MEAN SQUARED ERROR COMPARISONS OF SOME BIASED REGRESSION ESTIMATORS

2001 ◽  
Vol 30 (2) ◽  
pp. 347-361 ◽  
Author(s):  
Sadullah Sakallioğlu ◽  
Selabattin Kaçiranlar ◽  
Fikri Akdeniz
Keyword(s):  
Mean Squared Error ◽  
Squared Error ◽  
Regression Estimators ◽  
Biased Regression

THE INTEGRATED MEAN SQUARED ERROR OF SERIES REGRESSION AND A ROSENTHAL HILBERT-SPACE INEQUALITY

2014 ◽  
Vol 31 (2) ◽  
pp. 337-361 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Hilbert Space ◽  
Least Squares ◽  
Mean Squared Error ◽  
Least Squares Estimators ◽  
Squared Error ◽  
Statistics And Probability ◽  
Uniform Approximations ◽  
Regression Estimators ◽  
Berkeley Symposium ◽  
Integrated Mean Squared Error

This paper develops uniform approximations for the integrated mean squared error (IMSE) of nonparametric series regression estimators, including both least-squares and averaging least-squares estimators. To develop these approximations, we also generalize an important probability inequality of Rosenthal (1970, Israel Journal of Mathematics 8, 273–303; 1972, Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 149–167. University of California Press) to the case of Hilbert-space valued random variables.

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

Image Quality Enhancing by Efficient Histogram Equalization

2014 ◽  
Vol 2 (2) ◽  
pp. 47-58
Author(s):  
Ismail Sh. Baqer
Keyword(s):  
Image Quality ◽  
Contrast Enhancement ◽  
Mean Squared Error ◽  
Signal To Noise Ratio ◽  
Histogram Equalization ◽  
Gray Level ◽  
Signal To Noise ◽  
Squared Error ◽  
Noise Ratio

A two Level Image Quality enhancement is proposed in this paper. In the first level, Dualistic Sub-Image Histogram Equalization DSIHE method decomposes the original image into two sub-images based on median of original images. The second level deals with spikes shaped noise that may appear in the image after processing. We presents three methods of image enhancement GHE, LHE and proposed DSIHE that improve the visual quality of images. A comparative calculations is being carried out on above mentioned techniques to examine objective and subjective image quality parameters e.g. Peak Signal-to-Noise Ratio PSNR values, entropy H and mean squared error MSE to measure the quality of gray scale enhanced images. For handling gray-level images, convenient Histogram Equalization methods e.g. GHE and LHE tend to change the mean brightness of an image to middle level of the gray-level range limiting their appropriateness for contrast enhancement in consumer electronics such as TV monitors. The DSIHE methods seem to overcome this disadvantage as they tend to preserve both, the brightness and contrast enhancement. Experimental results show that the proposed technique gives better results in terms of Discrete Entropy, Signal to Noise ratio and Mean Squared Error values than the Global and Local histogram-based equalization methods

scholarly journals Thematic Maps for the Variation of Bearing Capacity of Soil Using SPTs and MATLAB

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 329
Author(s):  
Mahdi O. Karkush ◽  
Mahmood D. Ahmed ◽  
Ammar Abdul-Hassan Sheikha ◽  
Ayad Al-Rumaithi
Keyword(s):  
Bearing Capacity ◽  
Mean Squared Error ◽  
Ground Level ◽  
The Other ◽  
Thematic Maps ◽  
First Order ◽  
Squared Error ◽  
Order Polynomial ◽  
Interpolation Polynomials ◽  
Penetration Tests

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production of thematic maps showing the variation of the bearing capacity of the soil over the whole area of Al-Basrah city correlated with several depths. The bearing capacity of soil obtained from the suggested first-order polynomial matches well with those calculated from the results of SPTs with a deviation of ±30% at a 95% confidence interval.

scholarly journals Industrial Control under Non-Ideal Measurements: Data-Based Signal Processing as an Alternative to Controller Retuning

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1237
Author(s):  
Ivan Pisa ◽  
Antoni Morell ◽  
Ramón Vilanova ◽  
Jose Lopez Vicario
Keyword(s):  
Mean Squared Error ◽  
Control Strategies ◽  
Treatment Plant ◽  
Industrial Control ◽  
Output Data ◽  
Complex Processes ◽  
Squared Error ◽  
Complex Design ◽  
Solution Design ◽  
Delay Correction

Industrial environments are characterised by the non-lineal and highly complex processes they perform. Different control strategies are considered to assure that these processes are correctly performed. Nevertheless, these strategies are sensible to noise-corrupted and delayed measurements. For that reason, denoising techniques and delay correction methodologies should be considered but, most of these techniques require a complex design and optimisation process as a function of the scenario where they are applied. To alleviate this, a complete data-based approach devoted to denoising and correcting the delay of measurements is proposed here with a two-fold objective: simplify the solution design process and achieve its decoupling from the considered control strategy as well as from the scenario. Here it corresponds to a Wastewater Treatment Plant (WWTP). However, the proposed solution can be adopted at any industrial environment since neither an optimization nor a design focused on the scenario is required, only pairs of input and output data. Results show that a minimum Root Mean Squared Error (RMSE) improvement of a 63.87% is achieved when the new proposed data-based denoising approach is considered. In addition, the whole system performance show that similar and even better results are obtained when compared to scenario-optimised methodologies.

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