Abstract: Highlights • Regularization techniques for regression outperformed the classical regression techniques in predicting crop yields. • Different regression techniques with similar prediction accuracy showed different responses of major climatic variables to crop yield. • The regression models showed some responses of crop yield to climatic conditions that is mostly absent in process based crop models. Abstract Statistical regression models represent alternatives to process-based dynamic models for predicting the response of crop yields to variation in climatic conditions. Regression models can be used to quantify the effect of change in temperature and precipitation on yields. However, it is difficult to identify the most relevant input variables that should be included in regression models due to the high number of candidate variables and to their correlations. This paper compares several regression techniques for modeling response of winter oilseed rape yield to a high number of correlated input variables. Several statistical regression methods were fitted to a dataset including 689 observations of winter oilseed rape yield from replicated field experiments conducted in 239 sites in Denmark, covering nearly all regions of the country from 1992 to 2013. Regression methods were compared by cross-validation. The regression methods leading to the most accurate yield predictions were Lasso and Elastic Net, and the least accurate methods were ordinary least squares and stepwise regression. Partial least squares and ridge regression methods gave intermediate results. The estimated relative yield change for a +1°C temperature increase during flowering was estimated to range between 0 and +6 %, depending on choice of regression method. Precipitation was found to have an adverse effect on yield during autumn and winter. It was estimated that an increase in precipitation of +1 mm/day would result in a relative yield change ranging from 0 to −4 %. Soil type was also important for crop yields with lower yields on sandy soils compared to loamy soils. Later sowing was found to result in increased crop yield. The estimated effect of climate on yield was highly sensitive to the chosen regression method. Regression models showing similar performance led in some cases to different conclusions with respect to effect of temperature and precipitation. Hence, it is recommended to apply an ensemble of regression models, in order to account for the sensitivity of the data driven models for projecting crop yield under climate change.

Abstract: Statistical learning is a fairly new term referring to a set of supervised and unsupervised modelling and prediction techniques. It is based on traditional statistics but has been highly enhanced inspired by developments in machine learning and data mining. The main focus of statistical learning is to estimate the functions that quantify relations between several parameters and observed responses. These functions are further used for prediction, inference or a combination of both. For a particular case of quantitative responses, regularization techniques in regression are developed to overcome the weaknesses of ordinary least square (OLS) regression in prediction. These new shrinkage methods outperform OLS for prediction, especially in large datasets. In this study, a large dataset of field experiments on winter oilseed rape in Denmark for 22 years (1992 to 2013) was collected. Biweekly climatic data along with sowing date, harvest date, soil type and previous crop are considered as the explanatory variables. Yield of winter oilseed rape is considered as response variable. LASSO and Elastic Nets are the regularization techniques used to estimate the functions. Hold-one-out cross validation method for testing the prediction power reveals that these techniques are much useful in both prediction and inference. Since these techniques are included in recent versions of some software packages (e.g. R), they can be easily implemented by users at any level. The estimated function (model) is further used to predict the oilseed rape yield responses to climate change for several scenarios using representative weather data produced by a weather generator.