Finite Sample Mean Square Error of Forecast for the Difference Stationary and the Trend Stationary Processes

2012 ◽  
Author(s):  
Naresh C. Mallick
Keyword(s):  
Mean Square Error ◽  
Stationary Processes ◽  
Mean Square ◽  
Finite Sample ◽  
Sample Mean ◽  
The Difference

Time-Domain Filtering of Two-Dimensional Fluorescence Data

1986 ◽  
Vol 40 (4) ◽  
pp. 542-548 ◽  
Author(s):  
Maria Vicsek ◽  
Sharon L. Neal ◽  
Isiah M. Warner
Keyword(s):  
Error Analysis ◽  
Mean Square Error ◽  
Time Domain ◽  
Moving Average ◽  
Mean Square ◽  
Two Dimensional ◽  
Spline Method ◽  
Dimensional Version ◽  
The Difference ◽  
Polynomial Smoothing

Four time-domain filtering methods are applied to simulated and experimental two-dimensional fluorescence data in order to evaluate their performance. The methods that were evaluated are (1) moving average, (2) Savitsky-Golay polynomial smoothing, (3) Chebyshev filtering, and (4) bicubic spline filtering. The methods are compared with the use of mean square error analysis and the difference in the amplitudes of the filtered noisy and ideal data. The two-dimensional version of the Savitzky-Golay filtering and the spline method produced the best overall results.

Generalized Levinson–Durbin Sequences and Binomial Coefficients

Integers ◽  
2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Paul Shaman
Keyword(s):  
Stochastic Process ◽  
Sample Size ◽  
Mean Square Error ◽  
Discrete Time ◽  
Minimum Mean Square Error ◽  
Stationary Stochastic Process ◽  
Binomial Coefficients ◽  
Stationary Processes ◽  
Mean Square ◽  
Special Case

AbstractThe Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson–Durbin sequence is also defined, and we note that binomial coefficients constitute a special case of such a sequence. Generalized Levinson–Durbin sequences obey formulas which generalize relations satisfied by binomial coefficients. Some of these results are extended to vector stationary processes.

The Cramer–Rao lower bound in a non-AWGN model for the affine phase retrieval

2021 ◽  
pp. 2050089
Author(s):  
Zhitao Zhuang ◽  
Kaixin Wang
Keyword(s):  
Lower Bound ◽  
Mean Square Error ◽  
Gaussian Noise ◽  
Phase Retrieval ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Mean Square ◽  
Cramer Rao Lower Bound ◽  
The Difference

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

The Loss of Dexterity in the Bilateral Lower Extremities in Patients With Stroke

2011 ◽  
Vol 27 (2) ◽  
pp. 122-129 ◽  
Author(s):  
Ryoji Kiyama ◽  
Kiyohiro Fukudome ◽  
Toshiki Hiyoshi ◽  
Akihide Umemoto ◽  
Yoichi Yoshimoto ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Knee Extensor ◽  
Lower Extremities ◽  
Response Force ◽  
Mean Square ◽  
Control Subjects ◽  
The Difference ◽  
Mean Square Errors

The aim of this study was to examine the dexterity of both lower extremities in patients with stroke. Twenty patients with stroke and 20 age-matched control subjects participated in this study. To determine the dexterity of the lower extremities, we examined the ability to control muscle force during submaximal contractions in the knee extensor muscles using a force tracking task. The root mean square errors were calculated from the difference between the target and response force. The root mean square error was significantly greater in the affected limb of patients with stroke compared with those of the unaffected limb and the control subjects, and in the unaffected limb compared with that of the control subjects. Furthermore, the root mean square error of the affected limb was related significantly to motor function as determined by Fugl-Myer assessment. These results demonstrate impairment of the dexterity of both the affected and the unaffected lower extremities in patients with stroke.

scholarly journals A FULL DUAL MEAN SQUARE ERROR CRITERION FOR THE EQUIVALENT LINEARIZATION

2016 ◽  
Vol 54 (4) ◽  
pp. 557
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Minh Triet
Keyword(s):  
Mean Square Error ◽  
Nonlinear Function ◽  
Approximate Solutions ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Approximate Methods ◽  
Dual Approach ◽  
The Difference ◽  
Mean Square Error Criterion

Among approximate methods, the method of equivalent linearization proposed by N. Krylov and N. Bogoliubov and extended by Caughey has remained an effective tool for both deterministic and stochastic problems. The idea of the method is based on the replacement of a nonlinear oscillator by a linear one under the same excitation. The standard way of implementing this method is that the coefficients of linearization are to be found from a criterion of equivalence. When the difference between the nonlinear function and equivalent linear one is significant the replacement leads to unaccepted errors. In order to reduce the errors one may apply the dual approach. One of significant advantages of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. In this paper a special case of the weighted full dual mean square error criterion is introduced and investigated in detail. Numerical results are carried out to show that this special full dual mean square error criterion can give more accurate approximate solutions for both deterministic and random nonlinear systems.

