaire normale et les gamma GLMs, la non-robustesse est une conséquence des ailes exponentielles des densités. La différence entre les tendances de l’ensemble des données et celles des valeurs aberrantes donne lieu à des inférences et des prédictions biaisées. A notre connaissance, il n’existe pas d’approche bayésienne robuste spécifique pour les GLMs. La méthode la plus populaire est fréquentiste ; c’est celle de Cantoni and Ronchetti (2001). Leur approche consiste à adapter les M-estimateurs robustes pour la régression linéaire au contexte des GLMs. Cependant, leur estimateur est dérivé d’une modification de la dérivée de la log-vraisemblance, au lieu d’une modification de la vraisemblance (comme avec les M-estimateurs robustes pour la régression linéaire). Par conséquent, il n’est pas possible d’établir une correspondance claire entre la fonction modifiée à optimiser et un modèle. Le fait de proposer un modèle robuste présente deux avantages. Premièrement, il permet de comprendre et d’interpréter la modélisation. Deuxièmement, il permet l’analyse fréquentiste et bayésienne. La méthode que nous proposons s’inspire des idées de la régression linéaire robuste bayésienne. Nous adaptons l’approche proposée par Gagnon et al. (2020), qui consiste à utiliser une distribution normale modifiée avec des ailes plus relevées pour le terme d’erreur. Dans notre contexte, la distribution de la variable de réponse est une version modifiée où la partie centrale de la densité est conservée telle quelle, tandis que les extrémités sont remplacées par des ailes log-Pareto, se comportant comme (1/|x|)(1/ log |x|)λ. Ce mémoire se concentre sur les gamma GLMs. La performance est mesurée à la fois théoriquement et empiriquement, avec une analyse des données sur les coûts hospitaliers. / Generalized linear models (GLMs) form one of the most popular classes of models in statistics. This class contains a large variety of commonly used regression models, such as normal linear regression, logistic regression and gamma GLMs. In GLMs, the response variable distribution defines an exponential family. A drawback of these models is that they are non-robust against outliers. For models like the normal linear regression and gamma GLMs, the non-robustness is a consequence of the exponential tails of the densities. The difference in trends in the bulk of the data and the outliers yields skewed inference and prediction. To our knowledge, there is no Bayesian robust approach specifically for GLMs. The most popular method is frequentist; it is that of Cantoni and Ronchetti (2001). Their approach is to adapt the robust M-estimators for linear regression to the context of GLMs. However, their estimator is derived from a modification of the derivative of the log-likelihood, instead of from a modification of the likelihood (as with robust M-estimators for linear regression). As a consequence, it is not possible to establish a clear correspondence between the modified function to optimize and a model. Having a robust model has two advantages. First, it allows for an understanding and an interpretation of the modelling. Second, it allows for both frequentist and Bayesian analysis. The method we propose is based on ideas from Bayesian robust linear regression. We adapt the approach proposed by Gagnon et al. (2020), which consists of using a modified normal distribution with heavier tails for the error term. In our context, the distribution of the response variable is a modified version where the central part of the density is kept as is, while the extremities are replaced by log-Pareto tails, behaving like (1/|x|)(1/ log |x|)λ. The focus of this thesis is on gamma GLMs. The performance is measured both theoretically and empirically, with an analysis of hospital costs data.

Master of Science / Department of Statistics / Weixing Song / A robust estimation procedure for parametric regression models is proposed in the paper by assuming the error terms follow a Pearson type VII distribution. The estimation procedure is implemented by an EM algorithm based on the fact that the Pearson type VII distributions are a scale mixture of a normal distribution and a Gamma distribution. A trimmed version of proposed procedure is also discussed in this paper, which can successfully trim the high leverage points away from the data. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies, together with the comparisons made with other existing procedures in the literature.

Adventure tourism is a growing market sector worldwide including Australia. A range of research exists that examined participation in adventure tourism activities by consideration of various aspects such as socio-demographics, motivations, activity/setting preferences and involvement in the activity to understand the adventure tourist. While studies have been conducted that included several of these aspects, a holistic investigation of involvement, motivations and setting preferences together has not been conducted previously regarding adventure tourism in Australia in general and SCUBA diving in particular. Furthermore, in Australia, only limited information is available about those who participate in the adventure activity of SCUBA diving. The aim of this research is to investigate differences and similarities of involvement, motivations and setting preferences of SCUBA diving club members in Eastern Australia. In this study 294 SCUBA diving club members in New South Wales and Queensland were surveyed by utilisation of a web-based questionnaire in order to identify their involvement in SCUBA diving, socio-demographic characteristics, participation motives and setting preferences. Descriptive analysis was used to investigate the socio-demographic characteristics of divers, their motivations and setting preferences. Principal component analysis was applied on involvement variables as well as motivations to investigate the underlying constructs. Agglomerative and hierarchical cluster analyses were used to derive clusters of divers that differed in their involvement in SCUBA diving. Exact Pearson chi-square tests were conducted to test whether there were significant differences concerning sociodemographics between clusters. In addition, analyses of variance (ANOVAs) were conducted to determine differences and similarities of motivational components and setting preferences between clusters. This study found that SCUBA diving club members are a heterogeneous group regarding their involvement in SCUBA diving. Five clusters of divers emerged that differed in their involvement in SCUBA diving. While differences in socio-demographics across the different involvement clusters were revealed, they proved to be less valuable for interpretation purposes. Regarding divers� setting preferences, similar structures were observed across all clusters regardless of differences in involvement. Motivations showed a complex structure across the clusters in regard to divers� involvement in SCUBA diving. Based on the studies findings, recommendations for future research were suggested. These emphasised the need for a holistic examination of motivations and setting preferences of adventure tourists based on the concept of involvement, which would be important for theory development and segmentation of tourists. The same holistic approach would also be valuable for examining other types of tourists such as events tourists and heritage tourists to better understand tourist behaviour.

