Neparametarske statističke tehnike ocenjivanja regresionih koeficijenata i koeficijenta varijacije u korporativnim finansijama
Non-parametric statistical techniques for estimation of regression coefficients and coefficient of variation in corporate finance
Докторанд
Ivković, IvanaМентор
Rajić, VesnaЧланови комисије
Stanojević, JelenaLončar, Dragan
Janković, Irena
Jovanović, Milan
Метаподаци
Приказ свих података о дисертацијиСажетак
Predmet istraživanja disertacije je intervalno ocenjivanje regresionih koeficijenata u prostom linearnom regresionom modelu i kvadratnom regresionom modelu ako slučajna greška nema normalnu raspodelu i intervalno ocenjivanje mera disperzije ako osnovni skup ne sledi normalnu raspodelu.
Ako su narušene polazne pretpostavke, proporcija simuliranih intervala za regresione koeficijente i mere disperzije može znatno odstupati od nominalnog nivoa pouzdanosti.
U radu su razvijene originalne metode za intervalno ocenjivanje regresionih koeficijenata u prostom linearnom i kvadratnom regresionom modelu zasnovane na Edgeworth-ovom razvoju raspodele t statistika koje se koriste u pomenutim modelima. Dalje, predložene su transformacije metoda koje se koriste za intervalno ocenjivanje koeficijenta varijacije. Reč je o transformaciji zasnovanoj na odsečenoj sredini i bootstrap transformaciji.
Validnost predloženih metoda proverena je kroz simulacije koristeći različite raspodele, kao i podatke u obla...sti korporativnih finansija. Korporativne finansije obuhvataju praćenje efekata finansiranja kako bi se maksimizirala vrednost kompanije, kao i različite aspekte značajne za rast kompanije. Iz tog razloga, predmet razmatranja prilikom konstrukcije intervalnih ocena bili su podaci o indikatoru verovatnoće bankrotstva, količniku ukupnog duga, meri sistematskog rizika i dividendama.
Utvrđeno je da su, u većini razmatranih slučajeva, proporcije simuliranih intervala zasnovanih na predloženim metodama bliže nominalnom nivou pouzdanosti u poređenju sa proporcijama intervala proučavanih u literaturi. Na osnovu rezultata dobijenih u empirijskom delu, date su preporuke za intervalno ocenjivanje koje se mogu koristiti za donošenje pouzdanih zaključaka, pre svega, u oblasti korporativnih finansija.
Ključne reči: proporcija simuliranih intervala poverenja, nominalni nivo pouzdanosti, regresioni koeficijent, prost linearni regresioni model, kvadratni regresioni model, koeficijent varijacije, Edgeworth-ov razvoj raspodele t statistike, odsečena sredina, korporativne finansije.
The subject of the research of dissertation is the interval estimation of the regression coefficients in the simple linear regression model and quadratic regression model if an error term does not have normal distribution and interval estimation of the measures of dispersion if the population does not follow normal distribution.
If the initial assumptions are violated, the proportion of the simulated intervals for the regression coefficients and measures of dispersion can noticeably deviate from the nominal confidence level.
The original methods for the interval estimation of the regression coefficients in the simple linear and quadratic regression model, based on the Edgeworth's expansion of the distribution of the t statistics which are used in the mentioned models, were developed. Further, the transformations of the methods used for the interval estimation of the coefficient of variation were proposed. It is about the transformation based on the trimmed mean and the bootstrap transf...ormation.
The validation of the proposed methods was checked through simulations using different distributions, as well as the data in the field of corporate finance. Corporate finance includes monitoring the effects of financing in order to maximize a company’s value, as well as various aspects important to the company’s growth. For that reason, the data on the bankruptcy probability indicator, total debt ratio, systematic risk measure and dividends were considered in order to construct the interval estimates.
It was found that, in most of the considered cases, the proportions of the simulated intervals based on the proposed methods are closer to the nominal confidence level compared with the proportions of the intervals studied so far in the literature. Based on the results obtained in the empirical part, the recommendations for the interval estimation, which can be used to draw the reliable conclusions, primarily, in the field of corporate finance, were given.
Key words: proportion of the simulated confidence intervals, nominal confidence level, regression coefficient, simple linear regression model, quadratic regression model, coefficient of variation, Edgeworth's expansion of the distribution of the t statistic, trimmed mean, corporate finance.