On the Simulation Study of Jackknife and Bootstrap MSE Estimators of a Domain Mean Predictor for Fay‑Herriot Model

We consider the problem of the estimation of the mean squared error (MSE) of some domain mean predictor for Fay‑Herriot model. In the simulation study we analyze properties of eight MSE estimators including estimators based on the jackknife method (Jiang, Lahiri, Wan, 2002; Chen, Lahiri, 2002; 2003) and parametric bootstrap (Gonzalez‑Manteiga et al., 2008; Buthar, Lahiri, 2003). In the standard Fay‑Herriot model the independence of random effects is assumed, and the biases of the MSE estimators are small for large number of domains. The aim of the paper is the comparison of the properties of MSE estimators for different number of domains and the misspecification of the model due to the correlation of random effects in the simulation study.

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Two Different Classes of Shrinkage Estimators for the Scale Parameter of the Rayleigh Distribution

Journal of Modern Applied Statistical Methods ◽

10.22237/jmasm/1608553440 ◽

2021 ◽

Vol 19 (1) ◽

pp. 2-21

Author(s):

Talha Omer ◽

Zawar Hussain ◽

Muhammad Qasim ◽

Said Farooq Shah ◽

Akbar Ali Khan

Keyword(s):

Simulation Study ◽

Mean Squared Error ◽

Scale Parameter ◽

Rayleigh Distribution ◽

Shrinkage Estimators ◽

Unbiased Estimators ◽

Squared Error ◽

The Mean ◽

Simulation Results

Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

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Modifying Two-Parameter Ridge Liu Estimator Based on Ridge Estimation

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v15i4.2575 ◽

2019 ◽

pp. 881-890

Author(s):

Tarek Mahmoud Omara

Keyword(s):

Simulation Study ◽

Mean Squared Error ◽

Error Matrix ◽

Liu Estimator ◽

Mean Squared Error Matrix ◽

Ridge Estimation ◽

Squared Error ◽

The Mean ◽

Two Parameter

In this paper, we introduce the new biased estimator to deal with the problem of multicollinearity. This estimator is considered a modification of Two-Parameter Ridge-Liu estimator based on ridge estimation. Furthermore, the superiority of the new estimator than Ridge, Liu and Two-Parameter Ridge-Liu estimator were discussed. We used the mean squared error matrix (MSEM) criterion to verify the superiority of the new estimate. In addition to, we illustrated the performance of the new estimator at several factors through the simulation study.

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The change in estimate method for selecting confounders: A simulation study

Statistical Methods in Medical Research ◽

10.1177/09622802211034219 ◽

2021 ◽

pp. 096228022110342

Author(s):

Denis Talbot ◽

Awa Diop ◽

Mathilde Lavigne-Robichaud ◽

Chantal Brisson

Keyword(s):

Confidence Intervals ◽

Simulation Study ◽

Mean Squared Error ◽

Real Data ◽

Significance Test ◽

Simulation Studies ◽

Squared Error ◽

Estimate Method ◽

The Mean ◽

Work And Health

Background The change in estimate is a popular approach for selecting confounders in epidemiology. It is recommended in epidemiologic textbooks and articles over significance test of coefficients, but concerns have been raised concerning its validity. Few simulation studies have been conducted to investigate its performance. Methods An extensive simulation study was realized to compare different implementations of the change in estimate method. The implementations were also compared when estimating the association of body mass index with diastolic blood pressure in the PROspective Québec Study on Work and Health. Results All methods were susceptible to introduce important bias and to produce confidence intervals that included the true effect much less often than expected in at least some scenarios. Overall mixed results were obtained regarding the accuracy of estimators, as measured by the mean squared error. No implementation adequately differentiated confounders from non-confounders. In the real data analysis, none of the implementation decreased the estimated standard error. Conclusion Based on these results, it is questionable whether change in estimate methods are beneficial in general, considering their low ability to improve the precision of estimates without introducing bias and inability to yield valid confidence intervals or to identify true confounders.

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Meta-analysis of rare binary events in treatment groups with unequal variability

Statistical Methods in Medical Research ◽

10.1177/0962280217721246 ◽

2017 ◽

Vol 28 (1) ◽

pp. 263-274 ◽

Cited By ~ 4

Author(s):

Lie Li ◽

Xinlei Wang

Keyword(s):

Random Effects ◽

Mean Squared Error ◽

Meta Analysis ◽

Random Effects Model ◽

Treatment Groups ◽

Continuity Correction ◽

Large Samples ◽

Squared Error ◽

The Mean ◽

Simple Average

Meta-analysis has been widely used to synthesize information from related studies to achieve reliable findings. However, in studies of rare events, the event counts are often low or even zero, and so standard meta-analysis methods such as fixed-effect models with continuity correction may cause substantial bias in estimation. Recently, Bhaumik et al. developed a simple average estimator for the overall treatment effect based on a random effects model. They proved that the simple average method with the continuity correction factor 0.5 (SA_0.5) is the least biased for large samples and showed via simulation that it has superior performance when compared with other commonly used estimators. However, the random effects models used in previous work are restrictive because they all assume that the variability in the treatment group is equal to or always greater than that in the control group. Under a general framework that explicitly allows treatment groups with unequal variability but assumes no direction, we prove that SA_0.5 is still the least biased for large samples. Meanwhile, to account for a trade-off between the bias and variance in estimation, we consider the mean squared error to assess estimation efficiency and show that SA_0.5 fails to minimize the mean squared error. Under a new random effects model that accommodates groups with unequal variability, we thoroughly compare the performance of various methods for both large and small samples via simulation and draw conclusions about when to use which method in terms of bias, mean squared error, type I error, and confidence interval coverage. A data example of rosiglitazone meta-analysis is used to provide further comparison.

