Debiased machine learning of conditional average treatment effects and other causal functions

Summary This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine learning tools. We represent this structural function as a conditional expectation of an unbiased signal that depends on a nuisance parameter, which we estimate by modern machine learning techniques. We first adjust the signal to make it insensitive (Neyman-orthogonal) with respect to the first-stage regularisation bias. We then project the signal onto a set of basis functions, which grow with sample size, to get the best linear predictor of the structural function. We derive a complete set of results for estimation and simultaneous inference on all parameters of the best linear predictor, conducting inference by Gaussian bootstrap. When the structural function is smooth and the basis is sufficiently rich, our estimation and inference results automatically target this function. When basis functions are group indicators, the best linear predictor reduces to the group average treatment/structural effect, and our inference automatically targets these parameters. We demonstrate our method by estimating uniform confidence bands for the average price elasticity of gasoline demand conditional on income.

Effect of Septoria brown spot on soybean yield in Illinois

Brown spot caused by Septoria glycines is a prevalent foliar disease in all soybean production areas. Application of foliar fungicides after bloom reduces the disease severity, yet yield responses are not consistent among locations and years. Our research goal was to determine the effect of different levels of Septoria brown spot on yield. Different levels of disease severity were effectively obtained in the field by weekly application of chlorothalonil for three, six, and nine times after disease inoculation at V3/V4 stage. Fungicide treatments had a significant effect on vertical progress and chlorotic area with no statistically significant effect on yield. Soybean yield was negatively correlated with vertical progress of the disease (r = −0.36). The vertical progress was the best linear predictor of yield. Based on this model, when the vertical progress of brown spot at R6 increased by 10%, the yield decreased by 142.13 kg/ha (3.4%). A variance component analyses of our data showed that location was the most critical factor, illustrating the significant effect of local environmental conditions on the disease. Power analyses indicated that at least eight locations are needed to detect an effect of 269 kg/ha. Our results provide useful information to improve the experimental design for future experiments addressing the yield constrain by late season diseases of soybean.

Linear Prediction of a True Score From a Direct Estimate and Several Derived Estimates

Statistical prediction problems often involve both a direct estimate of a true score and covariates of this true score. Given the criterion of mean squared error, this study determines the best linear predictor of the true score given the direct estimate and the covariates. Results yield an extension of Kelley’s formula for estimation of the true score to cases in which covariates are present. The best linear predictor is a weighted average of the direct estimate and of the linear regression of the direct estimate onto the covariates. The weights depend on the reliability of the direct estimate and on the multiple correlation of the true score with the covariates. One application of the best linear predictor is to use essay features provided by computer analysis and an observed holistic score of an essay provided by a human rater to approximate the true score corresponding to the holistic score.

MSE of the best linear predictor in nonorthogonal models

The problem of computing the mean squared error (MSE) of the best linear predictor (BLP) in finite discrete spectrum with an additive white noise models(FDSWNMs) for an observed time series is considered. This is done under the assumption that the corresponding vectors in models for finite observation of this time series are not orthogonal.

Using the best linear predictor (BLP) in the selection between and among half-sib progenies of the CMS-39 maize population

Data of corn ear production (kg/ha) of 196 half-sib progenies (HSP) of the maize population CMS-39 obtained from experiments carried out in four environments were used to adapt and assess the BLP method (best linear predictor) in comparison with to the selection among and within half-sib progenies (SAWHSP). The 196 HSP of the CMS-39 population developed by the National Center for Maize and Sorghum Research (CNPMS-EMBRAPA) were related through their pedigree with the recombined progenies of the previous selection cycle. The two methodologies used for the selection of the twenty best half-sib progenies, BLP and SAWHSP, led to similar expected genetic gains. There was a tendency in the BLP methodology to select a greater number of related progenies because of the previous generation (pedigree) than the other method. This implies that greater care with the effective size of the population must be taken with this method. The SAWHSP methodology was efficient in isolating the additive genetic variance component from the phenotypic component. The pedigree system, although unnecessary for the routine use of the SAWHSP methodology, allowed the prediction of an increase in the inbreeding of the population in the long term SAWHSP selection when recombination is simultaneous to creation of new progenies.