Universal Point Estimation, with Applications in Economics, Business and Decision Sciences

Authors

  • Buu-Chau Truong Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City
  • Thi Diem-Chinh Ho Faculty of Mathematics and Statistics, University of Sciences, Ho Chi Minh City, Vietnam; General Faculty, Binh Duong Economics & Technology University, Binh Duong
  • Thu-Quang Luu Faculty of Finance, Banking University of Ho Chi Minh City
  • Michael McAleer Department of Finance, Asia University

DOI:

https://doi.org/10.6000/1929-7092.2019.08.90

Keywords:

Universal approach, Maximum likelihood, Moment method, Bayesian method.

Abstract

Estimation is used widely in numerous disciplines, including Mathematics, Statistics, Economics, Business, and Decision Sciences, among others. Estimation is a process for determining an approximation, which is a value that can be used for a number of purposes, even if input data are sufficient, incomplete, missing or unsecure. In practice, estimation relates to “using the value of a statistic inferred from a sample to estimate the value of a corresponding population parameterâ€. Estimation is usually separated into two categories, namely point estimation and interval estimation. The main purpose of this paper is to present a universal approach to the theory and practice of three methods in statistical inference to obtain point estimates, namely the moment, maximum likelihood, and Bayesian methods. The paper also discusses the advantages and disadvantages of the three universal approaches in practical applications in Economics, Business and Decision Sciences.

