Approximation for error rates associated with the discriminant function based on absolute deviation from the mean

2008 ◽  
Vol 11 (5) ◽  
pp. 861-881 ◽  
Author(s):  
S. Ganesalingam ◽  
Siva Ganesh ◽  
A. Nanthakumar
Keyword(s):  
Discriminant Function ◽  
Error Rates ◽  
Absolute Deviation ◽  
The Mean

scholarly journals Portfolio Optimization with a Mean–Absolute Deviation–Entropy Multi-Objective Model

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1266
Author(s):  
Weng Siew Lam ◽  
Weng Hoe Lam ◽  
Saiful Hafizah Jaaman
Keyword(s):  
Portfolio Optimization ◽  
Performance Ratio ◽  
Programming Approach ◽  
Mean Absolute Deviation ◽  
Diversification Strategy ◽  
Absolute Deviation ◽  
Multi Objective ◽  
Proposed Model ◽  
The Mean ◽  
Naïve Diversification

Investors wish to obtain the best trade-off between the return and risk. In portfolio optimization, the mean-absolute deviation model has been used to achieve the target rate of return and minimize the risk. However, the maximization of entropy is not considered in the mean-absolute deviation model according to past studies. In fact, higher entropy values give higher portfolio diversifications, which can reduce portfolio risk. Therefore, this paper aims to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by incorporating the maximization of entropy. In addition, the proposed model incorporates the optimal value of each objective function using a goal-programming approach. The objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. The proposed model is illustrated using returns of stocks of the Dow Jones Industrial Average that are listed in the New York Stock Exchange. This study will be of significant impact to investors because the results show that the proposed model outperforms the mean-absolute deviation model and the naive diversification strategy by giving higher a performance ratio. Furthermore, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy. Investors will be able to generate a well-diversified portfolio in order to minimize unsystematic risk with the proposed model.

scholarly journals Another Warning about Median Reaction Time --- Version of 11 Feb 2020

2020 ◽  
Author(s):  
Jeff Miller
Keyword(s):  
Type I Error ◽  
Reaction Times ◽  
Error Rates ◽  
Type I ◽  
Experimental Conditions ◽  
Type I Error Rates ◽  
Correction Technique ◽  
Inflated Type ◽  
The Mean ◽  
Rt Distributions

Contrary to the warning of Miller (1988), Rousselet and Wilcox (2020) argued that it is better to summarize each participant’s single-trial reaction times (RTs) in a given condition with the median than with the mean when comparing the central tendencies of RT distributions across experimental conditions. They acknowledged that median RTs can produce inflated Type I error rates when conditions differ in the number of trials tested, consistent with Miller’s warning, but they showed that the bias responsible for this error rate inflation could be eliminated with a bootstrap bias correction technique. The present simulations extend their analysis by examining the power of bias-corrected medians to detect true experimental effects and by comparing this power with the power of analyses using means and regular medians. Unfortunately, although bias-corrected medians solve the problem of inflated Type I error rates, their power is lower than that of means or regular medians in many realistic situations. In addition, even when conditions do not differ in the number of trials tested, the power of tests (e.g., t-tests) is generally lower using medians rather than means as the summary measures. Thus, the present simulations demonstrate that summary means will often provide the most powerful test for differences between conditions, and they show what aspects of the RT distributions determine the size of the power advantage for means.

scholarly journals Kajian Adaptive Neuro-Fuzzy Inference System (ANFIS) Dalam Memprediksi Penerimaan Mahasiswa Baru Pada Universitas Buana Perjuangan Karawang

2021 ◽  
Vol 6 (1) ◽  
pp. 44-54
Author(s):  
Tatang Rohana Cucu
Keyword(s):  
Error Rate ◽  
Fuzzy Inference ◽  
Percentage Error ◽  
Hybrid Technique ◽  
Mean Absolute Deviation ◽  
Absolute Deviation ◽  
Inference System ◽  
Neuro Fuzzy ◽  
New Students ◽  
The Mean

Abstract - The process of admitting new students is an annual routine activity that occurs in a university. This activity is the starting point of the process of searching for prospective new students who meet the criteria expected by the college. One of the colleges that holds new student admissions every year is Buana Perjuangan University, Karawang. There have been several studies that have been conducted on predictions of new students by other researchers, but the results have not been very satisfying, especially problems with the level of accuracy and error. Research on ANFIS studies to predict new students as a solution to the problem of accuracy. This study uses two ANFIS models, namely Backpropagation and Hybrid techniques. The application of the Adaptive Neuro-Fuzzy Inference System (ANFIS) model in the predictions of new students at Buana Perjuangan University, Karawang was successful. Based on the results of training, the Backpropagation technique has an error rate of 0.0394 and the Hybrid technique has an error rate of 0.0662. Based on the predictive accuracy value that has been done, the Backpropagation technique has an accuracy of 4.8 for the value of Mean Absolute Deviation (MAD) and 0.156364623 for the value of Mean Absolute Percentage Error (MAPE). Meanwhile, based on the Mean Absolute Deviation (MAD) value, the Backpropagation technique has a value of 0.5 and 0.09516671 for the Mean Absolute Percentage Error (MAPE) value. So it can be concluded that the Hybrid technique has a better level of accuracy than the Backpropation technique in predicting the number of new students at the University of Buana Perjuangan Karawang.   Keywords: ANFIS, Backpropagation, Hybrid, Prediction

scholarly journals Robust Confidence Intervals for PM2.5 Concentration Measurements in the Ecuadorian Park La Carolina

