scholarly journals Robust Regression-Ratio-Type Estimators of the Mean Utilizing Two Auxiliary Variables: A Simulation Study

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Tolga Zaman ◽  
Emre Dünder ◽  
Ahmed Audu ◽  
David Anekeya Alilah ◽  
Usman Shahzad ◽  
...  
Keyword(s):  
Simulation Study ◽  
Robust Regression ◽  
Regression Coefficients ◽  
Ratio Estimator ◽  
Auxiliary Variables ◽  
Numerical Examples ◽  
Empirical Results ◽  
Regression Techniques ◽  
The Mean ◽  
Theoretical Results

Many authors defined the modified version of the mean estimator by using two auxiliary variables. These proposed estimators highly depend on the calculated regression coefficients. In the presence of outliers, these estimators do not give satisfactory results. In this study, we improve the suggested estimators using several robust regression techniques while obtaining the regression coefficients. We compared the efficiencies between the suggested estimators and the estimators presented in the literature. We used two numerical examples and a simulation study to support these theoretical results. Empirical results show that the modified ratio estimator performs well in the presence of outliers when adopting robust regression techniques.

scholarly journals On Robust Estimation of Error Variance in (Highly) Robust Regression

2020 ◽  
Vol 20 (1) ◽  
pp. 6-14 ◽  
Author(s):  
Jan Kalina ◽  
Jan Tichavský
Keyword(s):  
Robust Estimation ◽  
Robust Regression ◽  
Error Variance ◽  
Random Regression ◽  
Estimation Of Parameters ◽  
Least Trimmed Squares ◽  
Estimation Of Error ◽  
Accuracy And Precision ◽  
The Mean ◽  
Theoretical Results

AbstractThe linear regression model requires robust estimation of parameters, if the measured data are contaminated by outlying measurements (outliers). While a number of robust estimators (i.e. resistant to outliers) have been proposed, this paper is focused on estimating the variance of the random regression errors. We particularly focus on the least weighted squares estimator, for which we review its properties and propose new weighting schemes together with corresponding estimates for the variance of disturbances. An illustrative example revealing the idea of the estimator to down-weight individual measurements is presented. Further, two numerical simulations presented here allow to compare various estimators. They verify the theoretical results for the least weighted squares to be meaningful. MM-estimators turn out to yield the best results in the simulations in terms of both accuracy and precision. The least weighted squares (with suitable weights) remain only slightly behind in terms of the mean square error and are able to outperform the much more popular least trimmed squares estimator, especially for smaller sample sizes.

scholarly journals The Kaldor–Kalecki stochastic model of business cycle

2011 ◽  
Vol 16 (2) ◽  
pp. 191-205 ◽  
Author(s):  
Gabriela Mircea ◽  
Mihaela Neamt¸u ◽  
Dumitru Opris
Keyword(s):  
Hopf Bifurcation ◽  
Business Cycle ◽  
Stochastic Model ◽  
Local Stability ◽  
Mean Values ◽  
Numerical Examples ◽  
Investment Demand ◽  
The Mean ◽  
Theoretical Results

This paper is concerned with the deterministic and the stochastic delayed Kaldor–Kalecki nonlinear business cycle models of the income. They will take into consideration the investment demand in the form suggested by Rodano. The existence of the Hopf bifurcation is studied and the direction and the local stability of the Hopf bifurcation is also taken into consideration. For the stochastic model, the dynamics of the mean values and the square mean values of the model’s variables are set. Numerical examples are given to illustrate our theoretical results.

scholarly journals Mean-Square Stability of Milstein Methods for Stochastic Pantograph Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Feiyan Xiao ◽  
Tingting Qin ◽  
Chengjian Zhang
Keyword(s):  
Stability Criterion ◽  
Mean Square ◽  
Numerical Examples ◽  
Mean Square Stability ◽  
The Mean ◽  
Theoretical Results

This paper deals with nonlinear stochastic pantograph equations. For solving the equations, a class of extended Milstein methods are suggested. A mean-square stability criterion for this type of equations is presented. It is proved that under the suitable conditions the Milstein methods preserve the mean-square stability. Numerical examples further illustrate the obtained theoretical results.

scholarly journals BREED AND SEX EFFECTS ON THE RELATIONSHIP BETWEEN WEIGHT AND FATNESS IN LACOMBE AND YORKSHIRE SWINE AND THEIR RECIPROCAL CROSSES

1965 ◽  
Vol 45 (1) ◽  
pp. 33-36
Author(s):  
G. W. Rahnefeld
Keyword(s):  
Body Weight ◽  
Sex Differences ◽  
Regression Coefficients ◽  
Average Depth ◽  
Constant Weight ◽  
Reciprocal Crosses ◽  
Sex Effects ◽  
Female Mating ◽  
The Mean ◽  
The Relationship

The relationship between thickness of fat measured at the shoulder, last rib, and loin of live pigs and market weight (86.2 to 95.2 kg) was studied in 1596 pigs from the Lacombe and Yorkshire breeds and their reciprocal crosses. No significant breed or sex differences were found in the proportion of fat at the three sites. Breed and sex differences were evident in the average depth of fat. The regression coefficients for the mean of three fat measurements on market weight were.016 ±.003,.019 ±.007, and.017 ±.004 for Lacombe males, barrows, and females respectively;.039 ±.002,.036 ±.005, and.041 ±.001 for Yorkshire males, barrows and females respectively;.027 ±.005 and.029 ±.004 for barrows and females from the Lacombe male × Yorkshire female mating; and.023 ±.007 and.021 ±.009 for barrows and females from the Yorkshire male × Lacombe female mating. Comparisons between animals measured at a relatively constant weight should be made after the fat measurement is adjusted for variations in body weight. The results of this study indicate that separate corrections should be applied for each breed. Separate corrections for sexes within breeds do not appear warranted.