References

Amiri, A., Allahyari, S. (2012), Change point estimation methods for control chart postsignal diagnostics: a literature review. Quality and Reliability Engineering International, 28(7), 673-685.
https://doi.org/10.1002/qre.1266
Anderson, P.M., Sherman, C.A. (2010), Applying the Fermi estimation technique to business problems. Journal of Applied Business and Economics, 10(5), 33.
Angelis, K., Alvarez-Carretero, S., Dos Reis, M., Yang, Z. (2017), An evaluation of different partitioning strategies for Bayesian estimation of species divergence times. Systematic Biology, 67(1), 61-77.
https://doi.org/10.1093/sysbio/syx061
Arvai, J.L., Campbell, V.E., Baird, A., Rivers, L. (2004), Teaching students to make better decisions about the environment: Lessons from the decision sciences. Journal of Environmental Education, 36(1), 33-44.
https://doi.org/10.3200/JOEE.36.1.33-44
Bafumi, J., Gelman, A., Park, D.K., Kaplan, N. (2005), Practical issues in implementing and understanding Bayesian ideal point estimation. Political Analysis, 13(2), 171-187.
https://doi.org/10.1093/pan/mpi010
Bernhard, J.E., Moreland, J.S., Bass, S.A. (2019), Bayesian estimation of the specific shear and bulk viscosity of quark–gluon plasma. Nature Physics, 1-5.
https://doi.org/10.1038/s41567-019-0611-8
Cao, X., Lam, J.S.L. (2019), Simulation-based severe weather-induced container terminal economic loss estimation. Maritime Policy & Management, 46(1), 92-116.
https://doi.org/10.1080/03088839.2018.1516049
Casciano, M.C., De Giorgi, V., Oropallo, F., Siesto, G. (2011), Estimation of structural business statistics for small firms by using administrative data. Rivista di statistica ufficiale, 13(2-3), 55-74.
Chang, C.C., Batmunkh, M.U., Wong, W.K., Jargalsaikhan, M. (2019), Relationship between capital structure and profitability: Evidence from Four Asian Tigers. Journal of Management Information and Decision Sciences, 22(2), 54-65.
https://doi.org/10.2139/ssrn.3411977
Chang, C.L., McAleer, M., Wong, W.K. (2017), Management information, decision sciences, and financial economics: A connection. Journal of Management Information and Decision Sciences, 20, 1-19.
https://doi.org/10.2139/ssrn.3103807
Chang, C.L., McAleer, M., Wong, W.K. (2018), Decision sciences, economics, finance, business, computing, and big data: Connections. Advances in Decision Sciences, 22, 1-58.
https://doi.org/10.2139/ssrn.3140371
Chen, W. (2015), Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A: Statistical Mechanics and its Applications, 429, 125-139.
https://doi.org/10.1016/j.physa.2015.02.060
Chen, X., Favilukis, J., Ludvigson, S.C. (2013), An estimation of economic models with recursive preferences. Quantitative Economics, 4(1), 39-83.
https://doi.org/10.3982/QE97
Chevillon, G., Hendry, D.F. (2005), Non-parametric direct multi-step estimation for forecasting economic processes. International Journal of Forecasting, 21(2), 201-218.
https://doi.org/10.1016/j.ijforecast.2004.08.004
Chib, S., Shin, M., Simoni, A. (2018), Bayesian estimation and comparison of moment condition models. Journal of the American Statistical Association, 113(524), 1656-1668.
https://doi.org/10.1080/01621459.2017.1358172
Chung, Y., Gelman, A., Rabe-Hesketh, S., Liu, J., Dorie, V. (2015), Weakly informative prior for point estimation of covariance matrices in hierarchical models. Journal of Educational and Behavioral Statistics, 40(2), 136-157.
https://doi.org/10.3102/1076998615570945
Dai, Z., Wen, F. (2018), Some improved sparse and stable portfolio optimization problems. Finance Research Letters, 27, 46-52.
https://doi.org/10.1016/j.frl.2018.02.026
Dupin, J., Matzke, N.J., Särkinen, T., Knapp, S., Olmstead, R.G., Bohs, L., Smith, S.D. (2017), Bayesian estimation of the global biogeographical history of the Solanaceae. Journal of Biogeography, 44(4), 887-899.
https://doi.org/10.1111/jbi.12898
Fouque, J.P., Sircar, R., Zariphopoulou, T. (2017), Portfolio optimization and stochastic volatility asymptotics. Mathematical Finance, 27(3), 704-745.
https://doi.org/10.1111/mafi.12109
Goplerud, M. (2019), A Multinomial Framework for Ideal Point Estimation. Political Analysis, 27(1), 69-89.
https://doi.org/10.1017/pan.2018.31
Gordois, A., Cutler, H., Pezzullo, L., Gordon, K., Cruess, A., Winyard, S., Chua, K. (2012), An estimation of the worldwide economic and health burden of visual impairment. Global public health, 7(5), 465-481.
https://doi.org/10.1080/17441692.2011.634815
Harchaoui, Z., Lvy-Leduc, C. (2010), Multiple change-point estimation with a total variation penalty. Journal of the American Statistical Association, 105(492), 1480-1493.
https://doi.org/10.1198/jasa.2010.tm09181
