Estimation on Varying-Coefficient Partially Linear Model With Different Smoothing Variables

The authors give the estimation on the varying-coefficient partially linear regression model with different smoothing variables. The efficient estimators of the intercept function and the coefficient functions are obtained by a one-step back-fitting technique based on their initial estimators given by local linear technique and the averaged method. Furthermore, their asymptotic normalities are given. Some simulation studies are used to illustrate the performances of the estimation.     

General Multivariate Weibull Processes

Two multivariate stationary processes with general multivariate Weibull marginals are developed and studied. The joint distribution of the two adjacent events in the processes and the distributions of the finite sample minima as well as the geometric minima are derived. The characterization properties of these two processes are also proved.     

Residual Kriging for Functional Spatial Prediction of Salinity Curves

Recently, several methodologies to perform geostatistical analysis of functional data have been proposed. All of them assume that the spatial functional process considered is stationary. However, in practice, we often have nonstationary functional data because there exists an explicit spatial trend in the mean. Here, we propose a methodology to extend kriging predictors for functional data to the case where the mean function is not constant through the region of interest. We consider an approach based on the classical residual kriging method used in univariate geostatistics. We propose a three steps procedure. Initially, a functional regression model is used to detrend the mean. Then we apply kriging methods for functional data to the regression residuals to predict a residual curve at a non-data location. Finally, the prediction curve is obtained as the sum of the trend and the residual prediction. We apply the methodology to salinity data corresponding to 21 salinity curves recorded at the Ciénaga Grande de Santa Marta estuary, located in the Caribbean coast of Colombia. A cross-validation analysis was carried out to track the performance of the proposed methodology.     

A Compressive Sensing Based Analysis of Anomalies in Generalized Linear Models

In this article, we present a compressive sensing based framework for generalized linear model regression that employs a two-component noise model and convex optimization techniques to simultaneously detect outliers and determine optimally sparse representations of noisy data from arbitrary sets of basis functions. We then extend our model to include model order reduction capabilities that can uncover inherent sparsity in regression coefficients and achieve simple, superior fits. Second, we use the mixed ?₂/?₁ norm to develop another model that can efficiently uncover block-sparsity in regression coefficients. By performing model order reduction over all independent variables and basis functions, our algorithms successfully deemphasize the effect of independent variables that become uncorrelated with dependent variables. This desirable property has various applications in real-time anomaly detection, such as faulty sensor detection and sensor jamming in wireless sensor networks. After developing our framework and inheriting a stable recovery theorem from compressive sensing theory, we present two simulation studies on sparse or block-sparse problems that demonstrate the superior performance of our algorithms with respect to (1) classic outlier-invariant regression techniques like least absolute value and iteratively reweighted least-squares and (2) classic sparse-regularized regression techniques like LASSO.     

Local Linear Estimation of Second-order Jump-diffusion Model

In this article, we propose the local linear estimators of the drift coefficient and diffusion coefficient in the second-order jump-diffusion model. We also show the consistency and asymptotic normality of these estimators under mild conditions.     

Non parametric portmanteau tests for detecting non linearities in high dimensions

ABSTRACT

We propose two non parametric portmanteau test statistics for serial dependence in high dimensions using the correlation integral. One test depends on a cutoff threshold value, while the other test is freed of this dependence. Although these tests may each be viewed as variants of the classical Brock, Dechert, and Scheinkman (BDS) test statistic, they avoid some of the major weaknesses of this test. We establish consistency and asymptotic normality of both portmanteau tests. Using Monte Carlo simulations, we investigate the small sample properties of the tests for a variety of data generating processes with normally and uniformly distributed innovations. We show that asymptotic theory provides accurate inference in finite samples and for relatively high dimensions. This is followed by a power comparison with the BDS test, and with several rank-based extensions of the BDS tests that have recently been proposed in the literature. Two real data examples are provided to illustrate the use of the test procedure.     

Bernoulli Processes with Non-Positive Correlations

We deal with sequences of dependent Bernoulli variables with non positive correlations. Some special models for 1-dependent and 2-dependent 0–1 valued variables are analyzed, namely Bernoulli variables obtained by clipping a linear combination of iid variables. Formulas describing dependence of their correlation function on the clipping parameters are derived. The lower bound for the sum of autocorrelations of Bernoulli variables obtained by clipping a Gaussian process is provided.     

Empirical Likelihood Inference for the Parameter in Additive Partially Linear EV Models

In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions.     

Weighted Searching Probability for Classes of Equivalent Search Designs Comparison

Search design is searching and estimating for a few non zero effects in a large set of effects along with estimation of elements in a set of unknown parameters. In presence of noise, the probability of discrimination between the true non zero effect from an alternative one depends on the design and an unknown parameter, say ρ. We develop a new criterion for design comparison which is independent of ρ and for a family density weight function show that it discriminates and ranks the designs precisely. This criterion is invariance to the variable noise which may be present between designs due to noise factors. This allows us to extend the design comparison to classes of equivalent designs.