قارن الطرق

	تخصيص احتياطيات الخسائر بطريقة السلم المتسلسل (نموذج ماك)	الاستدلال بالتمهيد	التقدير المربعات الصغرى المعممة (GLS)
المجال	العلوم الاكتوارية	الإحصاء	الإحصاء
العائلة	Regression model	Regression model	Regression model
سنة النشأة	1993	1979	1935
صاحب الطريقة	Thomas Mack	Bradley Efron	Alexander Craig Aitken
النوع	Stochastic loss reserving model	Resampling-based inference	Linear estimator
المصدر التأسيسي	Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225.	Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 7(1), 1-26.	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
الأسماء البديلة	Development Factor Method, Link Ratio Method, Loss Development Method, Zincir Merdiven Yöntemi	bootstrap, bootstrap resampling, nonparametric bootstrap, Bootstrap Çıkarımı	GLS, Aitken estimator, EGLS, feasible GLS
ذات صلة	3	5	3
الملخص	Chain-Ladder Reserving is a stochastic actuarial method for estimating outstanding claim liabilities from a run-off triangle of cumulative paid losses. Formalized by Thomas Mack in 1993, it provides distribution-free estimates of reserve amounts along with their standard errors, making it a cornerstone of property-casualty insurance reserving and regulatory practice worldwide.	Bootstrap inference, introduced by Bradley Efron in 1979, estimates the sampling distribution of a statistic by repeatedly resampling the observed data with replacement. It requires no distributional assumption and produces reliable confidence intervals even in small samples.	Generalized Least Squares (GLS) is a linear regression estimator that extends ordinary least squares to handle situations where the error terms are correlated or have non-constant variance (heteroscedasticity). Introduced by Alexander Craig Aitken in 1935, GLS achieves the Best Linear Unbiased Estimator (BLUE) under a general error covariance structure by weighting observations according to their precision, providing a theoretical bridge between OLS and modern linear mixed models.