Haward, M.F., Janvier, A. (2015), An introduction to behavioural decision?making theories for paediatricians. Acta Paediatrica, 104(4), 340-345.
https://doi.org/10.1111/apa.12948
Hawkins, D.M. (1976), Point estimation of the parameters of piecewise regression models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 25(1), 51-57.
https://doi.org/10.2307/2346519
Hodges, J.L., Lehmann, E.L. (2012), Some problems in minimax point estimation. In Selected Works of EL Lehmann, pp. 15-30. Springer, Boston, MA.
https://doi.org/10.1007/978-1-4614-1412-4_3
Hoderlein, S., Nesheim, L., Simoni, A. (2017), Semiparametric estimation of random coefficients in structural economic models. Econometric Theory, 33(6), 1265-1305.
https://doi.org/10.1017/S0266466616000396
Horton, N.J., Kleinman, K.P. (2007), Much ado about nothing: A comparison of missing data methods and software to fit incomplete data regression models. The American Statistician, 61(1), 79-90.
https://doi.org/10.1198/000313007X172556
Hsieh, S.H., Lee, S.M., Shen, P. (2009), Semiparametric analysis of randomized response data with missing covariates in logistic regression. Computational Statistics & Data Analysis, 53(7), 2673-2692.
https://doi.org/10.1016/j.csda.2009.01.011
Klein, L.R., Ozmucur, S. (2002), The estimation of China's economic growth rate. Journal of Economic and Social Measurement, 28(4), 187-202.
https://doi.org/10.3233/JEM-2003-0222
Lee, S.M., Li, C.S., Hsieh, S.H., Huang, L.H. (2012), Semiparametric estimation of logistic regression model with missing covariates and outcome. Metrika, 75(5), 621-653.
https://doi.org/10.1007/s00184-011-0345-9
Lehmann, E.L. (2004), Elements of large-sample theory. Springer Science & Business Media.
Lehmann, E.L., Casella, G. (2006), Theory of point estimation. Springer Science & Business Media.
Little, R. J. (1992), Regression with missing X’s: A review. Journal of the American Statistical Association, 87(420), 1227-1237.
https://doi.org/10.2307/2290664
Lukusa, T.M., Lee, S.M., Li, C.S. (2016), Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates. Metrika, 79(4), 457-483.
https://doi.org/10.1007/s00184-015-0563-7
Ly, S., Pho, K.H., Ly, S., Wong, W.K. (2019a), Determining distribution for the quotients of dependent and independent random variables by using copulas. Journal of Risk and Financial Management, 12(1), 1-42.
https://doi.org/10.3390/jrfm12010042
Ly, S., Pho, K.H., Ly, S., Wong, W.K. (2019b), Determining distribution for the product of random variables by using copulas. Risks, 7(1), 1-23.
https://doi.org/10.3390/risks7010023
Macedo, L.L., Godinho, P., Alves, M.J. (2017), Mean-semivariance portfolio optimization with multiobjective evolutionary algorithms and technical analysis rules. Expert Systems with Applications, 79, 33-43.
https://doi.org/10.1016/j.eswa.2017.02.033
Markowitz, H. (1952), Portfolio selection. Journal of Finance, 7(1), 77-91.
https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Marsman, M., Waldorp, L., Dablander, F., Wagenmakers, E.J. (2019), Bayesian estimation of explained variance in ANOVA designs. Statistica Neerlandica, 73(3), 351-372.
https://doi.org/10.1111/stan.12173
Matzke, D., Dolan, C.V., Batchelder, W.H., Wagenmakers, E.J. (2015), Bayesian estimation of multinomial processing tree models with heterogeneity in participants and items. Psychometrika, 80(1), 205-235.
https://doi.org/10.1007/s11336-013-9374-9
Mettler, T. (2010), Thinking in terms of design decisions when developing maturity models. International Journal of Strategic Decision Sciences, 1(4), 76-87.
https://doi.org/10.4018/jsds.2010100105
Obaidullah, M. (2016). Revisiting estimation methods of business zakat and related tax incentives. Journal of Islamic Accounting and Business Research, 7(4), 349-364.
https://doi.org/10.1108/JIABR-10-2014-0035
Olivares-Nadal, A.V., DeMiguel, V. (2018), A robust perspective on transaction costs in portfolio optimization. Operations Research, 66(3), 733-739.
https://doi.org/10.1287/opre.2017.1699
Pagell, M., Wiengarten, F., Fan, D., Humphreys, P., Lo, C.K. (2019), Managerial time horizons and the decision to put operational workers at risk: The role of debt. Decision Sciences, 50(3), 582-611.
https://doi.org/10.1111/deci.12338
Pearson, K. (1902), On the systematic fitting of curves to observations and measurements. Biometrika, 1(3), 265-303.
https://doi.org/10.2307/2331540
Pidgeon, N., Fischhoff, B. (2011), The role of social and decision sciences in communicating uncertain climate risks. Nature Climate Change, 1(1), 35.
https://doi.org/10.1038/nclimate1080