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Optimal choice between parametric and non-parametric bootstrap estimates

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100072121 ◽

1994 ◽

Vol 115 (2) ◽

pp. 335-363 ◽

Cited By ~ 7

Author(s):

Stephen Man Sing Lee

Keyword(s):

Mean Squared Error ◽

Parametric Bootstrap ◽

Tuning Parameter ◽

Squared Error ◽

Optimal Estimator ◽

Bootstrap Estimate ◽

The Mean ◽

Bootstrap Estimates ◽

Hybrid Estimator ◽

Non Parametric

AbstractA parametric bootstrap estimate (PB) may be more accurate than its non-parametric version (NB) if the parametric model upon which it is based is, at least approximately, correct. Construction of an optimal estimator based on both PB and NB is pursued with the aim of minimizing the mean squared error. Our approach is to pick an empirical estimate of the optimal tuning parameter ε∈[0, 1] which minimizes the mean square error of εNB+(1−ε) PB. The resulting hybrid estimator is shown to be more reliable than either PB or NB uniformly over a rich class of distributions. Theoretical asymptotic results show that the asymptotic error of this hybrid estimator is quite close in distribution to the smaller of the errors of PB and NB. All these errors typically have the same convergence rate of order . A particular example is also presented to illustrate the fact that this hybrid estimate can indeed be strictly better than either of the pure bootstrap estimates in terms of minimizing mean squared error. Two simulation studies were conducted to verify the theoretical results and demonstrate the good practical performance of the hybrid method.

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New Versions of Liu-type Estimator in Weighted and non-weighted Mixed Regression Model

Baghdad Science Journal ◽

10.21123/bsj.2020.17.1(suppl.).0361 ◽

2020 ◽

Vol 17 (1(Suppl.)) ◽

pp. 0361

Author(s):

Mustafa Ismaeel Naif Alheety

Keyword(s):

Regression Model ◽

Simulation Study ◽

Goodness Of Fit ◽

Prior Information ◽

Mean Squared Error ◽

Numerical Example ◽

Squared Error ◽

Mixed Regression ◽

The Mean ◽

Stochastic Restrictions

This paper considers and proposes new estimators that depend on the sample and on prior information in the case that they either are equally or are not equally important in the model. The prior information is described as linear stochastic restrictions. We study the properties and the performances of these estimators compared to other common estimators using the mean squared error as a criterion for the goodness of fit. A numerical example and a simulation study are proposed to explain the performance of the estimators.

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A comparative study of R functions for clustered data analysis

Trials ◽

10.1186/s13063-021-05900-7 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Wei Wang ◽

Michael O. Harhay

Keyword(s):

Data Analysis ◽

Confidence Intervals ◽

Simulation Study ◽

Generalized Estimating Equations ◽

Mean Squared Error ◽

Mixed Effects ◽

Mixed Effects Models ◽

Intra Class Correlation ◽

Squared Error ◽

The Mean

Abstract Background Clustered or correlated outcome data is common in medical research studies, such as the analysis of national or international disease registries, or cluster-randomized trials, where groups of trial participants, instead of each trial participant, are randomized to interventions. Within-group correlation in studies with clustered data requires the use of specific statistical methods, such as generalized estimating equations and mixed-effects models, to account for this correlation and support unbiased statistical inference. Methods We compare different approaches to estimating generalized estimating equations and mixed effects models for a continuous outcome in R through a simulation study and a data example. The methods are implemented through four popular functions of the statistical software R, “geese”, “gls”, “lme”, and “lmer”. In the simulation study, we compare the mean squared error of estimating all the model parameters and compare the coverage proportion of the 95% confidence intervals. In the data analysis, we compare estimation of the intervention effect and the intra-class correlation. Results In the simulation study, the function “lme” takes the least computation time. There is no difference in the mean squared error of the four functions. The “lmer” function provides better coverage of the fixed effects when the number of clusters is small as 10. The function “gls” produces close to nominal scale confidence intervals of the intra-class correlation. In the data analysis and the “gls” function yields a positive estimate of the intra-class correlation while the “geese” function gives a negative estimate. Neither of the confidence intervals contains the value zero. Conclusions The “gls” function efficiently produces an estimate of the intra-class correlation with a confidence interval. When the within-group correlation is as high as 0.5, the confidence interval is not always obtainable.

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Reducing the Bias of the Smoothed Log Periodogram Regression for Financial High-Frequency Data

Econometrics ◽

10.3390/econometrics8040040 ◽

2020 ◽

Vol 8 (4) ◽

pp. 40

Author(s):

Erhard Reschenhofer ◽

Manveer K. Mangat

Keyword(s):

Simulation Study ◽

High Frequency ◽

Mean Squared Error ◽

Estimation Methods ◽

High Frequency Data ◽

Frequency Data ◽

Periodic Patterns ◽

Typical Sample ◽

Squared Error ◽

Proper Interpretation

For typical sample sizes occurring in economic and financial applications, the squared bias of estimators for the memory parameter is small relative to the variance. Smoothing is therefore a suitable way to improve the performance in terms of the mean squared error. However, in an analysis of financial high-frequency data, where the estimates are obtained separately for each day and then combined by averaging, the variance decreases with the sample size but the bias remains fixed. This paper proposes a method of smoothing that does not entail an increase in the bias. This method is based on the simultaneous examination of different partitions of the data. An extensive simulation study is carried out to compare it with conventional estimation methods. In this study, the new method outperforms its unsmoothed competitors with respect to the variance and its smoothed competitors with respect to the bias. Using the results of the simulation study for the proper interpretation of the empirical results obtained from a financial high-frequency dataset, we conclude that significant long-range dependencies are present only in the intraday volatility but not in the intraday returns. Finally, the robustness of these findings against daily and weekly periodic patterns is established.

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