In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F . A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for the i...

Under left truncation, data (X(i), Y(i)) are observed only when Y(i) ≤ X(i). Usually, the distribution function F of the X(i) is the target of interest. In this paper, we study linear functionals ∫ φ dF(n) of the nonparametric maximum likelihood estimator (MLE) of F, the Lynden-Bell estimator F(n). A useful representation of ∫ φ dF(n) is derived which yields asymptotic normality under optimal m...

Studies of chronic diseases routinely sample individuals subject to conditions on an event time of interest. In epidemiology, for example, prevalent cohort studies aiming to evaluate risk factors for survival following onset of dementia require subjects to have survived to the point of screening. In clinical trials designed to assess the effect of experimental cancer treatments on survival, pat...

Let K[〈X〉] denote the large polynomial ring (in the sense of Halter-Koch [7]) on the set X = {x1, x2, x3, . . . } of indeterminates. For each integer n, there is a truncation homomorphism ρn : K[〈X〉] → K[x1, . . . , xn]. If I is a homogeneous ideal of K[〈X〉], then the N-graded Hilbert series of K[x1,...,xn] ρn(I) can be written as gn(t) (1−t) ; it was shown in [13] that if in addition I is what...

AMS 2000 subject classifications: primary 62G07 secondary 62G20 a b s t r a c t In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The estimation of the covariate's density is considered as well. U...

To determine the safety stock required to achieve a desired service level, demands are commonly assumed to follow a normal probability distribution. However, since demands are necessarily truncated at values below zero, this paper will show that this approach underestimates the actual demand level and results in achieved service levels that are less than those targeted. Use of a left-truncated ...