scholarly journals Wavefront Aberrations in Subjects Wearing Soft Aspheric Contact Lenses and Those Wearing Spherical Ones

2015 ◽  
Vol 77 (3) ◽  
pp. 13
Author(s):  
Alexandra Fraser ◽  
Nicolas Fontaine ◽  
Valérie Lambert
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Dry Eye ◽  
Contact Lens ◽  
Contact Lenses ◽  
Spherical Aberration ◽  
Mean Square ◽  
Similar Increase ◽  
Wavefront Aberrations ◽  
The Difference

Purpose: To measure the level of higher order aberrations (HOA) when wearing a soft aspheric contact lens (CL), compared to a spherical CL, in myopic subjects. Method: Fifteen myopic subjects aged 20-30 years were tested for the presence of dry eye. Aberrometry measurements were done without a contact lens as well as with a spherical CL and an aspheric CL. Root mean square error (RMS) of HOA, spherical aberration (SA) and coma were measured five times in an interval of 15 seconds without blinking for each of the 3 conditions. Results: Wearing a spherical CL produced a significant increase of SA and horizontal coma compared to an eye without a contact lens. When wearing an aspheric CL, there was a trend towards a smaller increase of these aberrations. However, the difference between both types of lens was not statistically significant. In terms of total HOA, these were higher when wearing the spherical CL, while they tended to be less with the aspheric CL. As for the variations between blinks, there was a similar increase in total HOA and individual modes with time for the three conditions. Conclusion : Wearers of aspheric CL seem to show a tendency towards smaller amounts of SA, horizontal coma and HOA in general in comparison with wearers of SCL. However, total HOA increases during a long interval between blinks, no matter the condition.

scholarly journals ANALISIS SPEKTRAL DALAM PENENTUAN PERIODISITAS SIKLUS CURAH HUJAN DI WILAYAH SELATAN JATILUHUR, KABUPATEN SUBANG, JAWA BARAT

2016 ◽  
Vol 36 (01) ◽  
pp. 89
Author(s):  
Dyah Susilokarti ◽  
Sigit Supadmo Arif ◽  
Sahid Susanto ◽  
Lilik Sutiarso
Keyword(s):  
Fourier Transform ◽  
Mean Square Error ◽  
Rainfall Data ◽  
Mean Square ◽  
Ann Model ◽  
Rainfall Prediction ◽  
Fourier Trans ◽  
Fast Fourier Trans ◽  
The Difference ◽  
The Time Domain

Rainfall data was studied to know how rainfall in the region has a span of time to form a repetitive pattern. The cycle is a change or a wave up and down within a period and repeated at other periods. The cycle has a frequency that can be completed in one period of time. Fourier transform is an algorithm to convert the time domain X to the domain or the frequency spectrum Y, by breaking the signal into a sinusoidal component. This study used the Fast Fourier Transform (FFT) to find the nature of the trend recurrence of rainfall in the southern region of Jatiluhur Subang. Simulation model was done using monthly rainfall data 1975 - 2012. The results showed a trend of rainfall in the study area was repeated every 12 months (1 cycle). Rainfall prediction was done by using a 5-year rainfall data and used the data observation of the next 5 years as a comparison result predicted to see the performance. Performance prediction was resulted using the Mean Square Error (MSE) used to obtain the difference between the standard derivation calculation of observed data and data modeling. The results of the analysis at the time of validation of the model was MSE    14.92 with a 95% confidence level. FFT used to calculate the value of the error (the difference between the values calculated by the ANN model and observed data) resulted in the change cycle of rainfall occurs over a period of months or approximately 71.68 months or 5-6 years.Keywords:  Rain!all, prediction, Fast Fourier Trans!orm (FFT), Mean Square Error (MSE), Subang District ABSTRAKData curah hujan dipelajari salah satunya untuk mengetahui bagaimana curah hujan di suatu wilayah mempunyai rentang waktu untuk membentuk suatu pola berulang. Siklus merupakan suatu perubahan atau gelombang naik dan turun dalam suatu periode serta berulang pada periode lain. Siklus mempunyai frekuensi yang dapat diselesaikan dalam 1 periode waktu. Transformasi Fourier merupakan algoritma untuk mengubah domain waktu X menjadi domain atau spectrum frekuensi Y, dengan cara menguraikan sinyal menjadi komponen sinusoidal.  Penelitian ini menggunakan metode Fast Fourier Trans!orm (FFT) untuk mencari sifat berulangnya trend curah hujan di wilayah selatan Jatiluhur Kabupaten Subang. Simulasi model menggunakan data curah hujan bulanan tahun 1975 - 2012. Hasilnya menunjukkan trend curah hujan di lokasi penelitian berulang setiap 12 bulan sekali (1 siklus). Prediksi curah hujan dilakukan dengan menggunakan data curah hujan 5 tahun dan menggunakan observasi data 5 tahun berikutnya sebagai pembanding hasil prediksi untuk melihat performa yang dihasilkan. Performa hasil prediksi menggunakan Mean Square Error (MSE) sebagai standar perhitungan derivasi perbedaaan antara data real dan data pemodelan. Hasil analisis pada saat validasi model didapatkan MSE    14,92 dengan tingkat kepercayaan 95%. Dengan menggunakan analisis FFT untuk menghitung nilai error (perbedaan antara nilai perhitungan model ANN dengan data sebenarnya), diperoleh perubahan siklus curah hujan terjadi dalam kurun waktu 71,68 bulan atau sekitar 5-6 tahun.Kata kunci:  Curah hujan, prediksi, Fast Fourier Trans!orm (FFT), Mean Square Error (MSE), Kabupaten Subang

