scholarly journals Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Usman Shahzad ◽  
Nadia H. Al-Noor ◽  
Noureen Afshan ◽  
David Anekeya Alilah ◽  
Muhammad Hanif ◽  
...  

Robust regression tools are commonly used to develop regression-type ratio estimators with traditional measures of location whenever data are contaminated with outliers. Recently, the researchers extended this idea and developed regression-type ratio estimators through robust minimum covariance determinant (MCD) estimation. In this study, the quantile regression with MCD-based measures of location is utilized and a class of quantile regression-type mean estimators is proposed. The mean squared errors (MSEs) of the proposed estimators are also obtained. The proposed estimators are compared with the reviewed class of estimators through a simulation study. We also incorporated two real-life applications. To assess the presence of outliers in these real-life applications, the Dixon chi-squared test is used. It is found that the quantile regression estimators are performing better as compared to some existing estimators.

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Javid Shabbir ◽  
Shakeel Ahmed ◽  
Aamir Sanaullah ◽  
Ronald Onyango

In this paper, a ratio-exponential-log type general class of estimators is proposed in estimating the finite population mean using two auxiliary variables when population parameters of the auxiliary variables are known. From the proposed estimator, some special estimators are identified as members of the proposed general class of estimators. The mean square error (MSE) expressions are obtained up to the first order of approximation. This study finds that the proposed general class of estimators outperforms as compared to the conventional mean estimator, usual ratio estimators, exponential-ratio estimators, log-ratio type estimators, and many other competitor regression type estimators. Four real-life applications are used for efficiency comparison.


Author(s):  
J. O. Muili ◽  
E. N. Agwamba ◽  
A. B. Odeyale ◽  
A. Adebiyi

A class of ratio estimators of finite population variance is proposed in this study. The properties of the proposed estimators have been derived using Taylor’s Series method up to first order of approximation. The efficiency conditions which are the mean square errors (MSEs) and percentage relative efficiency (PRE) of the proposed estimators over existing estimators have been established. The analytical illustration was also conducted to affirm the theoretical results. The results of the empirical study revealed that the proposed estimators are more efficient than the existing estimators considered in the study.


Author(s):  
A. Audu ◽  
O. O. Ishaq ◽  
A. Abubakar ◽  
K. A. Akintola ◽  
U. Isah ◽  
...  

Several imputation schemes and estimators have been proposed by different authors in sample survey. However, these estimators utilized quantitative information of auxiliary characters. In this study, some imputation methods were studied using qualitative information of auxiliary characters and two new imputation schemes using auxiliary attribute have been suggested. The mean squared errors of the proposed estimators were derived up to first order approximation using Taylor series approach. Numerical illustrations with two populations were conducted and the results revealed that the proposed estimator is more efficient.


Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 601 ◽  
Author(s):  
Rashad A. R. Bantan ◽  
Mohammed Elgarhy ◽  
Christophe Chesneau ◽  
Farrukh Jamal

The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the Rényi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of Rényi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Malik Muhammad Anas ◽  
Zhensheng Huang ◽  
David Anekeya Alilah ◽  
Ambreen Shafqat ◽  
Sajjad Hussain

Ratio type regression estimator is a prevalent and readily implemented heuristic under simple random sampling (SRS) and two-stage sampling for the estimation of population. But this existing method is based on the ordinary least square (OLS) regression coefficient which is not an effective approach in the presence outliers in the data. In this article, we proposed a class of estimators firstly for complete auxiliary information and, later on, for partial auxiliary information for the presence of outliers in the data. To address this problem, initially we presented a distinct class of estimators by introducing the characteristics of L-moments in the existing estimators. Later on, quantile regression estimators are defined as more robust in the presence of outliers. These techniques empowered the proposed estimators to handle the problem of outliers. To prove the better performance of the proposed estimators, numerical studies are carried out using R language. To calculate the mean square error (MSE), hypothetical equations are expressed for adapted and proposed estimators. Percentage Relative Efficiencies (PRE) are compared to justify the proposed estimators.