Pinto, T., Morais, H., Sousa, T.M., Sousa, T., Vale, Z., Praca, I., Pires, E.J.S. (2015), Adaptive portfolio optimization for multiple electricity markets participation. IEEE Transactions on Neural Networks and Learning Systems, 27(8), 1720-1733.
https://doi.org/10.1109/TNNLS.2015.2461491
Pho, K.H., Nguyen, V.T. (2018), Comparison of Newton-Raphson algorithm and Maxlik function. Journal of Advanced Engineering and Computation, 2(4), 281-292.
https://doi.org/10.25073/jaec.201824.219
Pho, K.H., Ho, T.D.C., Tran, T.K., Wong, W.K. (2019a), Moment generating function, expectation and variance of ubiquitous distributions with applications in decision sciences: A review. Advances in Decision Sciences, 23(2), 1-85.
https://doi.org/10.2139/ssrn.3430778
Pho, K.H., Ly, S., Ly, S., Lukusa, T.M. (2019b), Comparison among Akaike information criterion, Bayesian information criterion and Vuong’s test in model selection: A case study of violated speed regulation in Taiwan. Journal of Advanced Engineering and Computation, 3(1), 293-303.
https://doi.org/10.25073/jaec.201931.220
Pho, K.H., Tran, T.K., Ho, T.D.C., Wong, W.K. (2019c), Optimal solution techniques in decision sciences: A review. Advances in Decision Sciences 23(1), 1-47.
https://doi.org/10.2139/ssrn.3430764
Pomenkova, J. (2010), An alternative approach to the dating of business cycle: Nonparametric kernel estimation. Prague Economic Papers, 19(3), 251-272.
https://doi.org/10.18267/j.pep.375
Pouya, A.R., Solimanpur, M., Rezaee, M. J. (2016), Solving multi-objective portfolio optimization problem using invasive weed optimization. Swarm and Evolutionary Computation, 28, 42-57.
https://doi.org/10.1016/j.swevo.2016.01.001
Rizal, A., Sahidin, A., Herawati, H. (2018), Economic value estimation of mangrove ecosystems in Indonesia. Biodiversity International Journal, 2(1), 98-100.
https://doi.org/10.15406/bij.2018.02.00051
Sargan, J.D. (1958), The estimation of economic relationships using instrumental variables. Econometrica, 393-415.
https://doi.org/10.2307/1907619
Sargan, J.D. (1961), The maximum likelihood estimation of economic relationships with autoregressive residuals. Econometrica, 414-426.
https://doi.org/10.2307/1909642
Schafer, J.L., Graham, J.W. (2002), Missing data: our view of the state of the art. Psychological Methods, 7(2), 147.
https://doi.org/10.1037/1082-989X.7.2.147
Schennach, S.M. (2007), Point estimation with exponentially tilted empirical likelihood. Annals of Statistics, 35(2), 634-672.
https://doi.org/10.1214/009053606000001208
Schütt, H.H., Harmeling, S., Macke, J.H., Wichmann, F.A. (2016), Painfree and accurate Bayesian estimation of psychometric functions for (potentially) overdispersed data. Vision Research, 122, 105-123.
https://doi.org/10.1016/j.visres.2016.02.002
Smith, P. (2013), Sampling and estimation for business surveys. Designing and conducting business surveys, 165-218.
https://doi.org/10.1002/9781118447895.ch05
Taylor, G., McGuire, G. (2007), A synchronous bootstrap to account for dependencies between lines of business in the estimation of loss reserve prediction error. North American Actuarial Journal, 11(3), 70-88.
https://doi.org/10.1080/10920277.2007.10597467
Teulings, C.N., Zubanov, N. (2014), Is economic recovery a myth? Robust estimation of impulse responses. Journal of Applied Econometrics, 29(3), 497-514.
https://doi.org/10.1002/jae.2333
Tian. Y, Pho, K.H. (2019), A statistical view to study the aphorisms in Nahj al Balaghah. Digital Scholarship in the Humanities. (In Press).
https://doi.org/10.1093/llc/fqz075
Truong, B.C., Pho, K.H., Nguyen, V.B., Tuan, B.A., Wong, W.K. (2019), Graph theory and environmental algorithmic solutions to assign vehicles: Application to garbage collection in Vietnam. Advances in Decision Sciences, 23(2), 1-35.
https://doi.org/10.2139/ssrn.3430459
Tuan, B.A., Pudikova, G.N., Mahmoudi, M.R., Pho, K.H. (2019), Statistical approaches in literature: Comparing and clustering the alternatives of love in Divan of Hafiz. Digital Scholarship in the Humanities. (In Press).
https://doi.org/10.1093/llc/fqz069
Wang, C.Y., Chen, J.C., Lee, S.M., Ou, S.T. (2002), Joint conditional likelihood estimator in logistic regression with missing covariate data. Statistica Sinica, 555-574.
Yong, Z., Yuanyuan, L. (2007), The estimation of technological progress on the energy consumption returns effects. Economist, 2, 45-52.
Yoo, J.H., Lee, S.W., Park, S.K., Kim, D.H. (2017), A robust lane detection method based on vanishing point estimation using the relevance of line segments. IEEE Transactions on Intelligent Transportation Systems, 18(12), 3254-3266.
https://doi.org/10.1109/TITS.2017.2679222

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2019-12-13

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