In a nonparametric setting, the functional form of the relationship between the response variable and the associated predictor variables is unspecified; however it is assumed to be a smooth function. The main aim of nonparametric regression is to highlight an important structure in data without any assumptions about the shape of an underlying regression function. In regression, the random and fixed design models should be distinguished. Among the variety of nonparametric regression estimators currently in use, kernel type estimators are most popular. Kernel type estimators provide a flexible class of nonparametric procedures by estimating unknown function as a weighted average using a kernel function. The bandwidth which determines the influence of the kernel has to be adapted to any kernel type estimator. Our focus is on Nadaraya-Watson estimator and Local Linear estimator which belong to a class of kernel type regression estimators called local polynomial kerne l estimators. A closely related problem is the determination of an appropriate sample size that would be required to achieve a desired confidence level of accuracy for the nonparametric regression estimators. Since sequential procedures allow an experimenter to make decisions based on the smallest number of observations without compromising accuracy, application of sequential procedures to a nonparametric regression model at a given point or series of points is considered. The motivation for using such procedures is: in many applications the quality of estimating an underlying regression function in a controlled experiment is paramount; thus, it is reasonable to invoke a sequential procedure of estimation that chooses a sample size based on recorded observations that guarantees a preassigned accuracy. We have employed sequential techniques to develop a procedure for constructing a fixed-width confidence interval for the predicted value at a specific point of the independent variable. These fixed-width confidence intervals are developed using asymptotic properties of both Nadaraya-Watson and local linear kernel estimators of nonparametric kernel regression with data-driven bandwidths and studied for both fixed and random design contexts. The sample sizes for a preset confidence coefficient are optimized using sequential procedures, namely two-stage procedure, modified two-stage procedure and purely sequential procedure. The proposed methodology is first tested by employing a large-scale simulation study. The performance of each kernel estimation method is assessed by comparing their coverage accuracy with corresponding preset confidence coefficients, proximity of computed sample sizes match up to optimal sample sizes and contrasting the estimated values obtained from the two nonparametric methods with act ual values at given series of design points of interest. We also employed the symmetric bootstrap method which is considered as an alternative method of estimating properties of unknown distributions. Resampling is done from a suitably estimated residual distribution and utilizes the percentiles of the approximate distribution to construct confidence intervals for the curve at a set of given design points. A methodology is developed for determining whether it is advantageous to use the symmetric bootstrap method to reduce the extent of oversampling that is normally known to plague Stein's two-stage sequential procedure. The procedure developed is validated using an extensive simulation study and we also explore the asymptotic properties of the relevant estimators. Finally, application of our proposed sequential nonparametric kernel regression methods are made to some problems in software reliability and finance.

L'objectif général de cette thèse était de proposer une solution de localisation en intérieur à la fois simple et capable de surmonter les défis de la propagation dans les environnements en intérieur. Pour ce faire, un système de localisation basé sur la méthode des signatures et adoptant le temps d'arrivée du signal de l'émetteur au récepteur comme signature, a été proposé. Le système présente deux architectures différentes, une première orientée privée utilisant la méthode d'accès multiple à répartition par code et une deuxième centralisée basée sur la méthode d'accès multiple à répartition dans le temps. Le système calcule la position de l'objet d'intérêt par la méthode de noyau. Une comparaison expérimentale entre le système à architecture orientée privée et un système de localisation sonore déjà existant et basé sur la méthode de trilatération, a permis de confirmer les résultats trouvés dans le cas de la localisation par ondes radiofréquences. Cependant, nos expérimentations étaient les premières à montrer l'effet de la réverbération sur les approches de la localisation acoustique. Dans un second lieu, un système de localisation basé sur la technique de retournement temporel, permettant une localisation simultanée de sources avec différentes précisions, a été testé par simulations en faisant varier le nombre de sources. Ce système a été ensuite validé par expérimentations. Dans la dernière partie de notre étude, nous nous sommes intéressés à la réduction de l'audibilité du signal utile à la localisation par recours à la psycho-acoustique. Un filtre défini à partir du seuil d'audition absolu a été appliqué au signal de localisation. Nos résultats ont montré une amélioration de la précision de localisation comparé au système de localisation sans modèle psycho-acoustique et ce grâce à l'utilisation d'un filtre adapté au modèle psycho-acoustique à la réception. Par ailleurs, l'écoute du signal après application du modèle psycho-acoustique a montré une réduction significative de son audibilité comparée à celle du signal original. / The objective of this PhD is to propose a location solution that should be simple and robust to multipath that characterizes the indoor environments. First, a location system that exploits the time domain of channel parameters has been proposed. The system adopts the time of arrival of the path of maximum amplitude as a signature and estimates the target position through nonparametric kernel regression. The system was evaluated in experiments for two main configurations: a privacy-oriented configuration with code-division multiple-access operation and a centralized configuration with time-division multiple-access operation. A comparison between our privacy-oriented system and another acoustic location system based on code-division multiple-access operation and lateration method confirms the results found in radiofrequency-based localization. However, our experiments are the first to demonstrate the detrimental effect that reverberation has on acoustic localization approaches. Second, a location system based on time reversal technique and able to localize simultaneously sources with different location precisions has been tested through simulations for different values of the number of sources. The system has then been validated by experiments. Finally, we have been interested in reducing the audibility of the localization signal through psycho-acoustics. A filter, set from the absolute threshold of hearing, is then applied to the signal. Our results showed an improvement in precision, when compared to the location system without psychoacoustic model, thanks to the use of matched filter at the receiver. Moreover, we have noticed a significant reduction in the audibility of the filtered signal compared to that of the original signal.