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Handling auxiliary variables in survey sampling and nonresponse
Ce manuscrit est consacré à l’utilisation d’informations auxiliaires en échantillonnage et en non-réponse. Nous nous intéressons à l'intégration de variables auxiliaires dans les méthodes d'échantillonnage et au traitement de la non-réponse afin d'améliorer l'efficacité et la précision des enquêtes. Nous traitons également du calcul de la précision d'estimateurs. En effet, les variances deviennent rapidement difficiles à calculer lorsque les méthodes d’estimation sont sophistiquées. La thèse est organisée comme suit. Le premier chapitre consiste en une introduction à quelques concepts d’échantillonnage et de non-réponse. Dans le deuxième chapitre, nous développons un plan d'échantillonnage pour un inventaire forestier afin de satisfaire un certain nombre d'exigences. L’échantillon doit optimiser le travail des équipes au sol tout en assurant la sélection de tous les types d’arbres. Pour atteindre les objectifs, un plan d'échantillonnage équilibré et stratifié est utilisé dans un échantillon à deux degrés. Dans le troisième chapitre, nous discutons du calcul de la variance dans le cas d'une intersection entre deux échantillons indépendants. La variance et son estimateur peuvent être décomposés conditionnellement à un échantillon ou conditionnellement à l'autre. Dans des situations spécifiques, comme dans le cas de la non-réponse, il en résulte des simplifications bien pratiques. Le quatrième chapitre présente une méthode de linéarisation pour l'estimation de la variance en présence de non-réponse. Dans le cinquième chapitre, une méthode d'imputation pour une non-réponse en fromage suisse est développée. Cette méthode d'imputation utilise un plan d'échantillonnage équilibré et stratifié., This manuscript is dedicated to the use of auxiliary information in survey sampling and nonresponse. We are interested in the integration of auxiliary variables in sampling methods and in the treatment of nonresponse to improve the efficiency and the precision of surveys. We also deal with the calculation of the precision of estimators. Indeed, variances rapidly become difficult to calculate when the estimation methods are sophisticated. The thesis is organized as follows. The first chapter consists in an introduction to some concepts of survey sampling and nonresponse. In the second chapter, we develop a sampling design for a forest inventory in order to satisfy a number of requirements. The sample needs to optimize the work of the ground teams while ensuring the selection of every type of trees. To meet the objectives, stratified balanced sampling is used in a two-stage sample. In the third chapter, we discuss the calculation of the variance when two independent samples intersect. The variance and its estimator can be decomposed conditionally to one sample or conditionally to the other one. In specific situations, as in the nonresponse case, it results in convenient simplifications. The fourth chapter presents a linearization method for the estimation of the variance in the presence of nonresponse. In the fifth chapter, an imputation method for Swiss cheese nonresponse is developed. This imputation method uses stratified balanced sampling.
Incorporating spatial and operational constraints in the sampling designs for forest inventories
In the province of Quebec, Canada, the forest is examined through regular inventories. Requirements for the spreading and the type of trees and for the cost are difficult to manage. We show that modern and advanced sampling techniques can be used to improve the planning of the forest inventories, even if there are many requirements. Our design includes balanced sampling, highly stratified balanced sampling and sample spreading through a two stage sample. The impact of these techniques on the satisfaction of the requirements and on the precision of survey estimates is investigated using field data from a Quebec inventory.
Incorporating Spatial and Operational Constraints in the Sampling Designs for Forest Inventories
Goals of forest inventories include understanding the forest temporal evolution and monitoring fragile ecosystems. In the province of Quebec, Canada, their implementation faces challenging methodological problems. The survey area covers a large territory which is hardly accessible and has diverse forest. Main operational goals are to spread the sampled plots throughout the survey area and to well represent all forest types in the sample. They are hard to achieve while keeping the costs within budget. Usually, a two dimensional systematic sampling design is applied and the rich auxiliary information is only used at the estimation stage. We show how to use modern and advanced sampling techniques to improve the planning of forest inventories, considering many requirements. For the Quebec forest inventory, we build a two-stage sampling design that has clusters of plots to optimize field work and predetermined sample sizes for forest types. Constraints of spreading the sample in the whole territory and of balancing according to auxiliary variables are also implemented. To meet these requirements, we use unequal inclusion probabilities, balanced sampling, highly stratified balanced sampling, and sample spreading. The impact of these novel techniques on the implementation of requirements and on the precision of survey estimates is investigated using Quebec inventory data.
Incorporating spatial and operational constraints in the sampling designs for forest inventories
In the province of Quebec, Canada, the forest is examined through regular inventories. Requirements for the spreading and the type of trees and for the cost are difficult to manage. We show that modern and advanced sampling techniques can be used to improve the planning of the forest inventories, even if there are many requirements. Our design includes balanced sampling, highly stratified balanced sampling and sample spreading through a two stage sample. The impact of these techniques on the satisfaction of the requirements and on the precision of survey estimates is investigated using field data from a Quebec inventory.