Parmi les outils les plus classiques de l'Analyse Multivariée, les Composantes Principales sont aussi un des plus anciens puisqu'elles furent introduites il y a plus d'un siècle par Pearson (1901) et redécouvertes ensuite par Hotelling (1933). Aujourd'hui, cette méthode est abondamment utilisée en Sciences Sociales, en Economie, en Biologie et en Géographie pour ne citer que quelques disciplines. Elle a pour but de réduire de façon optimale (dans un certain sens) le nombre de variables contenues dans un jeu de données.<p>A ce jour, les méthodes d'inférence utilisées en Analyse en Composantes Principales par les praticiens sont généralement fondées sur l'hypothèse de normalité des observations. Hypothèse qui peut, dans bien des situations, être remise en question.<p><p>Le but de ce travail est de construire des procédures de test pour l'Analyse en Composantes Principales qui soient valides sous une famille plus importante de lois de probabilité, la famille des lois elliptiques. Pour ce faire, nous utilisons la méthodologie de Le Cam combinée au principe d'invariance. Ce dernier stipule que si une hypothèse nulle reste invariante sous l'action d'un groupe de transformations, alors, il faut se restreindre à des statistiques de test également invariantes sous l'action de ce groupe. Toutes les hypothèses nulles associées aux problèmes considérés dans ce travail sont invariantes sous l'action d'un groupe de transformations appellées monotones radiales. L'invariant maximal associé à ce groupe est le vecteur des signes multivariés et des rangs des distances de Mahalanobis entre les observations et l'origine. <p><p>Les paramètres d'intérêt en Analyse en composantes Principales sont les vecteurs propres et valeurs propres de matrices définies positives. Ce qui implique que l'espace des paramètres n'est pas linéaire. Nous développons donc une manière d'obtenir des procédures optimales pour des suite d'experiences locales courbées. <p>Les statistiques de test introduites sont optimales au sens de Le Cam et mesurables en l'invariant maximal décrit ci-dessus.<p>Les procédures de test basées sur ces statistiques possèdent de nombreuses propriétés attractives: elles sont valides sous la famille des lois elliptiques, elles sont efficaces sous une densité spécifiée et possèdent de très bonnes efficacités asymptotiques relatives par rapport à leurs concurrentes. En particulier, lorsqu'elles sont basées sur des scores Gaussiens, elles sont aussi efficaces que les procédures Gaussiennes habituelles et sont bien plus efficaces que ces dernières si l'hypothèse de normalité des observations n'est pas remplie. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Financial liberalization in South Africa was a process that took the form of various legal reforms very a long period of time. This study uses quarterly financial data from 1969 quarter one to 2009 quarter four to analyse this process. The data used was pertinent to the financial liberalization theorem by McKinnon (1973) and Shaw (1973). The examination of the relationships between the various macro economic variables has important implications for effective policy formulation. The empirical analysis is carried out in four phases: the preliminary analysis, the principal component analysis (PCA), the cointegration analysis and pair wise Granger causality tests. The preliminary analysis examines trends over the sample period and reports the on the correlation between the selected variables. The PCA analysis was used to create indexes for financial liberalization, taking into account the phase wise nature of legal reforms. The generated index was representative of the process of financial liberalization from 1969 to 2009. A financial development index was also created using the various traditional measures of financial development and through PCA which investigated interrelationships among the variables according to their common sources of movement. Cointegration analysis is carried out using the Johansen cointegration procedure which investigates whether there is long-run comovement between South African economic growth and the selected macroeconomic variables. Where cointegration is found, Vector Error-Correction Models (VECMs) are estimated in order to examine the short-run adjustments. For robustness, many control variables were added into the model. The results showed that there are positive long run relationships between economic growth and financial liberalization, financial development and a negative relationship with interest rates. The Granger results suggested that the MS hypothesis does not manifest accurately in the South African data. The implications of the results were that financial liberalization has had positive effects on economic growth and thus any impediments to full financial liberalization must be removed albeit with considerations towards employment and local productivity. Financial development also possessed positive long run relationships with economic growth, although results differed based on the financial development proxy used. Thus, financial development must be improved primarily through liberalizing the banking sector and spurring savings.

The performance of three methods of mortality modelling and forecasting are compared. These include the basic Lee–Carter and two functional demographic models; the basic Hyndman–Ullah and the weighted Hyndman–Ullah. Using age-specific data from the Human Mortality Database of two developed countries, France and the UK (England&amp;Wales), these methods are compared; through within-sample forecasting for the years 1999-2018. The weighted Hyndman–Ullah method is adjudged superior among the three methods through a comparison of mean forecast errors and qualitative inspection per the dataset of the selected countries. The weighted HU method is then used to conduct a 32–year ahead forecast to the year 2050.

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The Casas Grandes region of northern Mexico is an understudied, though important, part of the culture area that has come to be known as the Northwest/Southwest (NW/SW). What studies have been conducted in the Casas Grandes region have focused on the Medio Period (approximately 1200-1450 AD) and the large site of Paquimé. Only a small amount of research has been conducted on the preceding Viejo Period (approximately 700-1200 AD). In this thesis, I create a clearing house of published Viejo Period architectural features excavated in the Casas Grandes region. I also analyze those features to develop our understanding of the materials and technological choices used to construct these features, and to evaluate the validity of sub-regional zones which have begun to develop within the archaeological literature from this area. These analyses include a qualitative analysis of the excavated architectural features as well as statistical clustering methods, a Principal Components Analysis, and a Correspondence Analysis of available architectural data. I ultimately propose revisions to the existing architectural typology for the Viejo Period and the abandonment of the concept of sub-regional zones within the Casas Grandes region. I also observe some emerging patterns within the architectural data and suggest that further research is needed to fully understand the distribution of architectural features throughout the region.

The National Academy of Sciences recently published a report which calls for improvements to the field of forensic science. Their report criticized many forensic disciplines for failure to establish rigorously-tested methods of comparison, and encouraged more research in these areas to establish limitations and assess error rates. This study applies chemometric and statistical methods to current and developing analytical techniques in fiber analysis. In addition to analysis of commercially available dyed textile fibers, two pairs of dyes are selected based for custom fabric dyeing on the similarities of their absorbance spectra and dye molecular structures. Visible absorption spectra for all fiber samples are collected using microspectrophotometry (MSP) and mass spectra are collected using electrospray ionization (ESI) mass spectrometry. Statistical calculations are performed using commercial software packages and software written in-house. Levels of Type I and Type II error are examined for fiber discrimination based on hypothesis testing of visible absorbance spectra using a nonparametric permutation method. This work also explores evaluation of known and questioned fiber populations based on an assessment of p-value distributions from questioned-known fiber comparisons with those of known fiber self-comparisons. Results from the hypothesis testing are compared with principal components analysis (PCA) and discriminant analysis (DA) of visible absorption spectra, as well as PCA and DA of ESI mass spectra. The sensitivity of a statistical approach will also be discussed in terms of how instrumental parameters and sampling methods may influence error rates.

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