2021 ◽  
Vol 6 (12) ◽  
pp. 13592-13607
Author(s):  
Xuechen Liu ◽  
◽  
Muhammad Arslan ◽  

<abstract><p>This article deals with estimation of finite population mean using the auxiliary proportion under simple and two phase sampling scheme utilizing two auxiliary variables. Mathematical expressions for the mean squared errors of the proposed estimators are derived under first order of approximation. We compare the proposed class of estimators "theoretically and numerically" with the usual mean estimator of Naik and Gupta <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. The theoretical as well as numerical findings support the superiority of our proposed class of estimator as compared to estimators available in literature.</p></abstract>


2020 ◽  
pp. 112067212092727
Author(s):  
Marko Lukic ◽  
Gwyn Williams ◽  
Zaid Shalchi ◽  
Praveen J Patel ◽  
Philip G Hykin ◽  
...  

Purpose To assess visual and optical coherence tomography–derived anatomical outcomes of treatment with intravitreal aflibercept (Eylea®) for diabetic macular oedema in patients switched from intravitreal ranibizumab (Lucentis®). Design Retrospective, cohort study. Participants Ninety eyes (of 67 patients) receiving intravitreal anti–vascular endothelial growth factor therapy were included. Methods This is a retrospective, real-life, cohort study. Each patient had visual acuity measurements and optical coherence tomography scans performed at baseline and 12 months after the first injection of aflibercept was given. Main Outcome Measures We measured visual acuities in Early Treatment Diabetic Retinopathy Study letters, central foveal thickness and macular volume at baseline and at 12 months after the first aflibercept injection was given. Results Ninety switched eyes were included in this study. The mean (standard deviation) visual acuity was 63 (15.78) Early Treatment Diabetic Retinopathy Study letters. At baseline, the mean (standard deviation) central foveal thickness was 417.7 (158.4) μm and the mean macular volume was 9.96 (2.44) mm3. Mean change in visual acuity was +4 Early Treatment Diabetic Retinopathy Study letters (p = 0.0053). The mean change in macular volume was −1.53 mm 3 in SW group (p = 0.21), while the change in central foveal thickness was −136.8 μm (p = 0.69). Conclusion There was a significant improvement in visual acuity and in anatomical outcomes in the switched group at 12 months after commencing treatment with aflibercept for diabetic macular oedema.


2021 ◽  
pp. 112067212110057
Author(s):  
Pierre Gascon ◽  
Prithvi Ramtohul ◽  
Charles Delaporte ◽  
Sébastien Kerever ◽  
Danièle Denis ◽  
...  

Purpose: To report the visual and anatomic outcomes in treatment-naïve neovascular age-related macular degeneration (nAMD) patients treated with aflibercept under a standardized Treat and Extend (T&E) protocol for up to 3 years of follow-up in “real-life” practice. Methods: This retrospective, observational, multicenter study included patients with treatment-naïve nAMD and at least 12 months of follow-up. T&E regimen adjustment was initiated after loading phase. At each visit best-corrected visual acuity (BCVA) and optical coherence tomography parameters were performed. Results: One hundred and thirty-six eyes of 115patients had at least 1 year of follow-up with 114 and 82 eyes completing at least 2 and 3 years of follow-up, respectively (mean follow-up duration: 2.7 ± 1.3 years). Mean age was 78.6 ± 8.6 years old and 52% were women. Mean BCVA increased from 60.6 ± 18.7 letters at diagnosis to 66.9 ± 16.2 letters at 1 year (+6.3 letters, p = 0.003) and remained stable throughout the follow-up period (63.1 ± 20.3 letters (+2.5, p = 0.1) and 64.0 ± 20.1 letters (+3.4, p = 0.27) at 2 and 3 years, respectively). The mean central retinal thickness decreased significantly from 358.2 ± 87.9 µm at baseline to 302 ± 71.7 µm at 12 months and maintained stable after 36 months of follow-up (297.1 ± 76 µm, p < 0.0001). Mean number of injections was 6.6 ± 2.2, 4.8 ± 1.9, and 5.6 ± 1.7 at 1, 2, and 3 years, respectively. Mean cumulative number of 16.4 ± 5.6 injections after 3 years. Mean treatment interval was 6.8 ± 2.5 weeks at 1 year. Eight-week and 12-week treatment interval were achieved in 59.5% and 19.1%, 65.8%, and 36.8% and 69.5% and 41.5% at 1, 2, and 3 years, respectively. Conclusions: Our study demonstrated that intravitreal injections of aflibercept initiated under a standardized T&E for patients with treatment-naïve nAMD allow for significant visual improvement at 12 months, which was maintained over a 3-year follow-up period.


