scholarly journals Jump or kink: on super-efficiency in segmented linear regression breakpoint estimation

Biometrika ◽  
2020 ◽  
Author(s):  
Yining Chen
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Convergence Rate ◽  
Pointwise Convergence ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
The Other ◽  
Fixed Parameter ◽  
The Mean ◽  
Potential Remedy

Summary We consider the problem of segmented linear regression with a single breakpoint, with the focus on estimating the location of the breakpoint. If $n$ is the sample size, we show that the global minimax convergence rate for this problem in terms of the mean absolute error is $O(n^{-1/3})$. On the other hand, we demonstrate the construction of a super-efficient estimator that achieves the pointwise convergence rate of either $O(n^{-1})$ or $O(n^{-1/2})$ for every fixed parameter value, depending on whether the structural change is a jump or a kink. The implications of this example and a potential remedy are discussed.

scholarly journals A new hybrid of Fuzzy C-Means Method and Fuzzy Linear Regression Model in Predicting Manufacturing Income

2018 ◽  
Vol 7 (4.30) ◽  
pp. 473
Author(s):  
Nurfarawahida Ramly ◽  
Mohd Saifullah Rusiman ◽  
Norziha Che Him ◽  
Maria Elena Nor ◽  
Supar Man ◽  
...  
Keyword(s):  
Linear Regression ◽  
Mean Absolute Error ◽  
Human Perception ◽  
Absolute Error ◽  
Percentage Error ◽  
Fuzzy Linear Regression ◽  
Fuzzy C Means ◽  
Fuzzy Linear Regression Model ◽  
The Mean ◽  
Ambiguous Data

Analysis by human perception could not be solved using traditional method since uncertainty within the data have to be dealt with first. Thus, fuzzy structure system is considered. The objectives of this study are to determine suitable cluster by using fuzzy c-means (FCM) method, to apply existing methods such as multiple linear regression (MLR) and fuzzy linear regression (FLR) as proposed by Tanaka and Ni and to improve the FCM method and FLR model proposed by Zolfaghari to predict manufacturing income. This study focused on FLR which is suitable for ambiguous data in modelling. Clustering is used to cluster or group the data according to its similarity where FCM is the best method. The performance of models will measure by using the mean square error (MSE), the mean absolute error (MAE) and the mean absolute percentage error (MAPE). Results shows that the improvisation of FCM method and FLR model obtained the lowest value of error measurement with MSE=1.825 , MAE=115932.702 and MAPE=95.0366. Therefore, as the conclusion, a new hybrid of FCM method and FLR model are the best model for predicting manufacturing income compared to the other models.

Explanation Plus Prediction—The Logical Focus of Project Management Research

2021 ◽  
pp. 875697282199994
Author(s):  
Joseph F. Hair ◽  
Marko Sarstedt
Keyword(s):  
Project Management ◽  
Statistical Models ◽  
Predictive Power ◽  
Mean Absolute Error ◽  
Explanatory Power ◽  
Absolute Error ◽  
Model Parameters ◽  
Mean Square ◽  
Management Research ◽  
The Mean

Most project management research focuses almost exclusively on explanatory analyses. Evaluation of the explanatory power of statistical models is generally based on F-type statistics and the R 2 metric, followed by an assessment of the model parameters (e.g., beta coefficients) in terms of their significance, size, and direction. However, these measures are not indicative of a model’s predictive power, which is central for deriving managerial recommendations. We recommend that project management researchers routinely use additional metrics, such as the mean absolute error or the root mean square error, to accurately quantify their statistical models’ predictive power.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

scholarly journals Direct Calculation of Thermodynamic Wet-Bulb Temperature as a Function of Pressure and Elevation

2013 ◽  
Vol 30 (8) ◽  
pp. 1757-1765 ◽  
Author(s):  
Sayed-Hossein Sadeghi ◽  
Troy R. Peters ◽  
Douglas R. Cobos ◽  
Henry W. Loescher ◽  
Colin S. Campbell
Keyword(s):  
Air Temperature ◽  
Mean Absolute Error ◽  
Direct Calculation ◽  
Ambient Air ◽  
Absolute Error ◽  
Mean Square ◽  
Air Temperatures ◽  
Order Polynomial ◽  
The Mean ◽  
Very High

