Least absolute deviation estimation of linear econometric models: A literature review

Econometricians generally take for granted that the error terms in the econometric models are generated by distributions having a finite variance. However, since the time of Pareto the existence of error distributions with infinite variance is known. Works of many econometricians, namely, Meyer & Glauber (1964), Fama (1965) and Mandlebroth (1967), on economic data series like prices in financial and commodity markets confirm that infinite variance distributions exist abundantly. The distribution of firms by size, behaviour of speculative prices and various other recent economic phenomena also display similar trends. Further, econometricians generally assume that the disturbance term, which is an influence of innumerably many factors not accounted for in the model, approaches normality according to the Central Limit Theorem. But Bartels (1977) is of the opinion that there are limit theorems, which are just likely to be relevant when considering the sum of number of components in a regression disturbance that leads to non-normal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a non-normal distribution exists. The Least Squares method of estimation of parameters of linear (regression) models performs well provided that the residuals (disturbances or errors) are well behaved (preferably normally or near-normally distributed and not infested with large size outliers) and follow Gauss-Markov assumptions. However, models with the disturbances that are prominently non-normally distributed and contain sizeable outliers fail estimation by the Least Squares method. An intensive research has established that in such cases estimation by the Least Absolute Deviation (LAD) method performs well. This paper is an attempt to survey the literature on LAD estimation of single as well as multi-equation linear econometric models.Lad estimator; Least absolute deviation estimation; econometric model; LAD Estimator; Minimum Absolute Deviation; Robust; Outliers; L1 Estimator; Review of literature

Least absolute deviation estimation of linear econometric models: A literature review

Econometricians generally take for granted that the error terms in the econometric models are generated by distributions having a finite variance. However, since the time of Pareto the existence of error distributions with infinite variance is known. Works of many econometricians, namely, Meyer & Glauber (1964), Fama (1965) and Mandlebroth (1967), on economic data series like prices in financial and commodity markets confirm that infinite variance distributions exist abundantly. The distribution of firms by size, behaviour of speculative prices and various other recent economic phenomena also display similar trends. Further, econometricians generally assume that the disturbance term, which is an influence of innumerably many factors not accounted for in the model, approaches normality according to the Central Limit Theorem. But Bartels (1977) is of the opinion that there are limit theorems, which are just likely to be relevant when considering the sum of number of components in a regression disturbance that leads to non-normal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a non-normal distribution exists. The Least Squares method of estimation of parameters of linear (regression) models performs well provided that the residuals (disturbances or errors) are well behaved (preferably normally or near-normally distributed and not infested with large size outliers) and follow Gauss-Markov assumptions. However, models with the disturbances that are prominently non-normally distributed and contain sizeable outliers fail estimation by the Least Squares method. An intensive research has established that in such cases estimation by the Least Absolute Deviation (LAD) method performs well. This paper is an attempt to survey the literature on LAD estimation of single as well as multi-equation linear econometric models

Least absolute deviation estimation of linear econometric models: A literature review

Econometricians generally take for granted that the error terms in the econometric models are generated by distributions having a finite variance. However, since the time of Pareto the existence of error distributions with infinite variance is known. Works of many econometricians, namely, Meyer & Glauber (1964), Fama (1965) and Mandlebroth (1967), on economic data series like prices in financial and commodity markets confirm that infinite variance distributions exist abundantly. The distribution of firms by size, behaviour of speculative prices and various other recent economic phenomena also display similar trends. Further, econometricians generally assume that the disturbance term, which is an influence of innumerably many factors not accounted for in the model, approaches normality according to the Central Limit Theorem. But Bartels (1977) is of the opinion that there are limit theorems, which are just likely to be relevant when considering the sum of number of components in a regression disturbance that leads to non-normal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a non-normal distribution exists. The Least Squares method of estimation of parameters of linear (regression) models performs well provided that the residuals (disturbances or errors) are well behaved (preferably normally or near-normally distributed and not infested with large size outliers) and follow Gauss-Markov assumptions. However, models with the disturbances that are prominently non-normally distributed and contain sizeable outliers fail estimation by the Least Squares method. An intensive research has established that in such cases estimation by the Least Absolute Deviation (LAD) method performs well. This paper is an attempt to survey the literature on LAD estimation of single as well as multi-equation linear econometric models

Effect of Progressive Muscle Relaxation on the Adverse Cardiovascular Profile in Women with Polycystic Ovarian Syndrome

