Arithmetic Mean Estimator Research Articles

The impact of creative tourism on inclusive economic growth

The purpose of the article is to compile the author's characteristics of the values of inclusive tourism and creative development in an inclusive economy based on the analysis of international works of researchers, classification of the values of inclusive development and creative growth in the study of the influence of creative tourism on inclusive economic growth, to determine the level of priority indicators affecting economic growth, to determine the significance in the proportion of several indicators. The regulatory mechanisms necessary for the formation of the necessary level of creative tourism development in the study of development directions in inclusive economic growth are proposed. The relevance of the article lies in the fact that the dynamic development of tourism in the inclusive economic growth of the world's countries is becoming the main topic of research of the United Nations, the Organisation for Economic Cooperation Development, the World Bank and the whole world. In this regard, since 2021, the Republic of Kazakhstan has also embarked on the development of creative tourism along an inclusive path towards a creative economy. During the research of the article, methods of analyzing various indicators of sustainability, arithmetic mean estimation of the studied indicators and the significance of their specific weight, economic and statistical analysis, generalization, comparison were used. In conclusion, the various effects of several indicators on overall sustainability are identified, the priority weight of inclusive indicators in the development of tourism is determined, through the results obtained, to propose integrated approaches as a means of integration and systematization in ensuring the necessary level in the development of tourism.

Computational Methods for Estimating the Evidence and Bayes Factor in SEIR Stochastic Infectious Diseases Models Featuring Asymmetrical Dynamics of Transmission

Stochastic epidemic models may offer a vitally essential public health tool for comprehending and regulating disease progression. The best illustration of their importance and usefulness is perhaps the substantial influence that these models have had on the global COVID-19 epidemic. Nonetheless, these models are of limited practical use unless they provide an adequate fit to real-life epidemic outbreaks. In this work, we consider the problem of model selection for epidemic models given temporal observation of a disease outbreak through time. The epidemic models are stochastic individual-based transmission models of the Susceptible–Exposed–Infective–Removed (SEIR) type. The main focus is on the use of model evidence (or marginal likelihood), and hence the Bayes factor is a gold-standard measure of merit for comparing the fits of models to data. Even though the Bayes factor has been discussed in the epidemic modeling literature, little focus has been given to the fundamental issues surrounding its utility and computation. Based on various asymmetrical infection mechanism assumptions, we derive analytical expressions for Bayes factors which offer helpful suggestions for model selection problems. We also explore theoretical aspects that highlight the need for caution when utilizing the Bayes factor as a model selection technique, such as when the within-model prior distributions become more asymmetrical (diffuse or informative). Three computational methods for estimating the marginal likelihood and hence Bayes factor are discussed, which are the arithmetic mean estimator, the harmonic mean estimator, and the power posterior estimator. The theory and methods are illustrated using artificial data.

Särndal Approach and Separate Type Quantile Robust Regression Type Mean Estimators for Nonsensitive and Sensitive Variables in Stratified Random Sampling

Surprising perceptions may happen in survey sampling. The arithmetic mean estimator is touchy to extremely enormous or potentially small observations, whenever selected in a sample. It can give one‐sided (biased) results and eventually, enticed to erase from the selected sample. These extremely enormous or potentially small observations, whenever known, can be held in the sample and utilized as supplementary information to expand the exactness of estimates. Also, a supplementary variable is consistently a well‐spring of progress in the exactness of estimates. A suitable conversion/transformation can be utilized for getting much more precise estimates. In the current study, regarding population mean, we proposed a robust class of separate type quantile regression estimators under stratified random sampling design. The proposed class is based on extremely enormous or potentially small observations and robust regression tools, under the framework of Särndal. The class is at first defined for the situation when the nature of the study variable is nonsensitive, implying that it bargains with subjects that do not create humiliation when respondents are straightforwardly interrogated regarding them. Further, the class is stretched out to the situation when the study variable has a sensitive nature or theme. Sensitive and stigmatizing themes are hard to explore by utilizing standard information assortment procedures since respondents are commonly hesitant to discharge data concerning their own circle. The issues of a population related to these themes (for example homeless and nonregular workers, heavy drinkers, assault and rape unfortunate casualties, and drug users) contain estimation errors ascribable to nonresponses as well as untruthful revealing. These issues might be diminished by upgrading respondent participation by scrambled response devices/techniques that cover the genuine value of the sensitive variable. Thus, three techniques (namely additive, mixed, and Bar‐Lev) are incorporated for the purposes of the article. The productivity of the proposed class is also assessed in light of real‐life dataset. Lastly, a simulation study is also done to determine the performance of estimators.

Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate these five estimators using a groundwater transport model selection problem. SS and MOSS give the least biased BME estimation at an efficient computational cost. If the estimated BME has a bias that covariates with the true BME, this would not be a problem because we are interested in BME ratios and not their absolute values. On the contrary, the results show that BME estimation bias can be a function of model complexity. Thus, biased BME estimation results in inaccurate penalization of more complex models, which changes the model ranking. This was less observed with SS and MOSS as with the three other methods.

Improved Nested Sampling and Surrogate‐Enabled Comparison With Other Marginal Likelihood Estimators

AbstractEstimating marginal likelihood is of central importance to Bayesian model selection and/or model averaging. The nested sampling method has been recently used together with the Metropolis‐Hasting (M‐H) sampling algorithm for estimating marginal likelihood. This study develops a new implementation of nested sampling by using the DiffeRential Evolution Adaptive Metropolis (DREAMzs) sampling algorithm. The two implementations of nested sampling are evaluated for four models of a synthetic groundwater flow modeling. The DREAMzs‐based nested sampling outperforms the M‐H‐based nested sampling in terms of their accuracy, convergence, efficiency, and stability, which is attributed to the fact that DREAMzs is more robust than M‐H for parameter sampling. The nested sampling method is also compared with four other methods (arithmetic mean, harmonic mean, stabilized harmonic mean, and thermodynamic integration) commonly used for estimating marginal likelihood and posterior probability of the four groundwater models. The comparative study requires hundreds of millions of model executions, which would not be possible without using surrogate models to replace the original models. Using the arithmetic mean estimator as the reference, the comparison reveals that thermodynamic integration outperforms nested sampling in terms of accuracy and stability, whereas nested sampling is more computationally efficient to reach to convergence. The harmonic mean and stabilized harmonic mean methods give the worst marginal likelihood estimation. Accurate marginal likelihood estimation is important for accurate estimation of posterior model probability and better predictive performance of Bayesian model averaging.

Estimating the Marginal Likelihood Using the Arithmetic Mean Identity

In this paper we propose a conceptually straightforward method to estimate the marginal data density value (also called the marginal likelihood). We show that the marginal likelihood is equal to the prior mean of the conditional density of the data given the vector of parameters restricted to a certain subset of the parameter space, A, times the reciprocal of the posterior probability of the subset A. This identity motivates one to use Arithmetic Mean estimator based on simulation from the prior distribution restricted to any (but reasonable) subset of the space of parameters. By trimming this space, regions of relatively low likelihood are removed, and thereby the efficiency of the Arithmetic Mean estimator is improved. We show that the adjusted Arithmetic Mean estimator is unbiased and consistent.

A note on corporate valuation using imprecise cost of capital

We compare the estimator for discount rates according to Elsner and Krumholz (EK) (J Bus Econ 83:985–1014, 2013) to the approach propagated in Breuer et al. (BFM) (Eur J Financ 20:568–594, 2014). While the EK estimator is derived analytically and implies a correcting factor by which the original arithmetic mean estimator is adjusted, the BFM approach is based on a simple ad hoc modification and recommends to truncate the time horizon for cash flow projection up to about N = 30 years. The BFM approach is reasonable, as the most relevant bias problems are implied by terminal value computations. Rather surprisingly, for our main simulation analysis based on real-world capital market data for 19 countries over the period 2008–2012, the EK estimator turns out inferior to the BFM approach. However, results depend on the kind of bias measure and on the issue of whether using total historical returns or only excess returns for evaluation purposes. In any case, our findings imply that a rather straightforward rule of thumb for valuation may be of value to practitioners: ‘stick to the simple arithmetic mean estimator without terminal value computation, but consider future cash flows up to a time horizon of about 30 years’.

A Note on Corporate Valuation Using Imprecise Cost of Capital

We compare the estimator for discount rates according to Elsner and Krumholz (EK) (2013) to the approach propagated in Breuer et al. (2014) (BFM). While the EK estimator is derived analytically and implies a correcting factor by which the original arithmetic mean estimator is adjusted, the BFM approach is based on a simple ad hoc modification and recommends to truncate the time horizon for cash flow projection up to about N = 30 years. The BFM approach is reasonable, as the most relevant bias problems are implied by terminal value computations. Rather surprisingly, for our main simulation analysis based on real-world capital market data for 19 countries over the period 2008-2012, the EK estimator turns out inferior to the BFM approach. However, results depend on the kind of bias measure and on the issue of whether using total historical returns or only excess returns for evaluation purposes. In any case, our findings imply that a rather straightforward rule of thumb for valuation may be of value to practitioners: ‘stick to the simple arithmetic mean estimator without terminal value computation, but consider future cash flows up to a time horizon of about 30 years’.

Is It Time for the Cochrane Collaboration to Reconsider Its Meta-Analysis Methodology?

