Additional file 3 of A novel estimator of between-study variance in random-effects models
Nan WangJun ZhangLi XuJing QiBeibei LiuYiyang TangYinan JiangLiang ChengQinghua JiangXunbo YinShuilin Jin
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Additional file 3 Supplementary figures. Figure S1 Plot of the precision under the second hypothesis. Figure S2 Plot of the precision under the third hypothesis. Figure S3 Plot of the accuracy under the second hypothesis. Figure S4 Plot of the accuracy under the third hypothesis. Figure S5 Plot of the FPR under the second hypothesis. Figure S6 Plot of the FPR under the third hypothesis. Figure S7 Plot of the MCC under the second hypothesis. Figure S8 Plot of the MCC under the third hypothesis. Figure S9 Plot of the sensitivity under the second hypothesis. Figure S10 Plot of the sensitivity under the third hypothesis. Figure S11 Plot of the ROC curve and the AUC value under the second hypothesis. Figure S12 Plot of the ROC under the third hypothesis. The DSLD2 method is developed in this paper. Figure S13 Precision-recall plot under the second hypothesis. Figure S14 Precision-recall plot under the third hypothesis. Figure S15 Bias plot of 6 meta-analysis methods when τ2 is set to 1.0 and SMD is chosen as the effect size measure. Figure S16 RMSE plot of 6 meta-analysis methods when τ2 is set to 1.0 and SMD is chosen as the effect size measure. Figure S17 Bias plot of 6 meta-analysis methods when τ2 is set to 1.0 and MD is chosen as the effect size measure. Figure S18 RMSE plot of 6 meta-analysis methods when τ2 is set to 1.0 and MD is chosen as the effect size measure. Figure S19 Mean of I2 plot of 6 meta-analysis methods when τ2 is set to 1.0 and SMD is chosen as the effect size measure. Figure S20 Mean of I2 plot of 6 meta-analysis methods when τ2 is set to 1.0 and MD is chosen as the effect size measure.We develop new point estimators for the variance parameter of a steady-state simulation process. The estimators are based on jackknifed versions of nonoverlapping batch means, overlapping batch means, and standardized time series variance estimators. The new estimators have reduced bias---and can be manipulated to reduce their variance and mean-squared error---compared with their predecessors, facts which we demonstrate analytically and empirically.
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Formulae are developed for the variance of data based on the enumeration of subsamples of subsamples. The fractions of the initial samples that are enumerated determine the contribution of the initial population variance to the overall variance and the precision with which the initial variance can be estimated.
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Enumeration
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We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the high's and low's of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the well-known realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying log-price process is an It\^o stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies.
Bridge (graph theory)
Realized variance
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We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within n subsequent time-step intervals. The main purpose of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the highs and lows of the bridge associated with the original process makes these estimators significantly more efficient than the standard realized variance estimators and their generalizations. Adding the information on the occurrence times of the high and low values further improves the efficiency of the estimators, far exceeding that of the well-known realized variance estimator and those derived from the sum of the Garman and Klass spot variance estimators. The exact analytical results are derived for a case in which the underlying log-price process is an Ito stochastic process. Our results suggest more efficient ways to record financial prices at intermediate frequencies.
Bridge (graph theory)
Realized variance
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Abstract This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.
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<abstract><p>Estimation of population characteristics has been an area of interest for many years. Various estimators of the population mean and the population variance have been proposed from time-to-time with a view to improve efficiency of the estimates. In this paper, we have proposed some estimators for estimation of the general population parameters. The estimators have been proposed for single-phase and two-phase sampling using information of single and multiple auxiliary variables. The bias and mean square errors of the proposed estimators have been obtained. Some comparison of the proposed estimators has been done with some existing estimators of mean and variance. Some specific cases of the proposed estimators have been discussed. Simulation and numerical study have also been conducted to see the performance of the proposed estimators.</p></abstract>
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Population variance
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Some existing estimators based on auxiliary attribute have been proposed by many authors. In this paper, we use the concept of power transformation to modify some existing estimators in order to obtain estimators that are applicable when there is positive or negative correlation between the study and auxiliary variable. The properties (Biases and MSEs) of the proposed estimators were derived up to the first order of approximation using Taylor series approach. The efficiency comparison of the proposed estimators over some existing estimators considered in the study were established. The empirical studies were conducted using existing population parameters to investigate the proficiency of the proposed estimators over some existing estimators. The results revealed that the proposed estimators have minimum Mean Square Errors and higher Percentage Relative Efficiencies than the conventional and other competing estimators in the study. These implies that the proposed estimators are more efficient and can produce better estimates of the population mean compared to the existing estimators considered in the study.
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<abstract> <p>The estimation of a certain population characteristics is required for several situations. The estimates are built so that the error of estimation is minimized. In several situations estimation of the population mean is required. Different estimators for the mean are available but, there is still room for improvement. In this paper, a new class of ratio-type estimators is proposed for the estimation of the population mean. The estimators are proposed for single- and two-phase sampling schemes. The expressions for bias and mean square error are obtained for single-phase and two-phase sampling estimators. Mathematical comparison of the proposed estimators has been achieved by using some existing single-phase and two-phase sampling estimators. Extensive simulations have been conducted to compare the proposed estimators with some available single- and two-phase sampling estimators. It has been observed that the proposed estimators are better than the existing estimators. Consequently, the proposed ratio estimators are recommended for use by the practitioners in various fields of industry, engineering and medical and physical sciences.</p> </abstract>
Extremum estimator
Population mean
Bootstrapping (finance)
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The problem of non-response generally occurs due to the lack of interest, not at home, refusal etc. Many authors developed estimators for estimation of population mean in the presence of nonresponse. Sometimes estimation of product of two population means in the presence of non-response is also needed. Keeping this fact in the view, some estimators for the product of two population means using auxiliary attribute in the presence of non-response have been suggested. The properties of the suggested estimators are also studied. A comparative study of the suggested estimators with the relevant estimators is given. Using a real data set, a numerical study is also given to check the efficiency of the proposed estimators in comparison to the relevant estimators. From numerical study it has been found that the proposed estimators work better that the other exiting estimators in some given conditions.
Extremum estimator
Population mean
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We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the high's and low's of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the well-known realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying log-price process is an It\^o stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies.
Bridge (graph theory)
Realized variance
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Citations (1)