Abstract A simple analytical method was developed for directly calculating the thermodynamic wet-bulb temperature from air temperature and the vapor pressure (or relative humidity) at elevations up to 4500 m above MSL was developed. This methodology was based on the fact that the wet-bulb temperature can be closely approximated by a second-order polynomial in both the positive and negative ranges in ambient air temperature. The method in this study builds upon this understanding and provides results for the negative range of air temperatures (−17° to 0°C), so that the maximum observed error in this area is equal to or smaller than −0.17°C. For temperatures ≥0°C, wet-bulb temperature accuracy was ±0.65°C, and larger errors corresponded to very high temperatures (Ta ≥ 39°C) and/or very high or low relative humidities (5% < RH < 10% or RH > 98%). The mean absolute error and the root-mean-square error were 0.15° and 0.2°C, respectively.

scholarly journals Novel Spatiotemporal Feature Extraction Parallel Deep Neural Network for Forecasting Confirmed Cases of Coronavirus Disease 2019

2020 ◽  
Author(s):  
Chiou-Jye Huang ◽  
Yamin Shen ◽  
Ping-Huan Kuo ◽  
Yung-Hsiang Chen
Keyword(s):  
Neural Network ◽  
Deep Neural Network ◽  
Absolute Error ◽  
Mean Absolute Percentage Error ◽  
The Other ◽  
Percentage Error ◽  
Model Assessment ◽  
Absolute Percentage Error ◽  
Spatiotemporal Feature ◽  
The Mean

AbstractThe coronavirus disease 2019 pandemic continues as of March 26 and spread to Europe on approximately February 24. A report from April 29 revealed 1.26 million confirmed cases and 125 928 deaths in Europe. This study proposed a novel deep neural network framework, COVID-19Net, which parallelly combines a convolutional neural network (CNN) and bidirectional gated recurrent units (GRUs). Three European countries with severe outbreaks were studied—Germany, Italy, and Spain—to extract spatiotemporal feature and predict the number of confirmed cases. The prediction results acquired from COVID-19Net were compared to those obtained using a CNN, GRU, and CNN-GRU. The mean absolute error, mean absolute percentage error, and root mean square error, which are commonly used model assessment indices, were used to compare the accuracy of the models. The results verified that COVID-19Net was notably more accurate than the other models. The mean absolute percentage error generated by COVID-19Net was 1.447 for Germany, 1.801 for Italy, and 2.828 for Spain, which were considerably lower than those of the other models. This indicated that the proposed framework can accurately predict the accumulated number of confirmed cases in the three countries and serve as a crucial reference for devising public health strategies.

scholarly journals A Novel Neural Network Model for Blood Pressure Estimation Using Photoplethesmography without Electrocardiogram

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Ludi Wang ◽  
Wei Zhou ◽  
Ying Xing ◽  
Xiaoguang Zhou
Keyword(s):  
Neural Network ◽  
Blood Pressure ◽  
Mean Absolute Error ◽  
Wearable Sensors ◽  
Absolute Error ◽  
Noninvasive Estimation ◽  
Treatment Of Hypertension ◽  
The Mean ◽  
Artificial Neural Network Ann ◽  
Blood Pressure Estimation

The prevention, evaluation, and treatment of hypertension have attracted increasing attention in recent years. As photoplethysmography (PPG) technology has been widely applied to wearable sensors, the noninvasive estimation of blood pressure (BP) using the PPG method has received considerable interest. In this paper, a method for estimating systolic and diastolic BP based only on a PPG signal is developed. The multitaper method (MTM) is used for feature extraction, and an artificial neural network (ANN) is used for estimation. Compared with previous approaches, the proposed method obtains better accuracy; the mean absolute error is 4.02 ± 2.79 mmHg for systolic BP and 2.27 ± 1.82 mmHg for diastolic BP.

