It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects model. Typical approaches perform selection separately on each of the fixed and random effect components. However, changing the structure of one set of effects can lead to different choices of variables for the other set of effects. We propose simultaneous selection of the fixed and random factors in a linear mixed-effects model using a modified Cholesky decomposition. Our method is based on a penalized joint log-likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects. It performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero. A constrained EM algorithm is then used to obtain the final estimates. It is further shown that the proposed penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.

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Weakening of Indian summer monsoon rainfall (ISMR) is traditionally linked with large-scale perturbations and circulations. However, the impacts of local changes in land use and land cover (LULC) on ISMR have yet to be explored. Here, we analyzed this topic using the regional Weather Research and Forecasting model with European Center for Medium range Weather Forecast (ECMWF) reanalysis data for the years 2000–2010 as a boundary condition and with LULC data from 1987 and 2005. The differences in LULC between 1987 and 2005 showed deforestation with conversion of forest land to crop land, though the magnitude of such conversion is uncertain because of the coarse resolution of satellite images and use of differential sources and methods for data extraction. We performed a sensitivity analysis to understand the impacts of large-scale deforestation in India on monsoon precipitation and found such impacts are similar to the observed changes in terms of spatial patterns and magnitude. We found that deforestation results in weakening of the ISMR because of the decrease in evapotranspiration and subsequent decrease in the recycled component of precipitation.

A fundamental endeavor in exoplanetary research is to characterize the bulk compositions of planets via measurements of their masses and radii. With future sample sizes of hundreds of planets to come from TESS and PLATO, we develop a statistical method that can flexibly yet robustly characterize these compositions empirically, via the exoplanet M–R relation. Although the M–R relation has been explored in many prior works, they mostly use a power-law model, with assumptions that are not flexible enough to capture important features in current and future M–R diagrams. To address these shortcomings, a nonparametric approach is developed using a sequence of Bernstein polynomials. We demonstrate the benefit of taking the nonparametric approach by benchmarking our findings with previous work and showing that a power law can only reasonably describe the M–R relation of the smallest planets and that the intrinsic scatter can change non-monotonically with different values of a radius. We then apply this method to a larger data set, consisting of all the Kepler observations in the NASA Exoplanet Archive. Our nonparametric approach provides a tool to estimate the M–R relation by incorporating heteroskedastic measurement errors into the model. As more observations will be obtained in the near future, this approach can be used with the provided R code to analyze a larger data set for a better understanding of the M–R relation.