Nous étudions le comportement asymptotique de statistiques ou fonctionnelles liées à des processus à longue mémoire saisonnière. Nous nous concentrons sur les lignes de Donsker et sur le processus empirique. Les suites considérées sont de la forme $G(X_n)$ où $(X_n)$ est un processus gaussien ou linéaire. Nous montrons que les résultats que Taqqu et Dobrushin ont obtenus pour des processus à longue mémoire dont la covariance est à variation régulière à l'infini peuvent être en défaut en présence d'effets saisonniers. Les différences portent aussi bien sur le coefficient de normalisation que sur la nature du processus limite. Notamment nous montrons que la limite du processus empirique bi-indexé, bien que restant dégénérée, n'est plus déterminée par le degré de Hermite de la fonction de répartition des données. En particulier, lorsque ce degré est égal à 1, la limite n'est plus nécessairement gaussienne. Par exemple on peut obtenir une combinaison de processus de Rosenblatt indépendants. Ces résultats sont appliqués à quelques problèmes statistiques comme le comportement asymptotique des U-statistiques, l'estimation de la densité et la détection de rupture.

We consider time-of-arrival based robust geolocation in harsh line-of-sight/non-line-of-sight environments. Herein, we assume the probability density function (PDF) of the measurement error to be completely unknown and develop an iterative algorithm for robust position estimation. The iterative algorithm alternates between a PDF estimation step, which approximates the exact measurement error PDF (albeit unknown) under the current parameter estimate via adaptive kernel density estimation, and a parameter estimation step, which resolves a position estimate from the approximate log-likelihood function via a quasi-Newton method. Unless the convergence condition is satisfied, the resolved position estimate is then used to refine the PDF estimation in the next iteration. We also present the best achievable geolocation accuracy in terms of the Cramér-Rao lower bound. Various simulations have been conducted in both real-world and simulated scenarios. When the number of received range measurements is large, the new proposed position estimator attains the performance of the maximum likelihood estimator (MLE). When the number of range measurements is small, it deviates from the MLE, but still outperforms several salient robust estimators in terms of geolocation accuracy, which comes at the cost of higher computational complexity.

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With the advent of the internet and advances in computing power, the collection of very large high-dimensional datasets has become feasible { understanding and modelling high-dimensional data has thus become a crucial activity, especially in the field of pattern recognition. Since non-parametric density estimators are data-driven and do not require or impose a pre-defined probability density function on data, they are very powerful tools for probabilistic data modelling and analysis. Conventional non-parametric density estimation methods, however, originated from the field of statistics and were not originally intended to perform density estimation in high-dimensional features spaces { as is often encountered in real-world pattern recognition tasks. Therefore we address the fundamental problem of non-parametric density estimation in high-dimensional feature spaces in this study. Recent advances in maximum-likelihood (ML) kernel density estimation have shown that kernel density estimators hold much promise for estimating nonparametric probability density functions in high-dimensional feature spaces. We therefore derive two new iterative kernel bandwidth estimators from the maximum-likelihood (ML) leave one-out objective function and also introduce a new non-iterative kernel bandwidth estimator (based on the theoretical bounds of the ML bandwidths) for the purpose of bandwidth initialisation. We name the iterative kernel bandwidth estimators the minimum leave-one-out entropy (MLE) and global MLE estimators, and name the non-iterative kernel bandwidth estimator the MLE rule-of-thumb estimator. We compare the performance of the MLE rule-of-thumb estimator and conventional kernel density estimators on artificial data with data properties that are varied in a controlled fashion and on a number of representative real-world pattern recognition tasks, to gain a better understanding of the behaviour of these estimators in high-dimensional spaces and to determine whether these estimators are suitable for initialising the bandwidths of iterative ML bandwidth estimators in high dimensions. We find that there are several regularities in the relative performance of conventional kernel density estimators across different tasks and dimensionalities and that the Silverman rule-of-thumb bandwidth estimator performs reliably across most tasks and dimensionalities of the pattern recognition datasets considered, even in high-dimensional feature spaces. Based on this empirical evidence and the intuitive theoretical motivation that the Silverman estimator optimises the asymptotic mean integrated squared error (assuming a Gaussian reference distribution), we select this estimator to initialise the bandwidths of the iterative ML kernel bandwidth estimators compared in our simulation studies. We then perform a comparative simulation study of the newly introduced iterative MLE estimators and other state-of-the-art iterative ML estimators on a number of artificial and real-world high-dimensional pattern recognition tasks. We illustrate with artificial data (guided by theoretical motivations) under what conditions certain estimators should be preferred and we empirically confirm on real-world data that no estimator performs optimally on all tasks and that the optimal estimator depends on the properties of the underlying density function being estimated. We also observe an interesting case of the bias-variance trade-off where ML estimators with fewer parameters than the MLE estimator perform exceptionally well on a wide variety of tasks; however, for the cases where these estimators do not perform well, the MLE estimator generally performs well. The newly introduced MLE kernel bandwidth estimators prove to be a useful contribution to the field of pattern recognition, since they perform optimally on a number of real-world pattern recognition tasks investigated and provide researchers and practitioners with two alternative estimators to employ for the task of kernel density estimation. / PhD (Information Technology), North-West University, Vaal Triangle Campus, 2014