We introduce the notion of diversity order as a performance measure for distributed radar systems. We define the diversity order of a radar network as the slope of the probability of detection (PD) versus SNR evaluated at PD =0.5. We prove that the communication bandwidth between the sensors and the fusion center does not affect the growth in diversity order. We also prove that the OR rule leads to the best performance and its diversity order grows as (log K). We then introduce the notion of a random radar network to study the effect of geometry on overall system performance. We approximate the distribution of the SINR at each sensor by an exponential distribution, and we derive the moments for a specific system model. We then analyze multistatic systems and prove that each sensor should be large enough to cancel the interference in order to exploit the available spatial diversity.

This thesis uses archetypal theory as explained by Carol Pearson in The Hero Within: Six Archetypes We Live By to illustrate the heroic journey undertaken by the protagonist in Edna St. Vincent Millay's poem "Renascence." Feminist archetypal theory is a useful lens for gaining the reader access to the underlying paradigms of struggle experienced by the female literary character because it exposes the parallels that exist in separate female experiences. By applying Pearson's theory to Millay's work, readers are able to elucidate more clearly the methods used by the poet to create commonality and continuity with her female audience. Throughout the poem, the protagonist hero recursively circles through the Innocent, Orphan, Martyr, Wanderer, Warrior, and Magician phases. This essay utilizes a close reading strategy to illustrate its argument and provide evidence to its conclusions.

We introduce the notion of diversity order as a performance measure for distributed radar systems. We define the diversity order of a radar network as the slope of the probability of detection (PD) versus SNR evaluated at PD =0.5. We prove that the communication bandwidth between the sensors and the fusion center does not affect the growth in diversity order. We also prove that the OR rule leads to the best performance and its diversity order grows as (log K). We then introduce the notion of a random radar network to study the effect of geometry on overall system performance. We approximate the distribution of the SINR at each sensor by an exponential distribution, and we derive the moments for a specific system model. We then analyze multistatic systems and prove that each sensor should be large enough to cancel the interference in order to exploit the available spatial diversity.

To characterize the size distributions, concentrations and sources of heavy metal associated with suspended particles, a total of 12 months of sampling periods were taken by Micro-Orifice Uniform Deposit Impactor (MOUDI) in the Nantzu Export Processing Zone from January to December 2011, The concentrations of suspended particles ranged from 54.7 to 203 £gg/m3. Both autumn and winter had significantly higher levels of suspended particles than in spring and summer. The mass concentrations of fine particles accounted for ~50% of the mass concentrations of suspended particles. The mass concentrations of PM2.5 accounted for 50.2-70% of the mass concentrations of PM10. The mass concentrations of PM1 accounted for 24-38.3% of the mass concentrations of PM10. These results indicated that fine particles dominated in atmospheric particulates in Nanzih Export Processing Zone. In addition, among the PM10, PM2.5 and PM1, significant correlations were found. The crustal elements (Al, Fe, Ca, Mg, K and Na) and sulfate are dominant during the sampling periods, which accounting for ~95% of the total concentrations. The crustal elements were observed mainly in coarse particles, while sulfate was found mainly in fine particles. The concentrations of all crustal elements decreased in summer could be attributed to the meteorological conditions and chemical mechanism. By using the enrichment factor (EF) to distinguish the sources of heavy metals in PM10, PM2.5 and the results showed that EF values of crustal elements in PM10 ranged from 1 to 10, suggesting PM10 might come from the resuspension of soil and road dust. In addition, Pb, Zn, As, Se, Mo, Sb and sulfate were observed at higher EF values in both PM2.5 and PM1, indicating the influence of anthropogenic emissions in fine particles. The results from Pearson¡¦s correlations indicated that PM10 in the Nantzu Processing Zone were mainly from the resuspension of soil and road dust, while fine particles (PM2.5 and PM1) may be from the traffic emissions and petrochemical industry in Nanzih and Renwu.