M.Com. (Economics) / In this study the use of distributed lags in the estimation of econometric equations is discussed with special reference to Shirley Almon's model of polinomically distributed lags. In chapter 2 of this study possible reasons for the existence of distributed lags as well as a number of distributed lag models are discussed. In chapter 3 the estimation of Almon lag models with and without the existence of end restrictions is discussed with special mention of the practical problems associated with such estimations. In chapter 4 the estimation of multi-variable Almon lags and the benefit of computer programs in the estimation thereof are discussed. In chapter 5 a procedure is given for the estimation of Almon lag models with examples of the estimation of two fuctions: Investment: Private: Non-Agriculture (IPNL) and Exports Excluding Gold (XSG).

Sensor network plays a significant role in determining the performance of network inference tasks. A wireless sensor network with a large number of sensor nodes can be used as an effective tool for gathering data in various situations. One of the major issues in WSN is developing an efficient protocol which has a significant impact on the convergence of the network. Parameter estimation is one of the most important applications of sensor network. In order to model such large and complex networks for estimation, efficient strategies and algorithms which take less time to converge are being developed. To deal with this challenge, an approach of having multilayer network structure to estimate parameter and reach convergence in less time is estimated by comparing it with known gossip distributed algorithm. Approached Multicast multilayer algorithm on a network structure of Gaussian mixture model with two components to estimate parameters were compared and simulated with gossip algorithm. Both the algorithms were compared based on the number of iterations the algorithms took to reach convergence by using Expectation Maximization Algorithm.Finally a series of theoretical and practical results that explicitly showed that Multicast works better than gossip in large and complex networks for estimation in consensus building strategies.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Hydraulic tomography (HT) has become a mature aquifer test technology over the last two decades. It collects nonredundant information of aquifer heterogeneity by sequentially stressing the aquifer at different wells and collecting aquifer responses at other wells during each stress. The collected information is then interpreted by inverse models. Among these models, the geostatistical approaches, built upon the Bayesian framework, first conceptualize hydraulic properties to be estimated as random fields, which are characterized by means and covariance functions. They then use the spatial statistics as prior information with the aquifer response data to estimate the spatial distribution of the hydraulic properties at a site. Since the spatial statistics describe the generic spatial structures of the geologic media at the site rather than site-specific ones (e. g., known spatial distributions of facies, faults, or paleochannels), the estimates are often not optimal. To improve the estimates, we introduce a general statistical framework, which allows the inclusion of site-specific spatial patterns of geologic features. Subsequently, we test this approach with synthetic numerical experiments. Results show that this approach, using conditional mean and covariance that reflect site-specific large-scale geologic features, indeed improves the HT estimates. Afterward, this approach is applied to HT surveys at a kilometerscale- fractured granite field site with a distinct fault zone. We find that by including fault information from outcrops and boreholes for HT analysis, the estimated hydraulic properties are improved. The improved estimates subsequently lead to better prediction of flow during a different pumping test at the site.

Dans cette thèse, nous nous proposons d'étudier quelques paramètres fonctionnels lorsque les données sont générées à partir d'un modèle de régression à indice simple. Nous étudions deux paramètres fonctionnels. Dans un premier temps nous supposons que la variable explicative est à valeurs dans un espace de Hilbert (dimension infinie) et nous considérons l'estimation de la densité conditionnelle par la méthode de noyau. Nous traitons les propriétés asymptotiques de cet estimateur dans les deux cas indépendant et dépendant. Pour le cas où les observations sont indépendantes identiquement distribuées (i.i.d.), nous obtenons la convergence ponctuelle et uniforme presque complète avec vitesse de l'estimateur construit. Comme application nous discutons l'impact de ce résultat en prévision non paramétrique fonctionnelle à partir de l'estimation de mode conditionnelle. La dépendance est modélisée via la corrélation quasi-associée. Dans ce contexte nous établissons la convergence presque complète ainsi que la normalité asymptotique de l'estimateur à noyau de la densité condtionnelle convenablement normalisée. Nous donnons de manière explicite la variance asymptotique. Notons que toutes ces propriétés asymptotiques ont été obtenues sous des conditions standard et elles mettent en évidence le phénomène de concentration de la mesure de probabilité de la variable fonctionnelle sur des petites boules. Dans un second temps, nous supposons que la variable explicative est vectorielle et nous nous intéressons à un modèle de prévision assez général qui est la régression robuste. A partir d'observations quasi-associées, on construit un estimateur à noyau pour ce paramètre fonctionnel. Comme résultat asymptotique on établit la vitesse de convergence presque complète uniforme de l'estimateur construit. Nous insistons sur le fait que les deux modèles étudiés dans cette thèse pourraient être utilisés pour l'estimation de l'indice simple lorsque ce dernier est inconnu, en utilisant la méthode d'M-estimation ou la méthode de pseudo-maximum de vraisemblance, qui est un cas particulier de la première méthode. / In this thesis, we propose to study some functional parameters when the data are generated from a model of regression to a single index. We study two functional parameters. Firstly, we suppose that the explanatory variable take its values in Hilbert space (infinite dimensional space) and we consider the estimate of the conditional density by the kernel method. We establish some asymptotic properties of this estimator in both independent and dependent cases. For the case where the observations are independent identically distributed (i.i.d.), we obtain the pointwise and uniform almost complete convergence with rateof the estimator. As an application we discuss the impact of this result in fuctional nonparametric prevision for the estimation of the conditional mode. In the dependent case we modelize the later via the quasi-associated correlation. Note that all these asymptotic properties are obtained under standard conditions and they highlight the phenomenon of concentration properties on small balls probability measure of the functional variable. Secondly we suppose that the explanatory variable takes values in the _nite dimensional space and we interest in a rather general prevision model whichis the robust regression. From the quasi-associated data, we build a kernel estimator for this functional parameter. As an asymptotic result we establish the uniform almost complete convergence rate of the estimator. We point out by the fact that these two models studied in this thesis could be used for the estimation of the single index of the model when the latter is unknown, by using the method of M-estimation or the pseudo-maximum likelihood method which is a particular case of the first method.

