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.

We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator, which is further refined in the second stage by iteratively solving a sequence of convex programs with smaller precision tolerances. Theoretically, we establish a phase transition: the first stage has a sublinear iteration complexity, while the second stage achieves an improved linear rate of convergence. Though this framework is completely algorithmic, it provides solutions with optimal statistical performances and controlled algorithmic complexity for a large family

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test in At-Sahalia and Jacod (2009), our new test enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. We also propose a new procedure to locate the jumps. The jump identification problem reduces to a multiple comparison problem. We employ the false discovery rate approach to control the probability of type I error. Numerical studies further demonstrate the power of our new method.

The multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional FDR procedure can lack the ability to detect statistical significance, even if the p-values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the FDR procedure. This paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon(LIP) of the FDR procedure occurs. Second, we propose a new multiple comparison procedure, called FDR L, to accommodate the spatial information of neighboring p-values, via a local aggregation of p

Local quasi-likelihood estimation is useful for nonparametric modeling in a widely-used exponential family of distributions, called generalized linear models. Yet, the technique cannot be directly applied to situations where a response variable is missing at random. Three local quasi-likelihood estimation techniques are introduced: the local quasi-likelihood estimator using only complete-data; the locally weighted quasi-likelihood method; the local quasi-likelihood estimator with imputed values. These estimators share basically the same first order asymptotic biases and variances. Our simulation results show that substantial efficiency gains can be obtained by using the local quasi-likelihood estimator with imputed values. We develop the local quasi-likelihood imputation methods for estimating the mean functional of the response variable. It is shown that the proposed mean imputation estimators are asymptotically normal with asymptotic variance that can be easily estimated. Data from an ongoing environmental epidemiologic study is used to illustrate the proposed methods.