Background: The altered stress reactivity in polycystic ovarian syndrome (PCOS) may constitute a link between depression, overweight, and cardiovascular risk factors. Aims: To study the effects of progressive muscle relaxation (PMR) on the stress levels of PCOS patients and their influence on the cardiovascular risk factors. Subjects and Methods: This prospective pilot project was conducted on 100 PCOS patients in a tertiary care hospital of West Bengal, after receiving approval from the Institutional Ethical Committee and informed consent of the subjects. The stress levels were assessed and conventional autonomic function tests and the lipid profi les were analyzed. The subjects were divided into two groups using an online randomizer. One group received medication, while the other group received medication and practiced progressive muscle relaxation (PMR) for three months. All parameters were re‑evaluated at the end of three months. Results: The perceived stress scale was significantly less in subjects practicing relaxation exercises, as compared to subjects only on medication. The waist/hip ratio, pulse rate, and systolic blood pressure were significantly lower, while there was no difference in the body mass index (BMI) and diastolic blood pressure. Results of the autonomic function tests showed a significant parasympathetic tilt in subjects practicing PMR. In patients with PCOS, who were on PMR, cholesterol, triglycerides, and low‑density cholesterol (LDL) were significantly lower and high‑density cholesterol HDL was significantly higher. Conclusions: PCOS patients are a high‑risk group for developing the metabolic syndrome and relaxation therapies may be recommended as an adjuvant therapy, to tilt the autonomic balance to parasympathetic dominance, to improve the cardiovascular profile.Keywords: Autonomic functions, cardiovascular system, polycystic ovarian syndrome, stres

Centrosymmetric-noncentrosymmetric Structural Phase Transition in Quasi one-dimensional compound, (TaSe4_4)3_3I

(TaSe$_4$)$_3$I, a compound belonging to the family of quasi-one-dimensional transition-metal tetrachalcogenides, has drawn significant attention due to a recent report on possible coexistence of two antagonistic phenomena, superconductivity and magnetism below 2.5~K (Bera et. al, arXiv:2111.14525). Here, we report a structural phase transition of the trimerized phase at temperature, $T~\simeq$~145~K using Raman scattering, specific heat, and electrical transport measurements. The temperature-dependent single-crystal X-ray diffraction experiments establish the phase transition from a high-temperature centrosymmetric to a low-temperature non-centrosymmetric structure, belonging to the same tetragonal crystal family. The first-principle calculation finds the aforementioned inversion symmetry-breaking structural transition to be driven by the hybridization energy gain due to the off-centric movement of the Ta atoms, which wins over the elastic energy loss.Comment: 11 pages, 5 figures, Under review as a regular articl

A general framework for handling commitment in online throughput maximization

We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least $1+\varepsilon$ times its processing time, for some $\varepsilon>0$. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of $O(1/\varepsilon)$ is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job's slack becomes less than a $\delta$-fraction of its size, we prove a competitive ratio of $O(\varepsilon/((\varepsilon-\delta)\delta^2))$, for $0<\delta<\varepsilon$. When a provider must commit upon starting a job, our bound is $O(1/\varepsilon^2)$. Finally, we observe that for scheduling with commitment the restriction to the `unweighted' throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms

Evaluating the Viscoelastic Properties of Tissue from Laser Speckle Fluctuations

Most pathological conditions such as atherosclerosis, cancer, neurodegenerative, and orthopedic disorders are accompanied with alterations in tissue viscoelasticity. Laser Speckle Rheology (LSR) is a novel optical technology that provides the invaluable potential for mechanical assessment of tissue in situ. In LSR, the specimen is illuminated with coherent light and the time constant of speckle fluctuations, τ, is measured using a high speed camera. Prior work indicates that τ is closely correlated with tissue microstructure and composition. Here, we investigate the relationship between LSR measurements of τ and sample mechanical properties defined by the viscoelastic modulus, G*. Phantoms and tissue samples over a broad range of viscoelastic properties are evaluated using LSR and conventional mechanical testing. Results demonstrate a strong correlation between τ and |G*| for both phantom (r = 0.79, p <0.0001) and tissue (r = 0.88, p<0.0001) specimens, establishing the unique capability of LSR in characterizing tissue viscoelasticity

Equity and determinants of routine child immunisation programme among tribal and non-tribal populations in rural Tangail subdistrict, Bangladesh: A cohort study

Objectives The study estimated valid vaccination coverage of under 5 children in a rural area under Tangail subdistrict and examined their sociodemographic correlates including ethnicity. Setting The study sites are three primary areas where tribal and non-tribal population resides together in a rural subdistrict of Bangladesh. Participants Routine vaccination information of a cohort of 2802 children, born between 1 January 2011 and 31 December 2012, were retrieved from the Expanded Program on Immunization (EPI) registers maintained by the health assistants. Collected data were entered in an Oracle-based computer program. Univariate, bivariate and multivariate analyses were performed in SPSS V.20 to explore coverage and differentials for full valid vaccination coverage in the study area. Results Valid vaccination coverage was 90.6% among tribal population and 87.3% among non-tribal population(p=0.25). Compared with females, males had higher valid vaccination coverage (89.2% vs 85.9%) and lower invalid (5.4% vs 6.9%) and no-coverage (5.3% vs 7.3%) (p=0.03). Households with mobile phones had higher valid coverage (90.9% vs 86.5%) and lower invalid (4.5% vs 6.7%) and no coverage (4.5% vs 6.9%) compared with those without mobile phones (p=0.01). Coverage of valid vaccination was higher among children of Oronkhola union than in children of the other two unions. Conclusion The study documented that valid vaccination coverage was high in this rural area, and there was no significant ethnic variation which was one of the strengths of the national EPI. However, there is significant variation by gender of the child, household ownership of mobile phones and geographical location of households

