Detection and Extraction of Weak Pulse Signals in Chaotic Noise with PTAR and DLTAR Models

With the development in communications, the weak pulse signal is submerged in chaotic noise, which is very common in seismic monitoring and detection of ocean clutter targets, and is very difficult to detect and extract. Based on the threshold autoregressive model, pulse linear form, Markov chain Monte Carlo (MCMC), and profile least squares (PrLS) algorithm, phase threshold autoregressive (PTAR) model and double layer threshold autoregressive (DLTAR) model are proposed for detection and extraction of weak pulse signals in chaotic noise, respectively. Firstly, based on noisy chaotic observation, phase space is reconstructed according to Takens’s delay embedding theorem, and the phase threshold autoregressive (PTAR) model is presented to detect weak pulse signals, and then the MCMC algorithm is applied to estimate parameters in the PTAR model; lastly, we obtain one-step prediction error, which is used to realize adaptively detection of weak signals with the hypothesis test. Secondly, a linear form for the pulse signal and PTAR model is fused to build a DLTAR model to extract weak pulse signals. The DLTAR model owns two kinds of parameters, which are affected mutually. Here, the PrLS algorithm is applied to estimate parameters of the DLTAR model and ultimately extract weak pulse signals. Finally, accurate rate (Acc), receiver operating characteristic (ROC) curve, and area under ROC curve (AUC) are used as the detector performance index; mean square error (MSE), mean absolute percent error (MAPE), and relative error (Re) are used as the extraction accuracy index. The presented scheme does not need prior knowledge of chaotic noise and weak pulse signals, and simulation results show that the proposed PTAR-DLTAR model is significantly effective for detection and extraction of weak pulse signals under chaotic interference. Specifically, in very low signal-to-interference ratio (SIR), weak pulse signals can be detected and extracted compared with support vector machine (SVM) class and neural network model.

Dynamic Influence Prediction of Social Network Based on Partial Autoregression Single Index Model

Everything is connected in the world. From small groups to global societies, the interactions among people, technology, and policies need sophisticated techniques to be perceived and forecasted. In social network, it has been concluded that the microblog users influence and microblog grade are nonlinearly dependent. However, to the best of our knowledge, the nonlinear influence predication of social network has not been explored in the existing literature. This article proposes a partial autoregression single index model to combine network structure (linear) and static covariates (nonparametric) flexibly. Compared with previous work, our model has fewer limits and more applications. The profile least squares estimation is employed to infer this semiparametric model, and variables selection is performed via the smoothly clipped absolute deviation penalty (SCAD). Simulations are conducted to demonstrate finite sample behaviors.

Stochastic Restricted Estimation in Partially Linear Measurement Error Models

As a generalization of nonparametric regression model, partially linear model has been studied extensively in the last decades. This paper considers estimation of the semiparametric model under the situation that the covariates are measured with additive error in the linear part and some additional stochastic linear restrictions exist on the parametric component. Based on the corrected profile least-squares approach and mixed regression method, we propose a stochastic restricted estimator named the corrected profile mixed estimator for the parametric component, and discuss its statistical properties. We also construct a weighted stochastic restricted estimation for the parametric component. Finally, the proposed procedure is illustrated by simulation studies.

Principal Components Regression Estimation in Semiparametric Partially Linear Additive Models

<p>Partially linear additive model is useful in statistical modelling as a multivariate nonparametric fitting technique. This paper considers statistical inference for the semiparametric model in the presence of multicollinearity. Based on the profile least-squares approach, we propose a novel principal components regression estimator for the parametric component, and provide the asymptotic bias and covariance matrix of the proposed estimator. Some simulations are conducted to examine the performance of our proposed estimators and the results are satisfactory.</p>

Profile Inferences on Restricted Additive Partially Linear EV Models

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

Data reconstruction with shot-profile least-squares migration

We introduce shot-profile migration data reconstruction (SPDR). SPDR constructs a least-squares migrated shot gather using shot-profile migration and demigration operators. Both operators are constructed with a constant migration velocity model for efficiency and so that SPDR requires minimal information about the underlying geology. Applying the demigration operator to the least-squares migrated shot gather gives the reconstructed data gather. SPDR can reconstruct a shot gather from observed data that are spatially aliased. Given a constraint on the geological dips in an approximate model of the earth’s reflector, signal and aliased energy that interfere in the common shot data gather are disjoint in the migrated shot gather. In the least-squares migration algorithm, we construct weights to take advantage of this separation, suppressing the aliased energy while retaining the signal, and allowing SPDR to reconstruct a shot gather from aliased data. SPDR is illustrated with synthetic data examples and one real data example.