Meta-analysis is becoming more popular in the biomedical literature and of increasing importance to clinicians, policy makers, funding bodies, and researchers for synthesizing practice guidelines, grant justification, and making policy decisions. Meta-analysis involves a quantitative analysis of multiple study outcomes to reach conclusions regarding an intervention. Often these studies are different in their design and conduct. One method of meta-analysis endorsed by the Cochrane Collaboration that has raised significant controversy is the random-effects model, which assumes that underlying effects vary across differing study populations. Often larger studies, even if not well designed and meticulously conducted, have more information value than smaller studies. The random effects model redistributes weights in one direction only—from big to small studies—without addressing variations in study estimate related to study quality and conduct. Finally, this estimator cannot be expected to have a variance structure that is different from that of the arithmetic mean when heterogeneity is large. → See related article, page 40 In this issue of the journal, Doi1 has raised some very significant issues regarding meta-analysis models. He proposes a quality effect model that achieves variance reduction through additional information garnered from the conduct and design of the list of studies and makes the case that bias reduction is not possible, since bias cannot be quantified even after detailed assessment of the studies. This is in contrast to Greenland,2 whose aim was bias quantification and whose realization has eluded researchers, even though there has been a recent attempt.3 The concept of variance reduction through quality assessment was initially suggested by Doi and Thalib4 in 2008, and in this current paper, Doi thoroughly reviews further developments in its conceptualization and also informs readers about the software he and his colleagues have developed to help researchers perform the analysis (www.epigear.com). Recently, Shuster5 suggested that empirical weighting in meta-analysis should be abandoned, because he was able to demonstrate that empirical weighting of any form would lead to correlated weights and effect estimates, which in turn would lead to bias in the weighted estimator. The only system of weights that would not lead to such correlation was the arithmetic mean estimator, and Shuster, therefore, suggested that a solution to biased random effects models was to use unweighted (or equally weighted) estimators. The problem with this assertion is that, given empirical weighting always leads to bias, the aim of weighting has to be variance reduction, otherwise it serves no purpose at all. Indeed, Burton et al6 have stated that an unbiased estimator with large variance is also itself of no practical use. Therefore, for a weighted average to be more informative than an arithmetic mean, it has to be able to offset bias by a decrease in variance. Unfortunately, the random effects model redistributes weights away from inverse variance in the direction of equal weights and does not have any mechanism for variance reduction in the face of gross heterogeneity, and thus, is unable to offset model variance. Instead, what actually happens is that as the heterogeneity increases, the confidence interval around the weighted mean also increases to keep pace with the variance expansion. In this random effects scheme, variance reduction, which should be the goal for any weighted estimator, does not seem to be achieved. Doi has demonstrated, for the first time, how model variance reduction can be achieved by input of more individual study information into the model so that studies with an expectation of greater bias variance can be down-weighted. This reduces actual estimator variance and thus its variability, and the simulation study elegantly illustrates this. Finally, Doi demonstrates that the random effects model is a special case of the quality effects model, one in which the quality assessment has been totally uninformative. Given this finding, I conclude by questioning if the time has come for organizations such as Cochrane to seriously consider updating their methodologies. At the very least, they should make a serious scientific inquiry into the quality effects model, which has the potential to change the face of meta-analysis as we know it.

Estimating cost of capital in firm valuations with arithmetic or geometric mean – or better use the Cooper estimator?

We test the extent and determinants of bias effects of the arithmetic as well as the geometric mean estimator and the estimator of Cooper [1996. Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting. European Financial Management 2 (July): 157–67] regarding discount rate estimation for firm valuation by way of a bootstrap approach for 13 different countries. The Cooper estimator is superior to both the geometric and the (conventional) arithmetic mean estimator. However, a ‘truncated’ version of the arithmetic mean estimator leads generally to better estimation outcomes than the Cooper estimator. This means that, in order to reduce problems of upward-biased firm value estimates, expected cash flows beyond a certain time horizon are completely neglected in terminal value estimation. Such an approach seems particularly reasonable for the valuation of young growth companies as well as for companies from quickly developing countries such as Brazil, China, or Thailand, because the bias in terminal value estimation is increasing in the growth rate of future expected cash flows.

Estimating Cost of Capital in Firm Valuations with Arithmetic or Geometric Mean - Or Better Use the Cooper Estimator?

We test the extent and determinants of bias effects of the arithmetic as well as the geometric mean estimator and the estimator of Cooper (1996) regarding discount rate estimation for firm valuation by way of a bootstrap approach for thirteen different countries. The Cooper estimator is preferable only for firms with small growth rates of future expected cash flows, while for moderate to high growth rates the “truncated” arithmetic mean estimator should be applied. This means that, in order to reduce problems of upward biased firm value estimates, expected cash flows beyond a certain time horizon are completely neglected. Such an approach seems particularly reasonable for the valuation of young growth companies as well as in general for companies from quickly developing countries like Brazil, China, or Thailand.