Delirium risk screening and haloperidol prophylaxis program in hip fracture patients is a helpful tool in identifying high-risk patients, but does not reduce the incidence of delirium

Background: Delirium in patients with hip fractures lead to higher morbidity and mortality. Prevention in high-risk patients by prescribing low dose haloperidol is currently under investigation. Methods. This prospective cohort surveillance assessed hip fracture patients for risk of developing a delirium with the Risk Model for Delirium (RD) score. High-risk patients (score ≥5 points) were treated with a prophylactic low-dose of haloperidol according to hospital protocol. Primary outcome was delirium incidence. Secondary outcomes were differences between high- and low-risk patients in delirium, length of stay (LOS), return to pre-fracture living situation and mortality. Logistic regression analysis was performed with age, ASA-classification, known dementia, having a partner, type of fracture, institutional residence and psychotropic drug use as possible confounders. Results: 445 hip fracture patients aged 65 years and older were admitted from January 2008 to December 2009. The RD-score was completed in 378 patients, 173 (45.8%) high-risk patients were treated with prophylactic medication. Sensitivity was 71.6%, specificity 63.8% and the negative predictive value (NPV) of a score < 5 was 85.9%. Delirium incidence (27.0%) was not significantly different compared to 2007 (27.8%) 2006 (23.9%) and 2005 (29.0%) prior to implementation of the RD- protocol. Logistic regression analysis showed that high-risk patients did have a significant higher delirium incidence (42.2% vs. 14.1%, OR 4.1, CI 2.43-7.02). They were more likely to be residing at an alternative living situation after 3 months (62.3% vs. 17.0%, OR 6.57, CI 3.23-13.37) and less likely to be discharged from hospital before 10 days (34.9% vs. 55.9%, OR 1.63, CI 1.03-2.59). Significant independent risk factors for a delirium were a RD-score 5 (OR 4.13, CI 2.43-7.02), male gender (OR 1.93, CI 0.99-1.07) and age (OR 1.03, CI 0.99-1.07). Conclusions: Introducing the delirium prevention protocol did not reduce delirium incidence. The RD-score did identify patients with a high risk to develop a delirium. This high-risk group had a longer LOS and returned to pre-fracture living situation less often. The NPV of a score < 5 was high, as it should be for a screening instrument. Concluding, the RD-score is a useful tool to identify patients with poorer outcome

Prevention of delirium (POD) for older people in hospital: study protocol for a randomised controlled feasibility trial

Background: Delirium is the most frequent complication among older people following hospitalisation. Delirium may be prevented in about one-third of patients using a multicomponent intervention. However, in the United Kingdom, the National Health Service has no routine delirium prevention care systems. We have developed the Prevention of Delirium Programme, a multicomponent delirium prevention intervention and implementation process. We have successfully carried out a pilot study to test the feasibility and acceptability of implementation of the programme. We are now undertaking preliminary testing of the programme. Methods/Design: The Prevention of Delirium Study is a multicentre, cluster randomised feasibility study designed to explore the potential effectiveness and cost-effectiveness of the Prevention of Delirium Programme. Sixteen elderly care medicine and orthopaedic/trauma wards in eight National Health Service acute hospitals will be randomised to receive the Prevention of Delirium Programme or usual care. Patients will be eligible for the trial if they have been admitted to a participating ward and are aged 65 years or over. The primary objectives of the study are to provide a preliminary estimate of the effectiveness of the Prevention of Delirium Programme as measured by the incidence of new onset delirium, assess the variability of the incidence of new-onset delirium, estimate the intracluster correlation coefficient and likely cluster size, assess barriers to the delivery of the Prevention of Delirium Programme system of care, assess compliance with the Prevention of Delirium Programme system of care, estimate recruitment and follow-up rates, assess the degree of contamination due to between-ward staff movements, and investigate differences in financial costs and benefits between the Prevention of Delirium Programme system of care and standard practice. Secondary objectives are to investigate differences in the number, severity and length of delirium episodes (including persistent delirium); length of stay in hospital; inhospital mortality; destination at discharge; health-related quality of life and health resource use; physical and social independence; anxiety and depression; and patient experience. Discussion: This feasibility study will be used to gather data to inform the design of a future definitive randomised controlled trial. Trial registration: ISRCTN01187372. Registered 13 March 2014