Modified Ridge Parameters for Seemingly Unrelated Regression Model

In this paper, we modify a number of new biased estimators of seemingly unrelated regression (SUR) parameters which are developed by Alkhamisi and Shukur (2008), AS, when the explanatory variables are affected by multicollinearity. Nine ridge parameters have been modified and compared in terms of the trace mean squared error (TMSE) and (PR) criterion. The results from this extended study are the also compared with those founded by AS. A simulation study has been conducted to compare the performance of the modified ridge parameters. The results showed that under certain conditions the performance of the multivariate ridge regression estimators based on SUR ridge RMSmax is superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high the unbiased SUR, estimator produces a smaller TMSEs.Multicollinearity; modified SUR ridge regression; Monte Carlo simulations; TMSE

New Liu Estimators for the Poisson Regression Model: Method and Application

A new shrinkage estimator for the Poisson model is introduced in this paper. This method is a generalization of the Liu (1993) estimator originally developed for the linear regression model and will be generalised here to be used instead of the classical maximum likelihood (ML) method in the presence of multicollinearity since the mean squared error (MSE) of ML becomes inflated in that situation. Furthermore, this paper derives the optimal value of the shrinkage parameter and based on this value some methods of how the shrinkage parameter should be estimated are suggested. Using Monte Carlo simulation where the MSE and mean absolute error (MAE) are calculated it is shown that when the Liu estimator is applied with these proposed estimators of the shrinkage parameter it always outperforms the ML. Finally, an empirical application has been considered to illustrate the usefulness of the new Liu estimators.Estimation; MSE; MAE; Multicollinearity; Poisson; Liu; Simulation

Involving machine learning techniques in heart disease diagnosis: a performance analysis

Artificial intelligence is a science that is growing at a tremendous speed every day and has become an essential part of many domains, including the medical domain. Therefore, countless artificial intelligence applications can be seen in the medical domain at various levels, which are employed to enhance early diagnosis and prediction and reduce the risks associated with many diseases, including heart diseases. In this article, machine learning techniques (logistic regression, random forest, artificial neural network, support vector machines, and k-nearest neighbors) are utilized to diagnose heart disease from the Cleveland Clinic dataset got from the University of California Irvine machine learning (UCL) repository and Kaggle platform then create a comparison between the performance of these techniques. In addition, some literature related to machine learning and deep learning techniques that aim to provide reasonable solutions in monitoring, detecting, diagnosing, and predicting heart disease and how these technologies assist in making health decisions are reviewed. Ten studies are selected and summarized by the authors published between 2017 and 2022 are illustrated. After executing a series of tests, it is seen that the most profitable performance in diagnosing heart disease is the support vector machines, with a diagnostic accuracy of 96%. This article has concluded that these techniques play a significant and influential role in assisting physicians and health care workers in analyzing heart patients' data, making health decisions, and saving patients' lives

A New Liu Type of Estimator for the Restricted SUR Estimator

A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity

On developing ridge regression parameters : a graphical investigation

In this paper we review some existing and propose some new estimators for estimating the ridge parameter. All in all 19 different estimators have been studied. The investigation has been carried out using Monte Carlo simulations. A large number of different models have been investigated where the variance of the random error, the number of variables included in the model, the correlations among the explanatory variables, the sample size and the unknown coefficient vector were varied. For each model we have performed 2000 replications and presented the results both in term of figures and tables. Based on the simulation study, we found that increasing the number of correlated variable, the variance of the random error and increasing the correlation between the independent variables have negative effect on the mean squared error. When the sample size increases the mean squared error decreases even when the correlation between the independent variables and the variance of the random error are large. In all situations, the proposed estimators have smaller mean squared error than the ordinary least squares and other existing estimators

Characterizing the geometry of the Kirkwood-Dirac positive states

The Kirkwood-Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables $A$ and $B$. KD distributions behave similarly to classical joint probability distributions but can assume negative and nonreal values. In recent years, KD distributions have proven instrumental in mapping out nonclassical phenomena and quantum advantages. These quantum features have been connected to nonpositive entries of KD distributions. Consequently, it is important to understand the geometry of the KD-positive and -nonpositive states. Until now, there has been no thorough analysis of the KD positivity of mixed states. Here, we characterize how the full convex set of states with positive KD distributions depends on the eigenbases of $A$ and $B$. In particular, we identify three regimes where convex combinations of the eigenprojectors of $A$ and $B$ constitute the only KD-positive states: $(i)$ any system in dimension $2$; $(ii)$ an open and dense set of bases in dimension $3$; and $(iii)$ the discrete-Fourier-transform bases in prime dimension. Finally, we investigate if there can exist mixed KD-positive states that cannot be written as convex combinations of pure KD-positive states. We show that for some choices of observables $A$ and $B$ this phenomenon does indeed occur. We explicitly construct such states for a spin-$1$ system.Comment: 35 pages, 2 figure

Quantum simulations of time travel can power nonclassical metrology

Gambling agencies forbid late bets, placed after the winning horse crosses the finish line. A time-traveling gambler could cheat the system. We construct a gamble that one can win by simulating time travel with experimentally feasible entanglement manipulation. Our gamble echoes a common metrology protocol: A gambler must prepare probes to input into a metrology experiment. The goal is to infer as much information per probe as possible about a parameter's value. If the input is optimal, the information gained per probe can exceed any value achievable classically. The gambler chooses the input state analogously to choosing a horse. However, only after the probes are measured does the gambler learn which input would have been optimal. The gambler can "place a late bet" by effectively teleporting the optimal input back in time, via entanglement manipulation. Our Gedankenexperiment demonstrates that not only true time travel, but even a simulation offers a quantum advantage in metrology.Comment: 5+1 pages. 2 figures. Comments are welcomed