Experimental Comparison of Methods for Multivariable Frequency Response Function Estimation

Nonparametric estimation methods for the multivariable frequency response function are experimentally evaluated using closed-loop data from an industrial robot. Three classical estimators (H1, joint input-output, arithmetic mean) and two estimators based on nonlinear averaging techniques (harmonic mean, geometric/logarithmic mean) are considered. The estimators based on nonlinear averaging give the best results, followed by the arithmetic mean estimator, which gives a slightly larger bias. The joint input-output estimator, which is asymptotically unbiased in theory, turns out to give large bias errors for low frequencies. Finally, the H1 estimator gives the largest bias for all frequencies.

Bayesian ranking of biochemical system models

There often are many alternative models of a biochemical system. Distinguishing models and finding the most suitable ones is an important challenge in Systems Biology, as such model ranking, by experimental evidence, will help to judge the support of the working hypotheses forming each model. Bayes factors are employed as a measure of evidential preference for one model over another. Marginal likelihood is a key component of Bayes factors, however computing the marginal likelihood is a difficult problem, as it involves integration of nonlinear functions in multidimensional space. There are a number of methods available to compute the marginal likelihood approximately. A detailed investigation of such methods is required to find ones that perform appropriately for biochemical modelling. We assess four methods for estimation of the marginal likelihoods required for computing Bayes factors. The Prior Arithmetic Mean estimator, the Posterior Harmonic Mean estimator, the Annealed Importance Sampling and the Annealing-Melting Integration methods are investigated and compared on a typical case study in Systems Biology. This allows us to understand the stability of the analysis results and make reliable judgements in uncertain context. We investigate the variance of Bayes factor estimates, and highlight the stability of the Annealed Importance Sampling and the Annealing-Melting Integration methods for the purposes of comparing nonlinear models. Models used in this study are available in SBML format as the supplementary material to this article.

Glomerular basement membrane thickness in children: A stereologic assessment

Stereologic methods have emerged as the technique of choice in assessing glomerular basement membrane (GBM) thickness, following conceptual modeling comparing the stereologic technique of harmonic mean of the orthogonal intercept estimation (Th) with the model based method of arithmetic mean estimation (ATH), with no direct comparison undertaken. We undertook to establish the gold standard for GBM estimation and use this technique to establish a range for GBM thickness in children. Intra-observer and inter-glomerular variation was estimated in 34 cases with (presumed) normal GBM thickness, using Th, ATH and a rapid direct measurement technique, with intra-observer variation measured in 35 cases with GBM attenuation. A total of 34,011 measurements were undertaken to establish a range for Th in children on 212 biopsies from 199 patients (127 male) demonstrating minimal change nephropathy (N = 153), focal segmental glomerulosclerosis (24), no abnormality (24), and acute tubular necrosis (8), which were used as surrogates for normals. Th demonstrated less variation than ATH in both the normal and attenuated groups. GBM thickness increased throughout childhood, from 194 +/- 6.5 nm (mean +/- SE) at one year to 297 +/- 6.0 nm at 11 years, with a reduced rate of increase after age 11 years. Stereologic methods are superior to model based techniques in estimating GBM thickness and should be regarded as the technique of choice in this area. GBM thickness was observed to increase during childhood with no gender effect demonstrable as a main effect or interaction.

Intervalo de confiança "bootstrap" como ferramenta para classificar raças do nematóide de cisto da soja

Estimativas "bootstrap" da média aritmética dos genótipos de soja 'Pickett', 'Peking', PI88788 e PI90763 e os intervalos de confiança obtidos pela teoria normal e através da distribuição "bootstrap" deste estimador, como o percentil "bootstrap" e o BCa, correção para o viés e aceleração, do parâmetro de diferenciação da cultivar padrão de suscetibilidade Lee são utilizados para classificar raças do nematóide de cisto da soja. Os intervalos de confiança obtidos a partir da distribuição "bootstrap" apresentaram menor amplitude e foram muito similares, dessa forma, o limite inferior do intervalo de confiança percentil "bootstrap" foi tomado como nível de referência nas distribuições "bootstrap" do estimador da média aritmética dos genótipos diferenciadores, permitindo estimar a probabilidade empírica de uma reação positiva ou negativa, e, conseqüentemente, identificar a raça mais provável sob determinado teste.

Comparison of the efficiency for mean estimators in time series

The empirical performance of linear mean estimators satisfying some optimality conditions was studied and found to excel that of the arithmetic mean estimator particularly for processes generated by k-th differences in simulated data sets and empirical time series.

Asymptotic efficiency of the arithmetic-mean estimator of the unknown mean of a homogeneous random field

We consider the estimation of the unknown mean of a homogeneous random field from observations on a system of homothetically expanding regions. We examine the asymptotic behavior of the variance of the arithmetic-mean estimator. The arithmetic-mean estimator is shown to be asymptotically efficient in the class of linear estimators.