Browsing by Subject "Censoring"

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Open Access
Bayesian demand updating in lost sales newsvendor: a two moment approximation
(Elsevier, 2007-10) Berk, E.; Gürler, Ü.; Levine, R. A.
We consider Bayesian updating of demand in a lost sales newsvendor model with censored observations. In a lost sales environment, where the arrival process is not recorded, the exact demand is not observed if it exceeds the beginning stock level, resulting in censored observations. Adopting a Bayesian approach for updating the demand distribution, we develop expressions for the exact posteriors starting with conjugate priors, for negative binomial, gamma, Poisson and normal distributions. Having shown that non-informative priors result in degenerate predictive densities except for negative binomial demand, we propose an approximation within the conjugate family by matching the first two moments of the posterior distribution. The conjugacy property of the priors also ensure analytical tractability and ease of computation in successive updates. In our numerical study, we show that the posteriors and the predictive demand distributions obtained exactly and with the approximation are very close to each other, and that the approximation works very well from both probabilistic and operational perspectives in a sequential updating setting as well.
Open Access
Covariance function of a bivariate distribution function estimator for left truncated and right censored data
(Institute of Statistical Science, Academia Sinica, 1998) Gijbelsi I.; Gürler, Ü.
In left truncation and right censoring models one observes i.i.d. samples from the triplet (T, Z, δ) only if T ≤ Z, where Z = min(Y, C) and δ is one if Z = Y and zero otherwise. Here, Y is the variable of interest, T is the truncating variable and C is the censoring variable. Recently, Gürler and Gijbels (1996) proposed a nonparametric estimator for the bivariate distribution function when one of the components is subject to left truncation and right censoring. An asymptotic representation of this estimator as a mean of i.i.d. random variables with a negligible remainder term has been developed. This result establishes the convergence to a two time parameter Gaussian process. The covariance structure of the limiting process is quite complicated however, and is derived in this paper. We also consider the special case of censoring only. In this case the general expression for the variance function reduces to a simpler formula.
Open Access
Variance of the bivariate density estimator for left truncated right censored data
(Elsevier, 1999) Prewitt, K.; Gürler, Ü.
In this study the variance of the bivariate kernel density estimators for the left truncated and right censored (LTRC) observations are considered. In LTRC models, the complete observation of the variable Y is prevented by the truncating variable T and the censoring variable C. Consequently, one observes the i.i.d, samples from the triplets (T,Z,delta) only if T less than or equal to Z, Z=min(Y, C) and delta is one if Z=Y and zero otherwise. Gurler and Prewitt (1997, submitted for publication) consider the estimation of the bivariate density function via nonparametric kernel methods and establish an i.i.d. representation of their estimators. Asymptotic variance of the i.i.d, part of their representation is developed in this paper. Application of the results are also discussed for the data-driven and the least-squares cross validation bandwidth choice procedures. (C) 1999 published by Elsevier Science B.V. All rights reserved.