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.

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.  

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.

scholarly journals Snow depth mapping with unpiloted aerial system lidar observations: a case study in Durham, New Hampshire, United States

2021 ◽  
Vol 15 (3) ◽  
pp. 1485-1500
Author(s):  
Jennifer M. Jacobs ◽  
Adam G. Hunsaker ◽  
Franklin B. Sullivan ◽  
Michael Palace ◽  
Elizabeth A. Burakowski ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Confidence Intervals ◽  
Root Mean Square ◽  
Snow Depth ◽  
Coniferous Forest ◽  
Horizontal Resolution ◽  
Absolute Difference ◽  
Mean Square ◽  
Mean Absolute Difference

Abstract. Terrestrial and airborne laser scanning and structure from motion techniques have emerged as viable methods to map snow depths. While these systems have advanced snow hydrology, these techniques have noted limitations in either horizontal or vertical resolution. Lidar on an unpiloted aerial vehicle (UAV) is another potential method to observe field- and slope-scale variations at the vertical resolutions needed to resolve local variations in snowpack depth and to quantify snow depth when snowpacks are shallow. This paper provides some of the earliest snow depth mapping results on the landscape scale that were measured using lidar on a UAV. The system, which uses modest-cost, commercially available components, was assessed in a mixed deciduous and coniferous forest and open field for a thin snowpack (< 20 cm). The lidar-classified point clouds had an average of 90 and 364 points/m2 ground returns in the forest and field, respectively. In the field, in situ and lidar mean snow depths, at 0.4 m horizontal resolution, had a mean absolute difference of 0.96 cm and a root mean square error of 1.22 cm. At 1 m horizontal resolution, the field snow depth confidence intervals were consistently less than 1 cm. The forest areas had reduced performance with a mean absolute difference of 9.6 cm, a root mean square error of 10.5 cm, and an average one-sided confidence interval of 3.5 cm. Although the mean lidar snow depths were only 10.3 cm in the field and 6.0 cm in the forest, a pairwise Steel–Dwass test showed that snow depths were significantly different between the coniferous forest, the deciduous forest, and the field land covers (p < 0.0001). Snow depths were shallower, and snow depth confidence intervals were higher in areas with steep slopes. Results of this study suggest that performance depends on both the point cloud density, which can be increased or decreased by modifying the flight plan over different vegetation types, and the grid cell variability that depends on site surface conditions.

scholarly journals Parameter Estimation of Inverse Rayleigh Distribution under Competing Risk Model for Masked data

2015 ◽  
Vol 20 (2) ◽  
pp. 122-127 ◽  
Author(s):  
M.S. Panwar ◽  
Bapat Akanshya Sudhir ◽  
Rashmi Bundel ◽  
Sanjeev K. Tomer
Keyword(s):  
Sample Size ◽  
Mean Square Error ◽  
Confidence Intervals ◽  
Risk Model ◽  
Life Time ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Mean Square ◽  
True Value ◽  
The Mean

This paper tries to derive maximum likelihood estimators (MLEs) for the parameters of the inverse Rayleigh distribution (IRD) when the observed data is masked. MLEs, asymptotic confidence intervals (ACIs) and boot-p confidence intervals (boot-p CIs) for the lifetime parameters have been discussed. The simulation illustrations provided that as the sample size increases the estimated value approaches to the true value, and the mean square error decreases with the increase in sample size, and mean square error increases with increase in level of masking, the ACIs are always symmetric and the boot-p CIs approaches to symmetry as the sample size increases whereas the mean life time due to the local spread of the disease is less than that due to the metastasis spread in case of real data set.Journal of Institute of Science and Technology, 2015, 20(2): 122-127

scholarly journals Handle outliers for Frechet distribution

2021 ◽  
Vol 23 (09) ◽  
pp. 853-863
Author(s):  
Hager Ahmad Ibrahim ◽  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Simulation Study ◽  
Mean Square ◽  
Monte Carlo Simulation Study ◽  
Fréchet Distribution ◽  
Outlier Data ◽  
Frechet Distribution

This paper aims to handle outlier data for Frechet distribution. This study focused on two ways to deal with outliers. The rst way is to censor the ob- servation with the same percentage of outlier data. The second way is to trim outlier observations. A Monte Carlo simulation study is carried out to compare these ways in terms of estimate average, relative bias, and root mean square error (RMSE) using Mathematica-10.

Comparison of methods for control allocation in multiple arm studies using response adaptive randomization

2019 ◽  
Vol 17 (1) ◽  
pp. 52-60 ◽  
Author(s):  
Kert Viele ◽  
Kristine Broglio ◽  
Anna McGlothlin ◽  
Benjamin R Saville
Keyword(s):  
Mean Square Error ◽  
Simulation Study ◽  
Control Allocation ◽  
Mean Square ◽  
Comparison Of Methods ◽  
Single Treatment ◽  
Multiple Control ◽  
Adaptive Randomization ◽  
Selection Of

Background/Aims: Response adaptive randomization has many polarizing properties in two-arm settings comparing control to a single treatment. The generalization of these features to the multiple arm setting has been less explored, and existing comparisons in the literature reach disparate conclusions. We investigate several generalizations of two-arm response adaptive randomization methods relating to control allocation in multiple arm trials, exploring how critiques of response adaptive randomization generalize to the multiple arm setting. Methods: We perform a simulation study to investigate multiple control allocation schemes within response adaptive randomization, comparing the designs on metrics such as power, arm selection, mean square error, and the treatment of patients within the trial. Results: The results indicate that the generalization of two-arm response adaptive randomization concerns is variable and depends on the form of control allocation employed. The concerns are amplified when control allocation may be reduced over the course of the trial but are mitigated in the methods considered when control allocation is maintained or increased during the trial. In our chosen example, we find minimal advantage to increasing, as opposed to maintaining, control allocation; however, this result reflects an extremely limited exploration of methods for increasing control allocation. Conclusion: Selection of control allocation in multiple arm response adaptive randomization has a large effect on the performance of the design. Some disparate comparisons of response adaptive randomization to alternative paradigms may be partially explained by these results. In future comparisons, control allocation for multiple arm response adaptive randomization should be chosen to keep in mind the appropriate match between control allocation in response adaptive randomization and the metric or metrics of interest.

SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE

2009 ◽  
Vol 26 (3) ◽  
pp. 931-951 ◽  
Author(s):  
Yanqin Fan ◽  
Sang Soo Park
Keyword(s):  
Sample Size ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Simulation Study ◽  
Treatment Effect ◽  
Treatment Effects ◽  
Asymptotic Distributions ◽  
Finite Sample ◽  
Sharp Bounds ◽  
Nonparametric Estimators

In this paper, we propose nonparametric estimators of sharp bounds on the distribution of treatment effects of a binary treatment and establish their asymptotic distributions. We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than-nbootstrap to making inferences on these bounds. The finite sample performances of the confidence intervals for the bounds based on normal critical values, the standard bootstrap, and the fewer-than-nbootstrap are investigated via a simulation study. Finally we establish sharp bounds on the treatment effect distribution when covariates are available.

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