Tillé, Yves

2019, Ecker, Klaus, Meier, Eliane, Lanz, Adrian, Tillé, Yves

We describe a complex probability sampling design for a long-term monitoring program of agricultural species and habitats in Switzerland. The program aims to monitor farmland biodiversity in predefined regions and to assess the effectiveness of funded management in promoting it. Such monitoring requires the costly collection of {\it in situ} information on species, habitat types and structures at the plot and landscape level. Sample efficiency is challenging since the majority of habitats and species is typically rare, spatially structured and previously unknown in the sampling frame. Efficient sampling aims to minimize the collection of redundant information from the big regions and the dominant habitat types. The sample should be spatially spread and balanced across environmental gradients. Decisions should be made to allocate the sampling effort within and across sample sites. Finally, the survey organization has to be simple to implement in the field. In Switzerland zoological data are already collected on a regular grid of 1 km$^2$. We propose an additional three-stage sampling scheme for the static survey of habitats and plant species on the total agrarian landscape. An extra sample scheme is defined to monitor areas with funded biodiversity management. Both sampling designs use modern sampling techniques, such as unequal probability sampling, balancing, spatial spreading and self-weighting to ensure sample efficiency at all sampling stages. The efficiency of balancing, spreading and sample size allocation is demonstrated in simulation studies. A power analysis suggests that changes of $5-10\%$ can be statistically detected for a majority of the target habitats.

2015-6-15, Vallée, Audrey-Anne, Ferland-Raymond, Bastien, Rivest, Louis-Paul, Tillé, Yves

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.

, Nedyalkova, Desislava, Tillé, Yves

In some cases model-based and model-assisted inferences can lead to very different estimators. These two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator, a strategy being a pair composed of a sampling design and an estimator. We show that, under a linear model, the optimal model-assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the Horvitz–Thompson estimator. If the heteroscedasticity of the model is ‘fully explainable’ by the auxiliary variables, then this strategy is also optimal in a model-based sense. Moreover, under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model, the best linear unbiased estimator and the Horvitz–Thompson estimator are equal. Finally, it is possible to construct a single estimator for both the design and model variance. The inference can thus be valid under the sampling design and under the model.

, Langel, Matti, Tillé, Yves

This paper attempts to make the link between two of Corrado Gini’s contributions to statistics: the famous inequality measure that bears his name and his work in the early days of balanced sampling. Some important notions of the history of sampling such as representativeness, randomness, and purposive selection are clarified before balanced sampling is introduced. The Gini index is described, as well as its estimation and variance estimation in the sampling framework. Finally, theoretical grounds and some simulations on real data show how some well used auxiliary information and balanced sampling can enhance the accuracy of the estimation of the Gini index.

2015-9-3, Vallée, Audrey-Anne, Ferland-Raymond, Bastien, Rivest, Louis-Paul, Tillé, Yves

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.

2014-6, Hasler, Caren, Tillé, Yves

Balanced sampling is a very efficient sampling design when the variable of interest is correlated to the auxiliary variables on which the sample is balanced. Chauvet (2009) proposed a procedure to select balanced samples in a stratified population. Unfortunately, Chauvet's procedure can be slow when the number of strata is very large. In this paper, we propose a new algorithm to select balanced samples in a stratified population. This new procedure is at the same time faster and more accurate than Chauvet's. Balanced sampling can then be applied on a highly stratified population when only a few units are selected in each stratum. This algorithm turns out to be valuable for many applications. For instance, it can improve the quality of the estimates produced by multistage surveys for which only one or two primary sampling units are selected in each stratum. Moreover, this algorithm may be used to treat nonresponse.

, Hasler, Caren, Tillé, Yves

Balanced sampling is a very efficient sampling design when the variable of interest is correlated to the auxiliary variables on which the sample is balanced. A procedure to select balanced samples in a stratified population has previously been proposed. Unfortunately, this procedure becomes very slow as the number of strata increases and it even fails to select samples for some large numbers of strata. A new algorithm to select balanced samples in a stratified population is proposed. This new procedure is much faster than the existing one when the number of strata is large. Furthermore, this new procedure makes it possible to select samples for some large numbers of strata, which was impossible with the existing method. Balanced sampling can then be applied on a highly stratified population when only a few units are selected in each stratum. Finally, this algorithm turns out to be valuable for many applications as, for instance, for the handling of nonresponse

2015-7-15, Vallée, Audrey-Anne, Ferland-Raymond, Bastien, Rivest, Louis-Paul, Tillé, Yves

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.

2012-9-4, Nedyalkova, Desislava, Tillé, Yves

In model-based inference, the selection of balanced samples has been considered to give protection against misspecification of the model. A recent development in finite population sampling is that balanced samples can be randomly selected. There are several possible strategies that use balanced samples. We give a definition of balanced sample that embodies overbalanced, mean-balanced, and $\pi$-balanced samples, and we derive strategies in order to equalize a $d$-weighted estimator with the best linear unbiased estimator. We show the value of selecting a balanced sample with inclusion probabilities proportional to the standard deviations of the errors with the Horvitz-Thompson estimator. This is a strategy that is design-robust and efficient. We show its superiority compared to other strategies that use balanced samples in the model-based framework. In particular, we show that this strategy is preferable to the use of overbalanced samples in the polynomial model. The problem of bias-robustness is also discussed, and we show how overspecifying the model can protect against misspecification.

, Deville, Jean-Claude, Tillé, Yves

A balanced sampling design has the interesting property that Horvitz–Thompson estimators of totals for a set of balancing variables are equal to the totals we want to estimate, therefore the variance of Horvitz–Thompson estimators of variables of interest are reduced in function of their correlations with the balancing variables. Since it is hard to derive an analytic expression for the joint inclusion probabilities, we derive a general approximation of variance based on a residual technique. This approximation is useful even in the particular case of unequal probability sampling with fixed sample size. Finally, a set of numerical studies with an original methodology allows to validate this approximation.