Parameter Estimation of Multiple Frequency-Hopping Signals Based on Space-Time-Frequency Analysis by Atomic Norm Soft Thresholding with Missing Observations

In this paper,we address the problem of multiple frequency-hopping(FH)signal parameters estimation in the presence of random missing observations.A space-time matrix with random missing observations is acquired by a uniform linear array(ULA).We exploit the inherent incomplete data processing capability of atomic norm soft thresholding(AST)to analyze the space-time matrix and complete the accurate estimation of the hopping time and frequency of the received FH signals.The hopping time is obtained by the sudden changes of the spatial information,which is implemented as the boundary to divide the time domain signal so that each segment of the signal is a superposition of time-invariant multiple components.Then,the frequency of multiple signal components can be estimated precisely by AST within each segment.After obtaining the above two parameters of the hopping time and the frequency of signals,the direction of arrival(DOA)can be directly calculated by them,and the network sorting can be realized.Results of simulation show that the proposed method is superior to the existing technology.Even when a large portion of data observations is missing,as the number of array elements increases,the proposed method still achieves acceptable accuracy of multi-FH signal parameters estimation.

Quantile Regression of Ultra-high Dimensional Partially Linear Varying-coefficient Model with Missing Observations

In this paper,we focus on the partially linear varying-coefficient quantile regression with missing observations under ultra-high dimension,where the missing observations include either responses or covariates or the responses and part of the covariates are missing at random,and the ultra-high dimension implies that the dimension of parameter is much larger than sample size.Based on the B-spline method for the varying coefficient functions,we study the consistency of the oracle estimator which is obtained only using active covariates whose coefficients are nonzero.At the same time,we discuss the asymptotic normality of the oracle estimator for the linear parameter.Note that the active covariates are unknown in practice,non-convex penalized estimator is investigated for simultaneous variable selection and estimation,whose oracle property is also established.Finite sample behavior of the proposed methods is investigated via simulations and real data analysis.

How Deep Learning Networks could be Designed to Locate Mineral Deposits

Whether using a shallow neural network with one hidden layer,or a deep network with many hidden layers,the training data must represent subgroups of the deposit type being explored to be useful.Published examples of neural networks have mostly been limited to one individual mineral deposit for training.Variation of geologic features among deposits within a type are so large that a single deposit cannot provide proper information to train a neural net to generalize and guide exploration for other deposits.Models trained with only one deposit tend to be academic successes but are not of practical value in exploration for other deposits.This is why it takes much experience examining many deposits to properly train an economic geologist—a neural network is not any different.Two examples of shallow neural networks are used to demonstrate the power of neural networks to possibly locate undiscovered deposits and to provide some suggestions of how to deal with missing data.The training data needs to include information spatially related to known deposits and hopefully information from many different deposits of the type.Lessons learned from these and other examples point to a proposed sampling plan for data that could lead to a generalized neural network for exploration.In this plan,10 or more well-explored gold-rich porphyry copper deposits from around the world with 100 or more sample sites near and some distance from each deposit would probably capture important variability among such deposits and provide proper data to train and test a shallow neural network to predict locations of undiscovered deposits.

On Almost Sure Max-limit Theorems of Complete and Incomplete Samples from Stationary Sequences

Let Mn denote the partial maximum of a strictly stationary sequence （Xn）. Suppose some of the random variables of （Xn） can be observed and let Mn stand for the maximum of observed random variables from the set {X1,..., Xn}. In this paper, the almost sure limit theorems related to random vector （Mn, Mn） are considered in terms of i.i.d, case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.