Study of a Vibratory Feeder with Repulsive Surface Which Has Directional Characteristic

1980 ◽  
Vol 102 (1) ◽  
pp. 94-101 ◽  
Author(s):  
S. Okabe ◽  
Y. Yokoyama
Keyword(s):  
Experimental Studies ◽  
Directional Characteristic ◽  
Vibratory Feeder ◽  
The Mean ◽  
Theoretical Results

This paper treats the motion of a particle on a vibratory feeder whose track has directional characteristic in repulsive motion, for examples, obliquely bristled track, obliquely sliced track and so on. Under some assumptions, the practical equation for predicting the mean conveying velocity is shown and the relations between conveying condition and the mean conveying velocity are clarified theoretically. These relations are shown in various diagrams. Referring these diagrams, the optimum conveying conditions are discussed also. The theoretical results show that the mean conveying velocity is considerably larger than that of the ordinary feeder. The theoretical results are confirmed by experimental studies.

scholarly journals Computer Modelling For 4-Stroke Direct Injection Diesel Engine

2008 ◽  
Vol 33-37 ◽  
pp. 801-806
Author(s):  
Abdul Rahim Ismail ◽  
Rosli Abu Bakar ◽  
Semin Ali ◽  
Ismail Ali
Keyword(s):  
Diesel Engine ◽  
Simulation Study ◽  
Engine Speed ◽  
Computer Modelling ◽  
Direct Injection ◽  
One Dimension ◽  
Effective Pressure ◽  
Operational Parameters ◽  
Direct Injection Diesel Engine ◽  
Theoretical Results

Study on computational modeling of 4-stroke single cylinder direct injection diesel engine is presented. The engine with known specification is being modeled using one dimension CFD GT-Power software. The operational parameters of the engine such as power, torque, specific fuel consumption and mean effective pressure which are dependent to engine speed are being discussed. The results from the simulation study are compared with the theoretical results to get the true trend of the results.

Stochastic Analysis of Temperature Distribution in a Solid With Random Heat Conductivity

1988 ◽  
Vol 110 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Da Yu Tzou
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Heat Conductivity ◽  
Stochastic Analysis ◽  
Solid Medium ◽  
Mean Value ◽  
Random Response ◽  
Thermal Failure ◽  
Numerical Examples ◽  
The Mean

Stochastic temperature distribution in a solid medium with random heat conductivity is investigated by the method of perturbation. The intrinsic randomness of the thermal conductivity k(x) is considered to be a distribution function with random amplitude in the solid, and several typical stochastic processes are considered in the numerical examples. The formulation used in the present analysis describes a situation that the statistical orders of the random response of the system are the same as those of the intrinsic random excitations, which is characteristic for the problem with extrinsic randomness. The maximum standard deviation of the temperature distribution from the mean value in the solid medium reveals the amount of unexpected energy experienced by the solid continuum, which should be carefully inspected in the thermal-failure design of structures with intrinsic randomness.

Vibratory Feeding by Nonsinusoidal Vibration—Optimum Wave Form

1985 ◽  
Vol 107 (2) ◽  
pp. 188-195 ◽  
Author(s):  
S. Okabe ◽  
Y. Kamiya ◽  
K. Tsujikado ◽  
Y. Yokoyama
Keyword(s):  
Experimental Results ◽  
Wave Form ◽  
Velocity Wave ◽  
The Mean ◽  
Straight Lines ◽  
Vibratory Conveyor ◽  
Theoretical Results ◽  
Vibratory Feeding

This paper presents the conveying velocity on a vibratory conveyor whose track is vibrated by nonsinusoidal vibration. The velocity wave form of the vibrating track is approximated by six straight lines, and five distortion factors of the wave form are defined. Considering the modes of motion of the particle, the mean conveying velocity is calculated for various conditions. Referring to these results, the optimum wave form is clarified analytically. The theoretical results show that the mean conveying velocity is considerably larger than that of ordinary feeders if the proper conveying conditions are chosen. The theoretical results are confirmed by experimental results.

scholarly journals The Probability That a Measurement Falls within a Range of Standard Deviations from an Estimate of the Mean

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Louis M. Houston
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
General Equation ◽  
Sample Sizes ◽  
The Mean ◽  
Standard Deviations ◽  
Intermediate Value ◽  
Theoretical Results

We derive a general equation for the probability that a measurement falls within a range of n standard deviations from an estimate of the mean. So, we provide a format that is compatible with a confidence interval centered about the mean that is naturally independent of the sample size. The equation is derived by interpolating theoretical results for extreme sample sizes. The intermediate value of the equation is confirmed with a computational test.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

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