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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.
Systematic sampling is a minimal support design
In order to select a sample in a finite population of N units with given inclusion probabilities, it is possible to define asamplingdesign on at most N samples that have a positive probability of being selected. Designs defined on minimal sets of samples are called minimum supportdesigns. It is shown that, for any vector of inclusion probabilities, systematicsampling always provides a minimum supportdesign. This property makes it possible to extensively compute the samplingdesign and the joint inclusion probabilities. Random systematicsampling can be viewed as the random choice of a minimum supportdesign. However, even if the population is randomly sorted, a simple example shows that some joint inclusion probabilities can be equal to zero. Another way of randomly selecting a minimum supportdesign is proposed, in such a way that all the samples have a positive probability of being selected, and all the joint inclusion probabilities are positive.
A new resampling method for sampling designs without replacement: the doubled half bootstrap
A new and very fast method of bootstrap for sampling without replacement from a finite population is proposed. This method can be used to estimate the variance in sampling with unequal inclusion probabilities and does not require artificial populations or utilization of bootstrap weights. The bootstrap samples are directly selected from the original sample. The bootstrap procedure contains two steps: in the first step, units are selected once with Poisson sampling using the same inclusion probabilities as the original design. In the second step, amongst the non-selected units, half of the units are randomly selected twice. This procedure enables us to efficiently estimate the variance. A set of simulations show the advantages of this new resampling method.
A new resampling method for sampling designs without replacement: the doubled half bootstrap
A new and very fast method of bootstrap for sampling without replacement from a finite population is proposed. This method can be used to estimate the variance in sampling with unequal inclusion probabilities and does not require artificial populations or utilization of bootstrap weights. The bootstrap samples are directly selected from the original sample. The bootstrap procedure contains two steps: in the first step, units are selected once with Poisson sampling using the same inclusion probabilities as the original design. In the second step, amongst the non-selected units, half of the units are randomly selected twice. This procedure enables us to efficiently estimate the variance. A set of simulations show the advantages of this new resampling method.
A Direct Bootstrap Method for Complex Sampling Designs From a Finite Population
In complex designs, classical bootstrap methods result in a biased variance estimator when the sampling design is not taken into account. Resampled units are usually rescaled or weighted in order to achieve unbiasedness in the linear case. In the present article, we propose novel resampling methods that may be directly applied to variance estimation. These methods consist of selecting subsamples under a completely different sampling scheme from that which generated the original sample, which is composed of several sampling designs. In particular, a portion of the subsampled units is selected without replacement, while another is selected with replacement, thereby adjusting for the finite population setting. We show that these bootstrap estimators directly and precisely reproduce unbiased estimators of the variance in the linear case in a time-efficient manner, and eliminate the need for classical adjustment methods such as rescaling, correction factors, or artificial populations. Moreover, we show via simulation studies that our method is at least as efficient as those currently existing, which call for additional adjustment. This methodology can be applied to classical sampling designs, including simple random sampling with and without replacement, Poisson sampling, and unequal probability sampling with and without replacement.
Variance approximation under balanced sampling
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.
Fast Balanced Sampling for Highly Stratified Population
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.
Fast balanced sampling for highly stratified population
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