scholarly journals True versus perturbed forest inventory plot locations for modeling: a simulation study

2006 ◽  
Vol 36 (3) ◽  
pp. 801-807 ◽  
Author(s):  
John W Coulston ◽  
Kurt H Riitters ◽  
Ronald E McRoberts ◽  
Greg A Reams ◽  
William D Smith
Keyword(s):  
Linear Regression ◽  
Mean Square Error ◽  
Forest Inventory ◽  
Regression Models ◽  
Model Development ◽  
Forest Health ◽  
Mean Square ◽  
Linear Regression Models ◽  
Coarse Spatial Resolution ◽  
The Difference

USDA Forest Service Forest Inventory and Analysis plot information is widely used for timber inventories, forest health assessments, and environmental risk analyses. With few exceptions, true plot locations are not revealed; the plot coordinates are manipulated to obscure the location of field plots and thereby preserve plot integrity. The influence of perturbed plot locations on the development and accuracy of statistical models is unknown. We tested the hypothesis that the influence is related to the spatial structure of the data used in the models. For ordinary kriging we examined the difference in mean square error based on true and perturbed plot locations across a range of spatial autocorrelations. We also examined the difference in mean square error for regression models developed with true and perturbed plot locations across a range of spatial autocorrelations and spatial resolutions. Perturbing plot locations did not significantly influence the accuracy of kriging estimates, but in some situations linear regression model development and accuracy were significantly influenced. Unless the independent variable has high spatial autocorrelation, only coarse spatial resolution data should be used to develop linear regression models.

Analysis of S-box in Image Encryption Using Root Mean Square Error Method

2012 ◽  
Vol 67 (6-7) ◽  
pp. 327-332 ◽  
Author(s):  
Iqtadar Hussain ◽  
Tariq Shah ◽  
Muhammad Asif Gondal ◽  
Hasan Mahmood
Keyword(s):  
Statistical Analysis ◽  
Root Mean Square Error ◽  
Error Analysis ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Image Encryption ◽  
Visual Analysis ◽  
Original Data ◽  
Mean Square ◽  
The Difference

The use of substitution boxes (S-boxes) in encryption applications has proven to be an effective nonlinear component in creating confusion and randomness. The S-box is evolving and many variants appear in literature, which include advanced encryption standard (AES) S-box, affine power affine (APA) S-box, Skipjack S-box, Gray S-box, Lui J S-box, residue prime number S-box, Xyi S-box, and S8 S-box. These S-boxes have algebraic and statistical properties which distinguish them from each other in terms of encryption strength. In some circumstances, the parameters from algebraic and statistical analysis yield results which do not provide clear evidence in distinguishing an S-box for an application to a particular set of data. In image encryption applications, the use of S-boxes needs special care because the visual analysis and perception of a viewer can sometimes identify artifacts embedded in the image. In addition to existing algebraic and statistical analysis already used for image encryption applications, we propose an application of root mean square error technique, which further elaborates the results and enables the analyst to vividly distinguish between the performances of various S-boxes. While the use of the root mean square error analysis in statistics has proven to be effective in determining the difference in original data and the processed data, its use in image encryption has shown promising results in estimating the strength of the encryption method. In this paper, we show the application of the root mean square error analysis to S-box image encryption. The parameters from this analysis are used in determining the strength of S-boxes

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