scholarly journals REGRESSION-IN-RATIO ESTIMATORS IN THE PRESENCE OF OUTLIERS BASED ON REDESCENDINGM-ESTIMATOR

2019 ◽  
pp. 01-10
Author(s):  
Aamir Raza ◽  
Muhmmad Noor-ul-Amin ◽  
Muhammad Hanif
Keyword(s):  
Mean Square Error ◽  
Taylor Series ◽  
Simulation Study ◽  
Relative Efficiency ◽  
Mean Square ◽  
Extensive Simulation ◽  
Taylor Series Approximation ◽  
Series Approximation ◽  
M Estimator ◽  
Ratio Estimators

In this paper, a robust redescending M-estimator is used to construct the regression-inratio estimators to estimate population when data contain outliers. The expression of mean square error of proposed estimators is derived using Taylor series approximation up to order one. Extensive simulation study is conducted for the comparison between the proposed and existing class of ratio estimators. It is revealed form the results that proposed regression-in-ratio estimators have high relative efficiency (R.E) as compared to previously developed estimators. Practical examples are also cited to validate the performance of proposed estimators.  

scholarly journals Overlap coefficients based on Kullback-Leibler divergence: Exponential populations case

2017 ◽  
Vol 6 (4) ◽  
pp. 135
Author(s):  
Hamza Dhaker ◽  
Papa Ngom ◽  
Malick Mbodj
Keyword(s):  
Statistical Inference ◽  
Mean Square Error ◽  
Confidence Intervals ◽  
Taylor Series ◽  
Simulation Study ◽  
Invariance Property ◽  
Mean Square ◽  
Taylor Series Approximation ◽  
Leibler Divergence ◽  
Exponential Populations

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita’s measure ρ, Morisita’s measure λ and Weitzman’s measure ∆. A new overlap measure Λ based on Kullback-Leibler measure is proposed. The invariance property and a method of statistical inference of these coefficients also are presented. Taylor series approximation are used to construct confidence intervals for the overlap measures. The bias and mean square error properties of the estimators are studied through a simulation study.

Investigation of Accuracy of a Calibrated Estimator of a Ratio by Modelling

2005 ◽  
Vol 10 (4) ◽  
pp. 333-342
Author(s):  
V. Chadyšas ◽  
D. Krapavickaitė
Keyword(s):  
Mean Square Error ◽  
Taylor Series ◽  
Random Sampling ◽  
Finite Population ◽  
Taylor Series Expansion ◽  
Simple Random Sampling ◽  
Population Parameter ◽  
Mean Square ◽  
Parameter Ratio ◽  
Using Data

Estimator of finite population parameter – ratio of totals of two variables – is investigated by modelling in the case of simple random sampling. Traditional estimator of the ratio is compared with the calibrated estimator of the ratio introduced by Plikusas [1]. The Taylor series expansion of the estimators are used for the expressions of approximate biases and approximate variances [2]. Some estimator of bias is introduced in this paper. Using data of artificial population the accuracy of two estimators of the ratio is compared by modelling. Dependence of the estimates of mean square error of the estimators of the ratio on the correlation coefficient of variables which are used in the numerator and denominator, is also shown in the modelling.

scholarly journals The CSS and The Two-Staged Methods for Parameter Estimation in SARFIMA Models

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Erol Egrioglu ◽  
Cagdas Hakan Aladag ◽  
Cem Kadilar
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Simulation Study ◽  
Long Memory ◽  
Moving Average ◽  
Mean Square ◽  
Sample Sizes ◽  
Advantages And Disadvantages

Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) models are used in the analysis of seasonal long memory-dependent time series. Two methods, which are conditional sum of squares (CSS) and two-staged methods introduced by Hosking (1984), are proposed to estimate the parameters of SARFIMA models. However, no simulation study has been conducted in the literature. Therefore, it is not known how these methods behave under different parameter settings and sample sizes in SARFIMA models. The aim of this study is to show the behavior of these methods by a simulation study. According to results of the simulation, advantages and disadvantages of both methods under different parameter settings and sample sizes are discussed by comparing the root mean square error (RMSE) obtained by the CSS and two-staged methods. As a result of the comparison, it is seen that CSS method produces better results than those obtained from the two-staged method.