Validating the usefulness of sectorwise regression of visual field in the central 10°

2021 ◽  
pp. bjophthalmol-2020-317391
Author(s):  
Takashi Omoto ◽  
Hiroshi Murata ◽  
Yuri Fujino ◽  
Masato Matsuura ◽  
Takehiro Yamashita ◽  
...  
Keyword(s):  
Visual Field ◽  
Mean Absolute Error ◽  
Open Angle Glaucoma ◽  
Absolute Error ◽  
Open Angle ◽  
Clustering Method ◽  
Significant Difference ◽  
The Mean ◽  
Test Points

AimTo evaluate the usefulness of the application of the clustering method to the trend analysis (sectorwise regression) in comparison with the pointwise linear regression (PLR).MethodsThis study included 153 eyes of 101 patients with open-angle glaucoma. With PLR, the total deviation (TD) values of the 10th visual field (VF) were predicted using the shorter VF sequences (from first 3 to 9) by extrapolating TD values against time in a pointwise manner. Then, 68 test points were stratified into 29 sectors. In each sector, the mean of TD values was calculated and allocated to all test points belonging to the sector. Subsequently, the TD values of the 10th VF were predicted by extrapolating the allocated TD value against time in a pointwise manner. Similar analyses were conducted to predict the 11th–16th VFs using the first 10 VFs.ResultsWhen predicting the 10th VF using the shorter sequences, the mean absolute error (MAE) values were significantly smaller in the sectorwise regression than in PLR. When predicting from the 11th and 16th VFs using the first 10 VFs, the MAE values were significantly larger in the sectorwise regression than in PLR when predicting the 11th VF; however, no significant difference was observed with other VF predictions.ConclusionAccurate prediction was achieved using the sectorwise regression, in particular when a small number of VFs were used in the prediction. The accuracy of the sectorwise regression was not hampered in longer follow-up compared with PLR.

Accuracy Assessment of TanDEM-X 90 and CartoDEM Using ICESat-2 Datasets for Plain Regions of Ratlam City and Surroundings

2021 ◽  
Vol 10 (1) ◽  
pp. 59
Author(s):  
Unnati Yadav ◽  
Ashutosh Bhardwaj
Keyword(s):  
Mean Absolute Error ◽  
Accuracy Assessment ◽  
Absolute Error ◽  
Terrain Analysis ◽  
Mean Square ◽  
High Quality ◽  
Ice Cloud ◽  
The Mean ◽  
Cut And Fill ◽  
Statistical Results

The spaceborne LiDAR dataset from the Ice, Cloud, and Land Elevation Satellite (ICESat-2) provides highly accurate measurements of heights for the Earth’s surface, which helps in terrain analysis, visualization, and decision making for many applications. TanDEM-X 90 (90 m) and CartoDEM V3R1 (30 m) elevation are among the high-quality openly accessible DEM datasets for the plain regions in India. These two DEMs are validated against the ICESat-2 elevation datasets for the relatively plain areas of Ratlam City and its surroundings. The mean error (ME), mean absolute error (MAE), and root mean square error (RMSE) of TanDEM-X 90 DEM are 1.35 m, 1.48 m, and 2.19 m, respectively. The computed ME, MAE, and RMSE for CartoDEM V3R1 are 3.05 m, 3.18 m, and 3.82 m, respectively. The statistical results reveal that TanDEM-X 90 performs better in plain areas than CartoDEMV3R1. The study further indicates that these DEMs and spaceborne LiDAR datasets can be useful for planning various works requiring height as an important parameter, such as the layout of pipelines or cut and fill calculations for various construction activities. The TanDEM-X 90 can assist planners in quick assessments of the terrain for infrastructural developments, which otherwise need time-consuming traditional surveys using theodolite or a total station.

