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In general, the precise date of onset of pregnancy is unknown and may only be estimated from ultrasound biométrie measurements of the embryo. We want to estimate the density of the random variables corresponding to the interval between last menstrual period and true onset of pregnancy. The observations correspond to the variables of interest up to an additive noise. We suggest an estimation procedure based on deconvolution. It requires the knowledge of the density of the noise which is not available. But we have at our disposal another specific sample with replicate observations for twin pregnancies. This allows both to estimate the noise density and to improve the deconvolution step. Convergence rates of the final estimator are studied and compared with other settings. Our estimator involves a cut-off parameter for which we propose a cross-validation type procedure. Lastly, we estimate the target density in spontaneous pregnancies with an estimation of the noise obtained from replicate observations in twin pregnancies.

This chapter contains sections titled: Introduction Theory and formulae Bibliography Examples and use of the tables References

Rainfall onset date (ROD) influences farmer planting decisions, yet there is a dearth of information on the extent to which ROD influences crop yield. This study assesses the effect of ROD on the yield of four crops (Maize, millet, rice, and sorghum) in Ghana. It uses crop yields from the Ministry of Food and Agriculture (MoFA) and the Food and Agriculture Organization (FAO), and employs the Decision Support System for Agro-technology Transfer (DSSAT) crop model to simulate maize yields from 1985 to 2004. The crop model simulations were forced with weather data from the gridded Global Meteorological Forcing Dataset (GMFD). The relationship between crop yields and RODs from three datasets (observed, satellite, and GMFD) are studied. The results of the study show a good correlation between MoFA and FAO crop yield data (with correlation coefficient (r) of 0.97, 0.92, 0.77, and 0.99 for maize, millet, rice, and sorghum, respectively). RODs from satellite observation feature a high correlation with RODs from station observation (r = 0.72), but RODs from GMFD feature weak correlations (r < 0.3) with both observation datasets. The study finds a negative correlation between observed RODs and crop yields (i.e. an early onset corresponds to high yields) but a positive correlation between GMFD RODs and crop yields (i.e. an early onset correspondence to low yields). The DSSAT model reproduces the observed yield pattern, but with substantial biases. The findings of this study can be used to advise small-holder farmers on planting dates and crop variety selection.