The purpose of this paper is to propose methodologies for statistical inference of low dimensional parameters with high dimensional data.We focus on constructing confidence intervals for individual coefficients and linear combinations of several of them in a linear regression model, although our ideas are applicable in a much broader context.The theoretical results that are presented provide sufficient conditions for the asymptotic normality of the proposed estimators along with a consistent estimator for their finite dimensional covariance matrices. These sufficient conditions allow the number of variables to exceed the sample size and the presence of many small non-zero coefficients. Our methods and theory apply to interval estimation of a preconceived regression coefficient or contrast as well as simultaneous interval estimation of many regression coefficients. Moreover, the method proposed turns the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients, which can be used to select variables after proper thresholding. The simulation results that are presented demonstrate the accuracy of the coverage probability of the confidence intervals proposed as well as other desirable properties, strongly supporting the theoretical results.

We propose a deep learning-based method for object detection in UAV-borne thermal images that have the capability of observing scenes in both day and night. Compared with visible images, thermal images have lower requirements for illumination conditions, but they typically have blurred edges and low contrast. Using a boundary-aware salient object detection network, we extract the saliency maps of the thermal images to improve the distinguishability. Thermal images are augmented with the corresponding saliency maps through channel replacement and pixel-level weighted fusion methods. Considering the limited computing power of UAV platforms, a lightweight combinational neural network ComNet is used as the core object detection method. The YOLOv3 model trained on the original images is used as a benchmark and compared with the proposed method. In the experiments, we analyze the detection performances of the ComNet models with different image fusion schemes. The experimental results show that the average precisions (APs) for pedestrian and vehicle detection have been improved by 2%~5% compared with the benchmark without saliency map fusion and MobileNetv2. The detection speed is increased by over 50%, while the model size is reduced by 58%. The results demonstrate that the proposed method provides a compromise model, which has application potential in UAV-borne detection tasks.

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In this paper, we prove a CLT for the sample canonical correlation coefficients between two high-dimensional random vectors with finite rank correlations. More precisely, consider two random vectors $\wt{\bx}=\mathbf x + A \mathbf z $ and $\wt{\by}=\mathbf y + B \mathbf z $, where $\mathbf x \in \R^p$, $\mathbf y \in \R^q$ and $\mathbf z\in \R^r$ are independent random vectors with i.i.d.\;entries of mean zero and variance one, and $A \in \R^{p\times r}$ and $B\in \R^{q\times r}$ are two arbitrary deterministic matrices. Given $n$ samples of $\wt{\bx}$ and $\wt{\by}$, we stack them into two matrices $\cal X= X+AZ$ and $\cal Y= Y+BZ$, where $X\in \R^{p\times n}$, $Y\in \R^{q\times n}$ and $Z\in \R^{r\times n}$ are random matrices with i.i.d.\;entries of mean zero and variance one. Let $\wt\lambda_1 \ge \wt\lambda_2\ge \cdots \ge \wt\lambda_{r}$ be the largest $r$ eigenvalues of the sample canonical correlation (SCC) matrix $\cal C_{\cal X\cal Y}=(\cal X\cal X^\top)^{-1/2}\cal X\cal Y^\top (\cal Y\cal Y^\top)^{-1}\cal Y \cal X^\top (\cal X\cal X^\top)^{-1/2}$, and let $t_1\ge t_2 \ge \cdots\ge t_r$ be the squares of the population canonical correlation coefficients between $\wt{\bx}$ and $\wt{\by}$. Under certain moment assumptions, we show that there exists a threshold $t_c \in(0, 1)$ such that if $t_i>t_c$, then \smash{$\sqrt{n} (\wt\lambda_i-\theta_i)$} converges weakly to a centered normal distribution, where $\theta_i $ is a fixed outlier location determined by $t_i$. Our proof uses a self-adjoint linearization of the SCC matrix and a sharp local law on the inverse of the linearized matrix.

We have collected and cleaned two network data sets: Coauthorship and Citation networks for statisticians. The data sets are based on all research papers published in four of the top journals in statistics from 2003 to the first half of 2003 . We analyze the data sets from many different perspectives, focusing on (a) productivity, patterns and trends,(b) centrality and (c) community structures.

The EM algorithm is a widely used tool in maximum-likelihood estimation in incomplete data problems. Existing theoretical work has focused on conditions under which the iterates or likelihood values converge, and the associated rates of convergence. Such guarantees do not distinguish whether the ultimate fixed point is a near global optimum or a bad local optimum of the sample likelihood, nor do they relate the obtained fixed point to the global optima of the idealized population likelihood (obtained in the limit of infinite data). This paper develops a theoretical framework for quantifying when and how quickly EM-type iterates converge to a small neighborhood of a given global optimum of the population likelihood. For correctly specified models, such a characterization yields rigorous guarantees on the performance of certain two-stage estimators in which a suitable initial pilot estimator is refined with iterations of the EM algorithm. Our analysis is divided into two parts: a treatment of the EM and first-order EM algorithms at the population level, followed by results that apply to these algorithms on a finite set of samples. Our conditions allow for a characterization of the region of convergence of EM-type iterates to a given population fixed point, that is, the region of the parameter space over which convergence is guaranteed to a point within a small neighborhood of the specified population fixed point. We verify our conditions and give tight characterizations of the region of convergence for three canonical problems of interest: symmetric mixture of two Gaussians, symmetric mixture of two regressions and linear regression with covariates missing completely at random.

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.

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.

Large dimensional Gram type matrices are common objects in high-dimensional statistics and machine learning. In this paper, we study the limiting distribution of the edge eigenvalues for a general class of high-dimensional Gram type random matrices, including separable sample covariance matrices, sparse sample covariance matrices, bipartite stochastic block model and random Gram matrices with general variance profiles. Specifically, we prove that under (almost) sharp moment conditions and certain tractable regularity assumptions, the edge eigenvalues, i.e., the largest few eigenvalues of non-spiked Gram type random matrices or the extremal bulk eigenvalues of spiked Gram type random matrices, satisfy the Tracy-Widom distribution asymptotically. Our results can be used to construct adaptive, accurate and powerful statistics for high-dimensional statistical inference. In particular, we propose data-dependent statistics to infer the number of signals under general noise structure, test the one-sided sphericity of separable matrix, and test the structure of bipartite stochastic block model. Numerical simulations show strong support of our proposed statistics. The core of our proof is to establish the edge universality and Tracy-Widom distribution for a rectangular Dyson Brownian motion with regular initial data. This is a general strategy to study the edge statistics for high-dimensional Gram type random matrices without exploring the specific independence structure of the target matrices. It has potential to be applied to more general random matrices that are beyond the ones considered in this paper.

This paper studies hypothesis testing and parameter estimation in the context of the divide-and-conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from k subsamples of size n/k, where n is the sample size. In both low dimensional and sparse high dimensional settings, we address the important question of how large k can be, as n grows large, such that the loss of efficiency due to the divide-and-conquer algorithm is negligible. In other words, the resulting estimators have the same inferential efficiencies and estimation rates as an oracle with access to the full sample. Thorough numerical results are provided to back up the theory.