Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study was carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations

The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the growing dimension, i.e., p→∞ when n is fixed. Under some mild regularity conditions, we prove the proposed estimator’s consistency and derive its asymptotic properties. Some Monte Carlo simulation experiments are executed in their performance, and the implementation is considered to analyze a high-dimensional genetic dataset.

Detecting Rock Glacier Displacement in the Central Himalayas Using Multi-Temporal InSAR

Rock glaciers represent typical periglacial landscapes and are distributed widely in alpine mountain environments. Rock glacier activity represents a critical indicator of water reserves state, permafrost distribution, and landslide disaster susceptibility. The dynamics of rock glacier activity in alpine periglacial environments are poorly quantified, especially in the central Himalayas. Multi-temporal Interferometric Synthetic Aperture Radar (MT-InSAR) has been shown to be a useful technique for rock glacier deformation detection. In this study, we developed a multi-baseline persistent scatterer (PS) and distributed scatterer (DS) combined MT-InSAR method to monitor the activity of rock glaciers in the central Himalayas. In periglacial landforms, the application of the PS interferometry (PSI) method is restricted by insufficient PS due to large temporal baseline intervals and temporal decorrelation, which hinder comprehensive measurements of rock glaciers. Thus, we first evaluated the rock glacier interferometric coherence of all possible interferometric combinations and determined a multi-baseline network based on rock glacier coherence; then, we constructed a Delaunay triangulation network (DTN) by exploiting both PS and DS points. To improve the robustness of deformation parameters estimation in the DTN, we combined the Nelder–Mead algorithm with the M-estimator method to estimate the deformation rate variation at the arcs of the DTN and introduced a ridge-estimator-based weighted least square (WLR) method for the inversion of the deformation rate from the deformation rate variation. We applied our method to Sentinel-1A ascending and descending geometry data (May 2018 to January 2019) and obtained measurements of rock glacier deformation for 4327 rock glaciers over the central Himalayas, at least more than 15% detecting with single geometry data. The line-of-sight (LOS) deformation of rock glaciers in the central Himalayas ranged from −150 mm to 150 mm. We classified the active deformation area (ADA) of all individual rock glaciers with the threshold determined by the standard deviation of the deformation map. The results show that 49% of the detected rock glaciers (monitoring rate greater than 30%) are highly active, with an ADA ratio greater than 10%. After projecting the LOS deformation to the steep slope direction and classifying the rock glacier activity following the IPA Action Group guideline, 12% of the identified rock glaciers were classified as active and 86% were classified as transitional. This research is the first multi-baseline, PS, and DS network-based MT-InSAR method applied to detecting large-scale rock glaciers activity.

Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.

Inference for the Linear IV Model Ridge Estimator Using Training and Test Samples

The asymptotic distribution is presented for the linear instrumental variables model estimated with a ridge penalty and a prior where the tuning parameter is selected with a holdout sample. The structural parameters and the tuning parameter are estimated jointly by method of moments. A chi-squared statistic permits confidence regions for the structural parameters. The form of the asymptotic distribution provides insights on the optimal way to perform the split between the training and test sample. Results for the linear regression estimated by ridge regression are presented as a special case.

Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study were carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.