A primary focus of wildlife research is to understand how habitat conditions and human activities impact the health of wild animals. External factors, both natural and anthropogenic that impact the ability of an animal to acquire food and build energy reserves have important implications for reproductive success, avoidance of predators, and the ability to withstand disease, and periods of food scarcity. In the analyses presented here, I quantify the impacts of habitat quality and anthropogenic disturbance on indicators of health for individuals in a threatened grizzly bear population in Alberta, Canada. The first analysis relates spatial patterns of hair cortisol concentrations, a promising indicator of long-term stress in mammals, measured from 304 grizzly bears to a variety of continuous environmental variables representative of habitat quality (e.g., crown closure, landcover, and vegetation productivity), topographic conditions (e.g., elevation and terrain ruggedness), and anthropogenic disturbances (e.g., roads, forest harvest blocks, and oil and gas well-sites). Hair cortisol concentration point data were integrated with continuous variables by creating a stress surface for male and female bears using kernel density estimation validated through bootstrapping. The relationships between hair cortisol concentrations for males and females and environmental variables were quantified using random forests, and landscape scale stress levels for both genders was predicted based on observed relationships. Low female stress levels were found to correspond with regions with high levels of anthropogenic disturbance and activity. High female stress levels were associated primarily with high-elevation parks and protected areas. Conversely, low male stress levels were found to correspond with parks and protected areas and spatially limited moderate to high stress levels were found in regions with greater anthropogenic disturbance. Of particular concern for conservation is the observed relationship between low female stress and sink habitats which have high mortality rates and high energetic costs. Extending the first analysis, the second portion of this research examined the impacts of scale-specific habitat selection and relationships between biology, habitat quality, and anthropogenic disturbance on body condition in 85 grizzly bears represented using a body condition index. Habitat quality and anthropogenic variables were represented at multiple scales using isopleths of a utilization distribution calculated using kernel density estimation for each bear. Several hypotheses regarding the influence of biology, habitat quality, and anthropogenic disturbance on body condition quantified using linear mixed-effects models were evaluated at each habitat selection scale using the small sample Aikake Information Criterion. Biological factors were influential at all scales as males had higher body condition than females, and body condition increased with age for both genders. At the scale of most concentrated habitat selection, the biology and habitat quality hypothesis had the greatest support and had a positive effect on body condition. A component of biology, the influence of long-term stress, which had a negative impact on body condition, was most pronounced within the biology and habitat quality hypothesis at this scale. As the scale of habitat selection was represented more broadly, support for the biology and anthropogenic disturbance hypothesis increased. Anthropogenic variables of particular importance were distance decay to roads, density of secondary linear features, and density of forest harvest areas which had a negative relationship with body condition. Management efforts aimed to promote landscape conditions beneficial to grizzly bear health should focus on promoting habitat quality in core habitat and limiting anthropogenic disturbance within larger grizzly bear home ranges. / Graduate / 0768 / 0463 / 0478 / mathieub@uvic.ca

This thesis is divided into two parts. In the first part we describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, optimization, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. In the second part we present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.

The aim of this study is to develop novel forecasting methodologies. The applications of our proposed models lie in two different areas: macroeconomics and energy. Though we consider two very different applications, the common underlying theme of this thesis is to develop novel methodologies that are not only accurate, but are also parsimonious. For macroeconomic time series, we focus on generating forecasts for the US Gross National Product (GNP). The contribution of our study on macroeconomic forecasting lies in proposing a novel nonlinear and nonparametric method, called weighted random analogue prediction (WRAP) method. The out-of-sample forecasting ability of WRAP is evaluated by employing a range of different performance scores, which measure its accuracy in generating both point and density forecasts. We show that WRAP outperforms some of the most commonly used models for forecasting the GNP time series. For energy, we focus on two different applications: (1) Generating accurate short-term forecasts for the total electricity demand (load) for Great Britain. (2) Modelling Irish electricity smart meter data (consumption) for both residential consumers and small and medium-sized enterprises (SMEs), using methods based on kernel density (KD) and conditional kernel density (CKD) estimation. To model load, we propose methods based on a commonly used statistical dimension reduction technique, called singular value decomposition (SVD). Specifically, we propose two novel methods, namely, discount weighted (DW) intraday and DW intraweek SVD-based exponential smoothing methods. We show that the proposed methods are competitive with some of the most commonly used models for load forecasting, and also lead to a substantial reduction in the dimension of the model. The load time series exhibits a prominent intraday, intraweek and intrayear seasonality. However, most existing studies accommodate the ‘double seasonality’ while modelling short-term load, focussing only on the intraday and intraweek seasonal effects. The methods considered in this study accommodate the ‘triple seasonality’ in load, by capturing not only intraday and intraweek seasonal cycles, but also intrayear seasonality. For modelling load, we also propose a novel rule-based approach, with emphasis on special days. The load observed on special days, e.g. public holidays, is substantially lower compared to load observed on normal working days. Special day effects have often been ignored during the modelling process, which leads to large forecast errors on special days, and also on normal working days that lie in the vicinity of special days. The contribution of this study lies in adapting some of the most commonly used seasonal methods to model load for both normal and special days in a coherent and unified framework, using a rule-based approach. We show that the post-sample error across special days for the rule-based methods are less than half, compared to their original counterparts that ignore special day effects. For modelling electricity smart meter data, we investigate a range of different methods based on KD and CKD estimation. Over the coming decade, electricity smart meters are scheduled to replace the conventional electronic meters, in both US and Europe. Future estimates of consumption can help the consumer identify and reduce excess consumption, while such estimates can help the supplier devise innovative tariff strategies. To the best of our knowledge, there are no existing studies which focus on generating density forecasts of electricity consumption from smart meter data. In this study, we evaluate the density, quantile and point forecast accuracy of different methods across one thousand consumption time series, recorded from both residential consumers and SMEs. We show that the KD and CKD methods accommodate the seasonality in consumption, and correctly distinguish weekdays from weekends. For each application, our comprehensive empirical comparison of the existing and proposed methods was undertaken using multiple performance scores. The results show strong potential for the models proposed in this thesis.

