scholarly journals Monte Carlo study of confidence intervals for the mean as a function of sample size

1977 ◽  
Author(s):  
C Oster
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Confidence Intervals ◽  
Monte Carlo Study ◽  
The Mean

scholarly journals SEM-Based Methods to Form Confidence Intervals for Indirect Effect: Still Applicable Given Nonnormality, Under Certain Conditions

2020 ◽  
Vol 11 ◽  
Author(s):  
Ivan Jacob Agaloos Pesigan ◽  
Shu Fai Cheung
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Confidence Intervals ◽  
Indirect Effect ◽  
Likelihood Estimation ◽  
Ordinary Least Squares ◽  
Mediation Model ◽  
Coverage Probabilities ◽  
Serial Mediation ◽  
Normally Distributed

A SEM-based approach using likelihood-based confidence interval (LBCI) has been proposed to form confidence intervals for unstandardized and standardized indirect effect in mediation models. However, when used with the maximum likelihood estimation, this approach requires that the variables are multivariate normally distributed. This can affect the LBCIs of unstandardized and standardized effect differently. In the present study, the robustness of this approach when the predictor is not normally distributed but the error terms are conditionally normal, which does not violate the distributional assumption of ordinary least squares (OLS) estimation, is compared to four other approaches: nonparametric bootstrapping, two variants of LBCI, LBCI assuming the predictor is fixed (LBCI-Fixed-X) and LBCI based on ADF estimation (LBCI-ADF), and Monte Carlo. A simulation study was conducted using a simple mediation model and a serial mediation model, manipulating the distribution of the predictor. The Monte Carlo method performed worst among the methods. LBCI and LBCI-Fixed-X had suboptimal performance when the distributions had high kurtosis and the population indirect effects were medium to large. In some conditions, the problem was severe even when the sample size was large. LBCI-ADF and nonparametric bootstrapping had coverage probabilities close to the nominal value in nearly all conditions, although the coverage probabilities were still suboptimal for the serial mediation model when the sample size was small with respect to the model. Implications of these findings in the context of this special case of nonnormal data were discussed.

scholarly journals EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR

2018 ◽  
Vol 17 (2) ◽  
pp. 157
Author(s):  
S. UTAMI ◽  
I W. MANGKU ◽  
I G. P. PURNABA
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Observation Interval ◽  
Compound Poisson Process ◽  
Intensity Function ◽  
Significance Level ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean ◽  
Strongly Consistent

<em>Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be </em>𝑒𝑥𝑝(𝛼+𝛽𝑠) <em>with </em>0&lt;𝛽&lt;<em>∞</em>, <em>where </em>𝛽 <em>is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to </em>1−𝛼 <em>of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level </em>𝛼<em>, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to </em>1−𝛼<em>.</em>

A Solution to the Effect of Sample Size on Outlier Elimination

1994 ◽  
Vol 47 (3) ◽  
pp. 631-650 ◽  
Author(s):  
Mark Van Selst ◽  
Pierre Jolicoeur
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Sample Size ◽  
Monte Carlo Study ◽  
The Other ◽  
Recursive Procedure ◽  
Elimination Procedure ◽  
New Procedures

Results from a Monte Carlo study demonstrate how a non-recursive, a simple recursive, a modified recursive, and a hybrid outlier elimination procedure are influenced by population skew and sample size. All the procedures are based on computing a mean and a standard deviation from a sample in order to determine whether an observation is an outlier. Miller (1991) showed that the estimated mean produced by the simple non-recursive procedure can be affected by sample size and that this effect can produce a bias in certain kinds of experiments. We extended this result to the other three procedures. We also create two new procedures in which the criterion used to identify outliers is adjusted as a function of sample size so as to produce results that are unaffected by sample size.

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 Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1351 ◽  
Author(s):  
Tiago M. Magalhães ◽  
Diego I. Gallardo ◽  
Héctor W. Gómez
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Censored Data ◽  
Maximum Likelihood Estimators ◽  
Monte Carlo Study ◽  
Parameter Distribution ◽  
Regression Parameter ◽  
Skewness Coefficient ◽  
Matrix Formula

In this paper, we obtain a matrix formula of order n − 1 / 2 , where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.

Percentile and Percentile-t Bootstrap Confidence Intervals: A Practical Comparison

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Christopher J. Elias
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Monte Carlo Study ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Percentile

AbstractThis paper employs a Monte Carlo study to compare the performance of equal-tailed bootstrap percentile-

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