Intraocular lenses optic power calculation with seven formulas in short eyes

2021 ◽  
pp. 57-61
Author(s):  
K.B. Pershin ◽  
◽  
N.F. Pashinova ◽  
I.A. Likh ◽  
А.Y. Tsygankov ◽  
...  
Keyword(s):  
Axial Length ◽  
Mean Absolute Error ◽  
Optical Power ◽  
Absolute Error ◽  
Intraocular Lenses ◽  
Power Calculation ◽  
Retrospective Comparison ◽  
Monofocal Iol ◽  
The Mean ◽  
Axial Eye Length

Purpose. The choice of the optimal formula for calculating the IOL optical power in patients with an axial eye length of less than 20 mm. Material and methods. A total of 78 patients (118 eyes) were included in the prospective study. 1st group included 30 patients (52 eyes) with short eyes (average axial eye length of 19.60±0.42 (18.54–20.0) mm), 2nd group consisted of 48 patients (66 eyes) with a axial length 22.75±0.46 (22.0–23.77) mm. Various monofocal IOL models were used. The average follow-up period was 13 months. IOL optical power was calculated using the SRK/T formula, retrospective comparison – according to the formulas Hoffer-Q, Holladay II, Olsen, Haigis, Barrett Universal II and Kane. Results. In 1st group, the mean absolute error was determined for the formulas Haigis, Olsen, Barrett Universal II, Kane, SRK/T, Holladay II and Hoffer-Q (0.85, 0.78, 0.21, 0.17, 0.79, 0.73, 0.19 respectively). When comparing the formulas, significant differences were found for the formulas Hoffer-Q, Barrett Universal II and Kane in comparison with the formulas Haigis, Olsen, SRK/T and Holladay II (p<0.05) in all cases, respectively. In 2nd group, the mean absolute error was determined for the formulas Haigis, Olsen, Barrett Universal II, Kane, SRK/T, Holladay II and Hoffer-Q (0.15, 0.16, 0.23, 0.10, 0.19, 0.23, 0,29 respectively). In 2nd group, there were no significant differences between the studied formulas (p>0.05). Conclusion. This paper presents an analysis of data on the effectiveness of seven formulas for calculating the IOL optical power in short (less than 20 mm) eyes in comparison with the normal axial length. The advantage of the Hoffer-Q, Barrett Universal II and Kane formulas over Haigis, Holladay II, Olsen, and SRK/T is shown. Key words: cataract, hypermetropia, short eyes, calculation of the IOL optical power.

scholarly journals Day-Ahead Photovoltaic Forecasting: A Comparison of the Most Effective Techniques

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1621 ◽  
Author(s):  
Alfredo Nespoli ◽  
Emanuele Ogliari ◽  
Sonia Leva ◽  
Alessandro Massi Pavan ◽  
Adel Mellit ◽  
...  
Keyword(s):  
Hybrid Method ◽  
Mean Absolute Error ◽  
Weather Forecast ◽  
Absolute Error ◽  
The Other ◽  
Pv System ◽  
Weather Forecasts ◽  
Forecasting Method ◽  
Forecasting Performance ◽  
Stable Performance

We compare the 24-hour ahead forecasting performance of two methods commonly used for the prediction of the power output of photovoltaic systems. Both methods are based on Artificial Neural Networks (ANN), which have been trained on the same dataset, thus enabling a much-needed homogeneous comparison currently lacking in the available literature. The dataset consists of an hourly series of simultaneous climatic and PV system parameters covering an entire year, and has been clustered to distinguish sunny from cloudy days and separately train the ANN. One forecasting method feeds only on the available dataset, while the other is a hybrid method as it relies upon the daily weather forecast. For sunny days, the first method shows a very good and stable prediction performance, with an almost constant Normalized Mean Absolute Error, NMAE%, in all cases (1% < NMAE% < 2%); the hybrid method shows an even better performance (NMAE% < 1%) for two of the days considered in this analysis, but overall a less stable performance (NMAE% > 2% and up to 5.3% for all the other cases). For cloudy days, the forecasting performance of both methods typically drops; the performance is rather stable for the method that does not use weather forecasts, while for the hybrid method it varies significantly for the days considered in the analysis.

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