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This article addresses the opportunistic use of satellite downlink attenuation measurements for the site-specific estimation of rainfall rate. In particular, this article proposes a regression model characterized by the introduction of correction elements extracted from the frequency-domain analysis of the attenuation time series, and the use of a simple linear regression function with a small modification, which allows to using a negative intercept with the goal of minimizing the maximum error (large underestimation/overestimation). The performance, assessed using attenuation measurements of a satellite downlink in Q/V band shows that the proposed model allows to estimate the rainfall rate with low average error and low maximum error with respect to a more standard ITU model, so as to offer more reliable estimations. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the mean of a symmetric log-concave distribution under the constraint that only a single bit per sample from this distribution is available to the estimator. We study the mean squared error as a function of the sample size (and hence the number of bits). We consider three settings: first, a centralized setting, where an encoder may release $n$ bits given a sample of size $n$ , and for which there is no asymptotic penalty for quantization; second, an adaptive setting in which each bit is a function of the current observation and previously recorded bits, where we show that the optimal relative efficiency compared to the sample mean is precisely the efficiency of the median; lastly, we show that in a distributed setting where each bit is only a function of a local sample, no estimator can achieve optimal efficiency uniformly over the parameter space. We additionally complement our results in the adaptive setting by showing that one round of adaptivity is sufficient to achieve optimal mean-square error. [ABSTRACT FROM AUTHOR]

• Estimation error with model-based sampling can be related to samples properties. • A criterion can be derived from the expression of theoretical estimation errors. • Such a criterion can guide sampling sites selection to minimise estimation errors. • The framework demonstrates the interest in clustering approaches for sampling. Model sampling has proven to be an interesting approach to optimize the sampling of an agronomic variable of interest at the field level. The use of a model improves the quality of the estimates by making it possible to integrate the information provided by one or more auxiliary data. It has been shown that such an approach gives better estimations compared to more traditional approaches. Through a statistical work describing the properties of model sampling variance, this paper details how the different factors either related to sample characteristics or to the correlation between the auxiliary data and the variable of interest, affect estimation error. The resulting equations show that the use of samples with a mean close to the field mean and with a substantial dispersion reduces the estimation variance. On the basis of these statistical considerations, a variance criterion is defined to compare sample properties. The lower the value of the criterion of a sample, the lower the variance of the estimate and the expected errors. These theoretical insights were applied to real commercial vine fields in order to validate the demonstration. Nine vine fields were considered with the objective to provide the best yield estimation. High resolution vegetative index derived from airborne multispectral image was used to drive the sampling and the estimation. The theoretical considerations were verified on the nine fields; as the observed estimation errors correspond quite well to the values predicted by the equations. The selection of a large number of random samples from these fields confirms that samples associated with higher values of the chosen criterion result, on average, in larger yield estimation errors. Samples with the highest criterion values are associated with mean estimation errors up to two times larger than those of average samples. Random sampling is also compared to two target sampling approaches (Clustering based on quantiles or on k-means algorithm) commonly considered in the literature, whose characteristics improve the value of the proposed criterion. It is shown that these sampling strategies produce samples associated with criterion values up to 100 times smaller than random sampling. The use of these easy-to-implement methods thus guarantees to reduce the variance of the estimation and the estimation errors. [ABSTRACT FROM AUTHOR]