scholarly journals VARX and GSTARX Models for Forecasting Currency Inflow and Outflow with Multiple Calendar Variations Effect

MATEMATIKA ◽  
2018 ◽  
Vol 34 (3) ◽  
pp. 57-72 ◽  
Author(s):  
Suhartono Suhartono ◽  
Muhammad Munawir Gazali ◽  
Dedy Dwi Prastyo
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Simulation Study ◽  
Forecast Accuracy ◽  
Forecasting Model ◽  
Mean Square ◽  
Simulation Studies ◽  
Exogenous Variables ◽  
Vector Autoregressive ◽  
Weight Model

VARX and GSTARX models are an extension of Vector Autoregressive (VAR) and Generalized Space-Time Autoregressive (GSTAR) models. These models include exogenous variable to increase the forecast accuracy. The objective of this research is to develop and compare the forecast accuracy of VARX and GSTARX models in predicting currency inflow and outflow in Bali, West Nusa Tenggara, and East Nusa Tenggara that contain multiple calendar variations effects. The exogenous variables that are used in this research are holidays in those three locations, i.e. EidFitr, Galungan, and Nyepi. The proposed VARX and GSTARX models are evaluated through simulation studies on the data that contain trend, seasonality, and multiple calendar variations representing the occurrence of EidFitr, Galungan, and Nyepi. The criteria for selecting the best forecasting model is Root Mean Square Error (RMSE). The results of a simulation study show that VARX and GSTARX models provide similar forecast accuracy. Furthermore, the results of currency inflow and outflow data in Bali,West Nusa Tenggara, and East Nusa Tenggara show that the best model for forecasting inflow and outflow in these three locations are VARX and GSTARX (with uniform weight) model, respectively. Both models show that currency inflow and outflow in Bali, West Nusa Tenggara, and East Nusa Tenggara have a relationship in space and time, and contain trends, seasonality and multiple calendar variations.

Conservation Law of Energy Using Fractional Taylor Series

2016 ◽  
Vol 841 ◽  
pp. 105-109
Author(s):  
Ali Soroush ◽  
Farzam Farahmand
Keyword(s):  
Taylor Series ◽  
Conservation Law ◽  
Control Volume ◽  
Fractional Differentiation ◽  
Linear Flow ◽  
First Order ◽  
Taylor Series Approximation ◽  
Series Approximation ◽  
Non Linear ◽  
Flow Power

Customary conservation law of energy is commonly derived using first-order Taylor series, which is only valid for situation of linear changes in the flow of energy in control volume. It is shown that using high-order Taylor series will approximate non-linear changes in the flow of energy but in fact some error remains. We used fractional Taylor series which exactly represent non-linear flow of energy in control volume. By replacing the customary integer-order Taylor series approximation with the fractional-order Taylor series approximation, limitation of the linear flow of energy in the control volume and the restriction that the control volume must be infinitesimal is omitted. The innovation of this paper is we show that as long as the order of fractional differentiation is equal with flow power-law, the fractional conservation law of energy will be exact and it can be used for fluid in a porous medium.

scholarly journals Squaring Technique using Vedic Mathematics

2021 ◽  
Author(s):  
Jasmine Bajaj ◽  
Babita Jajodia
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Number System ◽  
Approximation Technique ◽  
Approximation Techniques ◽  
Vedic Mathematics ◽  
Decimal Number ◽  
Taylor Series Approximation ◽  
Series Approximation ◽  
Interesting Approach

Vedic Mathematics provides an interesting approach to modern computing applications by offering an edge of time and space complexities over conventional techniques. Vedic Mathematics consists of sixteen sutras and thirteen sub-sutras, to calculate problems revolving around arithmetic, algebra, geometry, calculus and conics. These sutras are specific to the decimal number system, but this can be easily applied to binary computations. This paper presented an optimised squaring technique using Karatsuba-Ofman Algorithm, and without the use of Duplex property for reduced algorithmic complexity. This work also attempts Taylor Series approximation of basic trigonometric and inverse trigonometric series. The advantage of this proposed power series approximation technique is that it provides a lower absolute mean error difference in comparison to previously existing approximation techniques.

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