Ce sujet de recherche revêt, d'une part, un caractère théorique puisqu'il aborde le problème d'estimation des systèmes singuliers linéaires et non linéaires à temps discret pour lesquels très peu de résultats sont disponibles et, d'autre part, un aspect pratique, car le modèle utilisé est d'une station d'épuration des eaux usées à boues activées. Dans la partie théorique, nous nous sommes intéressés, dans un premier temps, à l'estimation d'état des systèmes singuliers linéaires en utilisant l'approche d'estimation à horizon glissant. Deux estimateurs optimaux, au sens des moindres carrés et au sens de la variance minimale, ont été présentés. L'analyse de la convergence et de la stabilité de ces estimateurs est traités. Ensuite, nous avons présenté une approche pour l'observation de la classe des systèmes non linéaires lipschitziens à temps discret. En supposant que la partie linéaire de cette classe de systèmes est variante dans le temps, le problème de l'estimation d'état d'un système non linéaire est transformé en un problème d'estimation d'état d'un système LPV. La condition de stabilité de l'observateur proposé est exprimée en terme d'inégalités matricielles linéaires (LMI). Enfin, dans la partie pratique, les résultats obtenus sont validés par une application à un modèle d'une station d'épuration des eaux usées à boues activées. / This subject of research holds, on the one hand, a theoretical character since it tackles the state estimation problem for linear and nonlinear singular discrete time systems for which very few results are available and, on the other hand, a practical aspect because the used model is an activated sludge process for wastewater treatment. In the theoretical part, we were interested firstly in the state estimation problem of linear singular systems using the moving horizon approach. We have presented two optimal estimators with the least squares and the minimum variance formulations. The analysis of the convergence and the stability of the estimators are derived. Then, an observers synthesis method for nonlinear Lipschitz discrete-time systems is proposed. By supposing that the linear part of this class of systems is time-varying, the state estimation problem of nonlinear system is transformed into a state estimation problem for LPV system. The stability condition of the proposed observer is derived in the form of linear matrix inequalities (LMIs). Finally, in the practical part, the obtained results are validated by an application to an activated sludge process for wastewater treatment.

The study of interest pass through has been on the core attention of researchers since it serves as an incentive to evaluate the accuracy of monetary policy transmission mechanism. Therefore there are a lot of studies conducted under this topic encompassing a large number of countries and data. My aim, inspired by the great previous works, is to develop the same topic but by focusing on Balkan countries and more specifically on Albania. Being a developing country located on the heart of Balkan while aspiring the EU integration, Albania has gone under a considerable number of economic reforms which are also reflected on the degree and speed of transmission of policy rates to landing rates and on the determinants of such rates. Crisis of 2008 had a global impact but yet several conducted studies revealed that Albania was not directly affected by it. My contribution to this thesis consists in measuring how the pass-through mechanism performance was affected by the crisis and the implications derived from it. Powered by TCPDF (www.tcpdf.org)

Contemporary cosmology is a vibrant field, with data and observations increasing rapidly. This allows for accurate estimation of the parameters describing our cosmological model. In this thesis we present new research based on two different types of cosmological observations, which probe the universe at multiple epochs. We begin by reviewing the current concordance cosmological paradigm, and the statistical tools used to perform parameter estimation from cosmological data. We highlight the initial conditions in the universe and how they are detectable using the Cosmic Microwave Background radiation. We present the angular power spectrum data from temperature observations made with the Atacama Cosmology Telescope (ACT) and the methods used to estimate the power spectrum from temperature maps of the sky. We then present a cosmological analysis using the ACT data in combination with observations from the Wilkinson Microwave Anisotropy Probe to constrain parameters such as the effective number of relativistic species and the spectral index of the primordial power spectrum, which we constrain to deviate from scale invariance at the 99% confidence limit. We then use this combined dataset to constrain the primordial power spectrum in a minimally parametric framework, finding no evidence for deviation from a power-law spectrum. Finally we present Bayesian Estimation Applied to Multiple Species, a parameter estimation technique using photometric Type Ia Supernova data to estimate cosmological parameters in the presence of contaminated data. We apply this algorithm to the full season of the Sloan Digital Sky Survey II Supernova Search, and find that the constraints are improved by a factor of three relative to the case where one uses a smaller, spectroscopically confirmed subset of supernovae.

Master of Science / Department of Statistics / James W. Neill