In this master's thesis I presented a new statistical method KDE+ (Kernel Density Estimation plus) that allows detecting clusters of points on the linear data. I created a self-standing application that enables anybody to try the method and apply it on their own data. One possible usage of the method and application is for the detection of critical roads sections with a high concentration of traffic accidents. Development of the application includes analysis of KDE+ statistical method, design of appropriate program structures and the implementation. Optimization were carried out to achieve higher performance after creating the prototype. At the end the software was validated by analysing vehicle collision data from the police database of the Czech Republic.

Dyer Island is thought to host one of the most abundant populations of white sharks on the planet; this is often credited to the large (55 – 60,000) Cape fur seal colony at Geyser Rock. Yet relatively little work has ever been produced from the area. This may be attributed to the harshness in its location as a study site, exposed to wind and swell from west to east which limits research periods. This study accounts for over 220 hrs of manual tracking at Dyer Island with a further 68 added from the inshore shallow areas of the bay. Sharks focused their movements and habitat use to reefs or channels that allowed access to Cape fur seals. Movement- Based Kernel Estimates (MKDE) were used to compute home range estimates for shark movements through and around the heterogeneous structures of Dyer Island and Geyser Rock. Inshore two core areas were revealed, one being the major reef system at Joubertsdam and the other at a kelp reef where the tracked shark had fed on a Cape fur seal. At Dyer Island one core area was identified in a narrow channel, ‘Shark Alley’, here a second tracked shark foraged for entire days within meters of rafting Cape fur seals. Rate of Movement (ROM) and Linearity (LI) of tracks were low during daytime and movements were focused around areas such as Shark Alley or other areas close to the seal colony before moving into deeper water or distant reefs with higher rates of ROM and LI at night. If moonlight was strong foraging would take place to the south of Geyser Rock but with higher ROM and LI than observed during the day. Foraging patterns in this study contrast studies from other sites in South Africa and home range and activity areas were comparatively much smaller than observed in Mossel Bay. It has been established that several known white sharks forage at Dyer Island and the other studied aggregation sites, such differences in foraging would suggest that they are able to adapt their foraging behaviour to suit the environment they are in; making them site specific in their foraging ecology. Both satellite and acoustic telemetry are revealing aggregation hotspots of white sharks in South Africa. It is important that such information is used to assist the recovery of the species which has been protected since 1991, yet is rarely considered in planning of coastal developments. / Dissertation (MSc)--University of Pretoria, 2012. / Zoology and Entomology / MSc / Unrestricted

The use of past archaeological survey data for examination of landscape dynamics became very popular during the last decades of the 20th century, when Geographical Information Systems analysis were introduced in archaeology. In the present thesis, past survey data from Northern Messenia’s Middle and Late Helladic periods are combined to the topography and the environment of the region. These data are examined under the GIS prism, which attempts to update our knowledge on this geographical area.             The main scope of this thesis is to examine potential settlement patterns and land use, connectivity between sites and sites’ hierarchies. In the first query, the Kernel Density analysis has been used for estimating settlements’ patterns, and to consequently estimate preference of specific topographical features for land use, such as slope. Based on the patterns formed as a result of the analysis conducted in the first query, connectivity and hierarchy between sites is being tested with the use of cost connectivity and visibility tools.             The outcome of this analysis shows that the inhabitants of the past were significantly interacting with the landscape, since they preferred to nest around the protective slopes of the Soulima and the Kyparissian valleys. The area around their settlements reveals that these inhabitants opted to cultivate in flat or marginal land, while visibility from the sites seems to be an important factor for monitoring the region. However, it has been proved that a good number of collaborating sites were required to supervise the entire territory, which disproves any hierarchical ranking between them. On the other hand, connectivity depicts potential movement over Northern Messenia’s terrain and indicates that a few sites in the heart of the study area were to be considered as panoptic meeting grounds of the eastern and the western side. In conclusion, the overall analysis reveals a potential spatial bond between sites rather than a relationship based on rivalry.