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 654 ◽  
Author(s):  
Wilmar Hernandez ◽  
Alfredo Mendez ◽  
Rasa Zalakeviciute ◽  
Angela Maria Diaz-Marquez
Keyword(s):  
Air Pollution ◽  
Standard Deviation ◽  
Confidence Intervals ◽  
Quality Index ◽  
Urban Park ◽  
Absolute Deviation ◽  
The Mean ◽  
Concentration Measurements ◽  
Pm2.5 Concentration

In this article, robust confidence intervals for PM2.5 (particles with size less than or equal to 2.5   μ m ) concentration measurements performed in La Carolina Park, Quito, Ecuador, have been built. Different techniques have been applied for the construction of the confidence intervals, and routes around the park and through the middle of it have been used to build the confidence intervals and classify this urban park in accordance with categories established by the Quito air quality index. These intervals have been based on the following estimators: the mean and standard deviation, median and median absolute deviation, median and semi interquartile range, a -trimmed mean and Winsorized standard error of order a , location and scale estimators based on the Andrew’s wave, biweight location and scale estimators, and estimators based on the bootstrap- t method. The results of the classification of the park and its surrounding streets showed that, in terms of air pollution by PM2.5, the park is not at caution levels. The results of the classification of the routes that were followed through the park and its surrounding streets showed that, in terms of air pollution by PM2.5, these routes are at either desirable, acceptable or caution levels. Therefore, this urban park is actually removing or attenuating unwanted PM2.5 concentration measurements.

scholarly journals Comparable surgery time for robotic assisted total knee arthroplasty after initial learning curve

2020 ◽  
Vol 8 (5_suppl4) ◽  
pp. 2325967120S0031
Author(s):  
Peter Savov ◽  
Lars-René Tücking ◽  
Henning Windhagen ◽  
Max Ettinger
Keyword(s):  
Learning Curve ◽  
Robotic System ◽  
Robotic Group ◽  
Absolute Deviation ◽  
Robotic Assisted ◽  
Time Of Surgery ◽  
Implant Positioning ◽  
Initial Learning ◽  
Manual Group ◽  
The Mean

Aims and Objectives: In the past years, further development in knee replacement still continues. Computer-assisted surgery techniques in total knee arthroplasty (TKA) are on the rise. One point of criticism is the prolonged time of surgery and associated cost as known from old techniques like navigation. The primary objective of this study was to determine the learning curve for the time of surgery and accuracy in implant positioning for an imageless robotic system for TKA. Materials and Methods: In this prospective study, the first 30 robotic-assisted TKA from a single senior surgeon were analyzed with regard to time of surgery and accuracy of implant position on the basis of the intraoperative plan and the postoperative x-rays. This data was compared to the last 30 manual TKAs of the same surgeon with the same prosthesis. Evaluation of the learning curve was performed with CUSUM analysis. The time of surgery after finishing the learning curve in the robotic group was compared to the manual group. Results: The learning curve in the robotic group for surgery time was finished after 11 cases. The robotic experience did not affect the accuracy of implant positioning, such as limb alignment and restoration of the joint line. The mean absolute deviation of the postoperative limb alignment to the intraoperative plan was 2° (+/- 1,1). The mean absolute deviation of the medial proximal tibial (mPTA) and distal lateral femoral angle (dLFA) was 1° (+/- 0,9) for both. The mean surgery time in the robotic group after finishing the learning curve was 66 minutes (+/- 4,2) and in the total manual group 67 minutes (+/- 3,5) (n.s.). Conclusion: After finishing the initial learning curve of 11 cases for robotic-assisted TKA the time of surgery is equal to the manual conventional technique. However, there is no learning curve for implant positioning with the imageless robotic system. The implementation of the intraoperative plan is accurate to 1° with the robotic system.

Sequential probability ratio tests: conservative and robust

SIMULATION ◽  
2020 ◽  
Vol 97 (1) ◽  
pp. 33-43
Author(s):  
Jack P C Kleijnen ◽  
Wen Shi
Keyword(s):  
Error Rates ◽  
Normal Distributions ◽  
Probability Ratio ◽  
Monte Carlo Experiments ◽  
Actual Error ◽  
Sequential Probability Ratio Tests ◽  
Statistical Hypotheses ◽  
Sequential Probability ◽  
The Mean ◽  
Pilot Sample

Because computers (except for parallel computers) generate simulation outputs sequentially, we recommend sequential probability ratio tests (SPRTs) for the statistical analysis of these outputs. However, until now simulation analysts have ignored SPRTs. To change this situation, we review SPRTs for the simplest case; namely, the case of choosing between two hypothesized values for the mean simulation output. For this case, the classic SPRT of Wald (Wald A. Sequential tests of statistical hypotheses. Ann Math Stat 1945; 16: 117–186) allows general types of distribution, including normal distributions with known variances. A modification permits unknown variances that are estimated. Hall (Hall WJ. Some sequential analogs of Stein’s two-stage test. Biometrika 1962; 49: 367–378) developed a SPRT that assumes normal distributions with unknown variances estimated from a pilot sample. A modification uses a fully sequential variance estimator. In this paper, we quantify the performance of the various SPRTs, using several Monte Carlo experiments. In experiment #1, simulation outputs are normal. Whereas Wald’s SPRT with estimated variance gives too high error rates, Hall’s original and modified SPRTs are “conservative”; that is, the actual error rates are smaller than those prespecified (nominal). Furthermore, our experiment shows that the most efficient SPRT is Hall’s modified SPRT. In experiment #2, we estimate the robustness of these SPRTs for non-normal output. For these two experiments, we provide details on their design and analysis; these details may also be useful for simulation experiments in general.

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