In this paper we introduce a smooth version of local linear regression estimators and address their advantages. The MSE and MISE of the estimators are computed explicitly. It turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency-they are not only efficient in rates but also nearly efficient in constant factors. In the nonparametric regression context, the asymptotic minimax lower bound is developed via the heuristic of the" hardest onedimensional subproblem" of Donoho and Liu. Connections of the minimax risk with the modulus of continuity are made. The lower bound is also applicable for estimating conditional mean (regression) and conditional quantiles for both fixed and random design regression problems.

Financial econometrics is an interdisciplinary subject that uses statistical methods and economic theory to address a variety of quantitative problems in finance. This compact, master's-level textbook focuses on methodology and includes real financial data illustrations throughout. The mathematical level is purposely kept moderate, allowing the power of the quantitative methods to be understood without too much technical detail. Wherever possible, the authors indicate where to find the relevant R codes to implement the various methods. This book grew out of a course at Princeton University which is one of the world's flagship programs in computational finance and financial engineering. It will therefore be useful for those with an economics and finance background who are looking to sharpen their quantitative skills, and also for those with strong quantitative skills who want to learn how to apply them to finance.

Long term prediction such as multi-step time series prediction is a challenging prognostics problem. This paper proposes an improved AR time series model called ND-AR model (Nonlinear Degradation AutoRegression) for Remaining Useful Life (RUL) estimation of lithium-ion batteries. The nonlinear degradation feature of the lithiumion battery capacity degradation is analyzed and then the non-linear accelerated degradation factor is extracted to improve the linear AR model. In this model, the nonlinear degradation factor can be obtained with curve fitting, and then the ND-AR model can be applied as an adaptive datadriven prognostics method to monitor degradation time series data. Experimental results with CALCE battery data set show that the proposed nonlinear degradation AR model can realize satisfied prognostics for various lithium-ion batteries with low computing complexity.