6

OLS regressions have a set of assumption in order to have its point and interval estimates to be unbiased and efficient. Data missing not at random (MNAR) can pose serious estimations issues in the linear regression. In this study we evaluate the performance of OLS confidence interval estimates with MNAR data. We also suggest bootstrapping as a remedy for such data cases and compare the traditional confidence intervals against bootstrap ones. As we need to know the true parameters, we carry out a simulations study. Research results indicate that both approaches show similar results having similar intervals size. Given that bootstrap required a lot of computations, traditional methods is still recommended to be used even in case of MNAR

  • Read count 6
  • Date of publication 31-05-2024
  • Main LanguageIngliz
  • Pages492-502
Ўзбек

ОЛС регрессиялари нуқта ва интервалларни холис ва самарали баҳолаш учун бир қатор фаразларга эга. Тасодифий йўқолган маълумотлар (МНАР) чизиқли регрессияни баҳолашда жиддий муаммоларни келтириб чиқариши мумкин. Ушбу тадққотда биз МНАР маълумотлари билан ОЛС ишонч оралиғи баҳоларининг ишлашини баҳолаймиз. Биз, шунингдек, бундай маълумотлар ҳолатлари учун восита сифатида юклашни таклиф қиламиз ва анъанавий ишонч оралиқларини боотстрап билан солиштирамиз. Ҳақиқий параметрларни билишимиз кераклиги сабабли, биз симуляция тадқиқотини ўтказамиз. Тадқиқот натижалари шуни кўрсатадики, иккала ёндашув ҳам ўхшаш оралиқ ўлчамига эга ўхшаш натижаларни кўрсатади. Боотстрап жуда кўп ҳисобкитобларни талаб қилишини ҳисобга олиб, анъанавий усулларни МНАР ҳолатида ҳам қўллаш тавсия этилади.

Русский

Регрессии OLS имеют набор допущений, чтобы точечные и интервальные оценки были несмещенными и эффективными. Отсутствие данных не случайно (MNAR) может создать серьезные проблемы с оценками в линейной регрессии. В этом исследовании мы оцениваем эффективность оценок доверительного интервала OLS с данными MNAR. Мы также предлагаем загрузку как средство решения таких случаев данных и сравниваем традиционные доверительные интервалы с загрузочными интервалами. Поскольку нам необходимо знать истинные параметры, мы проводим моделирование. Результаты исследования показывают, что оба подхода показывают схожие результаты при одинаковом размере интервалов. Учитывая, что бутстрап требует большого количества вычислений, традиционные методы по-прежнему рекомендуется использовать даже в случае MNAR

English

OLS regressions have a set of assumption in order to have its point and interval estimates to be unbiased and efficient. Data missing not at random (MNAR) can pose serious estimations issues in the linear regression. In this study we evaluate the performance of OLS confidence interval estimates with MNAR data. We also suggest bootstrapping as a remedy for such data cases and compare the traditional confidence intervals against bootstrap ones. As we need to know the true parameters, we carry out a simulations study. Research results indicate that both approaches show similar results having similar intervals size. Given that bootstrap required a lot of computations, traditional methods is still recommended to be used even in case of MNAR

№ Name of reference
1 Carpenter, J. R., & Kenward, M. G. (2012). Missing data in clinical trials: a practical guide. Practical Guides to Biostatistics and Epidemiology. Cambridge University Press.
2 Chernick, M. R., and LaBudde, R. A. (2014). An introduction to bootstrap methods with applications to R. John Wiley & Sons.
3 Chernozhukov, V., and Hong, H. (2003). An MCMC approach to classical estimation. Journal of Econometrics, 115(2), 293-346.
4 Davison , A. C. , and Hinkley , D. V. (1997). Bootstrap Methods and Their Applications. Cambridge University Press, Cambridge .
5 DiCiccio , T., and Efron , B. (1992). More accurate confidence intervals in exponential families. Biometrika 79, 231 – 245 .
6 Efron , B., and Tibshirani , R. (1986). Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy. Statistical Science. Vol. 1 , 54 – 77
7 Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1-26.
8 Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia
9 Fan, Y., and Li, Q. (2004). A consistent model specification test based on the kernel density estimation. Econometrica, 72(6), 1845-1858.
10 Flachaire, E. (2007). Bootstrapping heteroscedastic regression models: wild bootstrap vs pairs bootstrap. Computational Statistics and Data Analysis, 49 (2), 361-376
11 Freedman , D. A. (1981). Bootstrapping regression models. Annals of Statistics, 9, 1218 – 1228
12 Graham, J. W. (2003). Adding missing-data-relevant variables to FIML-based structural equation models. Structural Equation Modeling, 10(1), 80-100.
13 Greene, W. H. (2021) Econometric Analysis, 8th edn, Pearson
14 Gujarati, D. N., Porter, D. C., and Gunasekar, S. (2012). Basic econometrics. McGraw-Hill Higher Education
15 He, Y., & Zaslavsky, A. M. (2012). Diagnostics for multiple imputation in surveys with missing data. Biometrika, 99(4), 731-745.
16 Horowitz, J. L., and Markatou, M. (1996). Semiparametric estimation of regression models for panel data. Review of Economic Studies, 63(1), 145-168.
17 James, G., Witten, D., Hastie, T., and Tibshirani, R. (2023). An Introduction to Statistical Learning. Publisher
18 Lind, D. A., Marchal, W. G., and Wathen, S. A. (1967). Statistical Techniques in Business and Economics (2nd ed). Publisher
19 Little, R. J. A., & Rubin, D. B. (1987). Statistical analysis with missing data. Wiley
20 Liu , R. Y. (1988). Bootstrap procedures under some non i.i.d. models . Annals of Statistics 16, 1696 – 1708
21 Politis, D. and Romano, J, (1994). The Stationary bootstap. The journal of American Statistical Association. 89 (428), 1303-1312
22 Schafer, J. L., & Graham, J. W. (2002). Multiple imputation for missing data: A cautionary tale. Sociological Methods & Research, 31(4), 445-454
Waiting