Yuehua Wu

On determination of the number of signals in spatially correlated noise

A method for determining the number of signals in a correlated noise field using two well-separated linear arrays of receivers was given by Zhang and Wong (1993). In this paper, we improve on this method with the use of new penalty functions. Three criteria are given, and it is proved that for a large class of penalty functions, the probability of incorrect detections by each of the new criteria is exponentially decreasing when the moment-generating function of the squared Euclidean norm of the observation vector is finite at some point. It is also proved that with these new criteria, the estimates of the number of signals are strongly consistent. Randomized penalty functions for the three criteria, based on samples, are presented, and their uses are then shown to give consistent estimation of the number of signals. The finite sample behavior of the proposed approaches are studied by Monte Carte simulation.

Determination of number of sources with multiple arrays in correlated noise fields

A detection scheme for signals in a noise field is considered. The information-theoretic criterion is derived, and it gives a consistent estimation of the number of signals. Comparison of this multiarray estimation and those of the two-array systems is given through simulations.

Consistency of l 1 estimates in censored linear regression models

In this paper, the regression model with a nonnegativity constraint on the dependent variable is considered. Under weak conditions, L 1 estimates of the regression coefficients are shown to be consistent.

M-estimation in exponential signal models

In this paper, we propose an M-estimation of the parameters in an undamped exponential signal model. Its asymptotic performance is investigated. Under mild assumptions, the estimation is consistent. The simulation studies of the performance of the M-estimation using Hubers function are provided when the sample size is small, and the comparisons between the performances of the M-estimation and the least squares estimation are also presented.

On a necessary condition for the consistency of the l1 estimates in linear regression models

In the usual linear model , denote by the L1 estimate of s0 Under some general conditions on {ei}, it is shown that is a necessary condition for the consistency of sn

Determining the number of sources in signal processing

The problem of detection in signal processing is often referred to determine the number of signal sources in a noisy environment. It has many engineering applications, ranging from military surveillance to mobile communications. The detection is also important in other areas of signal processing, such as the estimation of certain parameters: frequency spectrum and direction of arrival. The spectral peaks obtained from the Fourier transform of the data were used in early time to estimate these parameters, but the spectral resolutions are generally poor due to the practical limitations such as the time length of data record. Model-based parameter estimation has been an area of active research. Many high-resolution approaches have been developed, but they require certain prior knowledge, among them the number of signal sources is often most crucial. It is thus clear that signal detection plays an important role in parameter estimation, system modeling and identification, and stochastic realization. The detection problems are generally classified into two categories: determination of number of signals, each having different frequencies; and determination of signals, each coming from different locations.

Randomized penalty in detection of the number of signals

For the information theoretic criterion methods of detecting the number of signals, a penalty function which is of fixed form has been utilized. A new penalty, depending on samples, is introduced. It is shown that it gives a strongly consistent estimate of the number of signals. Simulation results show that for small samples, it performs well as compared with others, such as the Hannan criterion. >

An Estimate of a Change Point in Variance of Measurement Errors and Its Convergence Rate

In this article, an estimate of a change point in variance of measurement errors (ME) is given in terms of characteristic functions when the variances are known. Its modification is also given for the case that the variances are unknown. In addition, the consistency and convergence rates of the estimator and its modification are investigated. The simulation study shows that the proposed estimators perform well.

On Simultaneous Estimation of the Number of Signals and Frequencies of Multiple Sinusoids When Some Observations Are Missing

In an earlier article (Bai et al., 1999), the problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case that some observations are missing. The number of signals is estimated with an information theoretic criterion and the frequencies are estimated with eigenvariation linear prediction. Asymptotic properties of the procedure are investigated but the Monte Carlo simulation is not performed. In this article, a slightly different but scale invariant criterion for detection is proposed and the estimation of frequencies remains the same. Asymptotic properties of this new procedure are provided. Monte Carlo Simulation for both procedures is carried out. Furthermore, comparison on the real signals is also given.

A note on estimating the number of superimposed exponential signals by the cross-validation approach

In this paper, a procedure based on the delete-1 cross-validation is given for estimating the number of superimposed exponential signals, its limiting behavior is explored and it is shown that the probability of overestimating the true number of signals is greater than a positive constant for sufficiently large samples. Also a general procedure based on the cross-validation is presented when the deletion proceeds according to a collection of subsets of indices. The result is similar to the delete-1 cross-validation if the number of deletions is fixed. The simulation results are provided for the performance of the procedure when the collections of subsets of indices are chosen as those suggested by Shao [1]in a linear model selection problem.