2021 ◽  
Vol 80 (Suppl 1) ◽  
pp. 617.1-617
Author(s):  
H. Wohland ◽  
N. Leuchten ◽  
M. Aringer

Background:Fatigue is among the top complaints of patients with systemic lupus erythematosus (SLE), but only in part associated with SLE disease activity. Physical activity can help to reduce fatigue and should therefore be recommended to SLE patients. Vice versa, fatigue may arguably lead to reduced physical activity.Objectives:To investigate the extent of physical activity and the perception of fatigue and sleep quality in patients with SLE.Methods:Starting in February 2019, SLE patients were invited to participate in a cross-sectional survey study of fatigue and physical exercise during their routine outpatient clinic visits. Participants filled out a ten-page paper questionnaire focused on physical activity. To evaluate fatigue, we primarily used a 10 cm visual analogue scale (0-100 mm, with 100 meaning most fatigued), but also the FACIT fatigue score (range 0-52). Sleep quality was estimated using grades from 1 (excellent) to 6 (extremely poor).Results:93 SLE patients took part in the study. All patients fulfilled the European League Against Rheumatism/ American College of Rheumatology (EULAR/ACR) 2019 classification criteria for SLE. 91% of the patients were female. Their mean (SD) age was 45.5 (14.3) years and their mean disease duration 12.1 (9.4) years. The mean BMI was 25.2 (5.6). Of all patients, 7.5% had a diagnosis of (secondary) fibromyalgia. The mean fatigue VAS was 32 (27) mm and the mean FACIT fatigue score 35.7 (10.3). As expected, fatigue by VAS and FACIT was correlated (Spearman r=-0.61, p<0.0001). The mean SLEDAI was 1 (1) with a range of 0 to 6. Median glucocorticoid doses were 2 mg prednisolone equivalent, with a range from 0 to 10 mg.Out of 66 patients in payed jobs, 64 (97%) reported details on their working space. One person (2%) worked in a predominanty standing position, 37 (58%) worked in essentially sedentary jobs and 26 (40%) were in positions where they were mildly physically active in part. The mean fatigue VAS was 31 (24) mm for patients with partly active jobs and 27 (30) mm for those in sedentary jobs. Sleep was graded 2.9 (0.9) by those with active and 3.1 (1.3) by those with sedentary jobs.Half of the patients (51%) reported more than one physical recreational activity. 44 (47%) were walking and for five persons (5%) this was the only form of activity. Cycling was reported by 19 patients (20%), 18 of whom also practiced other activities. For transport, 52 (56%) in part chose active modes, such as walking and cycling. Patients who reported any of the above activities showed a mean fatigue VAS of 28 (25) mm, compared to 36 (28) mm in the patient group without a reported activity. Sleep quality was very similar: 3.1 (1.2) and 3.2 (1.1) for more active and more passive patients, respectively.65 (70%) patients regularly practiced sports. Of these, 39 (60%) practiced one kind of sport, 15 (23%) two, 7 (11%) three, and 2 (3%) each four and five kinds of sports. Fatigue VAS of patients practicing sports was 27 (25) mm versus 43 (28) in those who did not (p=0.0075). Sleep quality was 2.9 (1.1) in the sports cohort and 3.5 (1.1) in the no-sports cohort (p=0.0244).Conclusion:A majority of SLE patients in remission or low to moderate disease activity regularly practiced sports, and those doing so reported lesser fatigue and better sleep quality. The absolute values on the fatigue VAS were in a moderate range that made fatigue as the main cause of not performing sports rather unlikely for most patients.Disclosure of Interests:Helena Wohland: None declared, Nicolai Leuchten Speakers bureau: AbbVie, Janssen, Novartis, Roche, UCB, Consultant of: AbbVie, Janssen, Novartis, Roche, Martin Aringer Speakers bureau: AbbVie, Astra Zeneca, BMS, Boehringer Ingelheim, Chugai, Gilead, GSK, HEXAL, Lilly, MSD, Novartis, Pfizer, Roche, Sanofi, UCB, Consultant of: AbbVie, Astra Zeneca, BMS, Boehringer Ingelheim, GSK, Lilly, MSD, Roche, Sanofi, UCB


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