In reliability or medical studies, we may only observe each ongoing renewal process for a certain period of time. When the underlying distribution F is arithmetic, Vardi (Ann. Statist. 10 (1982b), 772-785) developed the RT algorithm for nonparametric estimation. In this paper we extend the study to the nonarithmetic case and show that the choice of an arbitrary constant in the RT algorithm can ...

In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a penalized likelihood, where the penalty is a function of the minimum of the ratios of the scale parameters and the sample size. It is shown that the penalized max...

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estim...

Let p1 ≤ p2 and consider estimating a fixed set {x : p1 ≤ f(x) ≤ p2} by the random set {x : p1 ≤ f̂n(x) ≤ p2}, where f̂n is a consistent estimator of the continuous function f . This paper gives consistency conditions for these sets, and provides a new method to construct confidence regions from empirical averages of sets. The method can also be used to construct confidence regions for sets of th...

Let p1 ≤ p2 and consider estimating a fixed set {x : p1 ≤ f(x) ≤ p2} by the random set {x : p1 ≤ f̂n(x) ≤ p2}, where f̂n is a consistent estimator of the continuous function f . This paper gives consistency conditions for these sets, and provides a new method to construct confidence regions from empirical averages of sets. The method can also be used to construct confidence regions for sets of th...

The distribution of an inhomogeneous Wiener process is determined by the mean function m(t) ss EW(t) and the variance function b(t) = V^(W(t)) which depend on unknown parameter d _ 0 . Observations are assumed to be in discrete time points where the sample size tends to infinity. Using the general theory of Ibragimow, Hasminskij [2] sufficient conditions for consistency of MLE i?n are establish...

Consider an i.i.d. sequence of random variables whose distribution f lies in one of a nested family of models (Mq)q∈N, Mq ⊂ Mq+1. The smallest index q such that Mq⋆ contains f is called the model order. We establish strong consistency of the penalized likelihood order estimator in a general setting with penalties of order η(q) log log n, where η(q) is a dimensional quantity. Moreover, such pena...

In studying individual consumption behavior, an important issue is the analysis of the relation between commodity expenditure and income (or total expenditure). In this paper we firstly review the more recent theoretical and empirical literature attempting to: (i) derive theory-consistent demand systems models which are able to account for empirically observed non-linearities in total expenditu...

This paper considers strong consistency of heteroscedasticity and autocorrelation consistent covariance matrix estimators. Sometimes such estimators in the literature are referred to as Newey-West estimators. Weak consistency proofs for these estimators can be found in White (1984), Newey and West (1987), Gallant and White (1988), Andrews (1991), Hansen (1992a), and De Jong and Davidson (1997)....

To verify fixed-time constraints in Grid workflow systems, consistency and inconsistency conditions have been defined in conventional verification work. However, with a view of the run-time uncertainty of activity completion duration, we argue that, although the conventional consistency condition is feasible, the conventional inconsistency condition is too restrictive and covers several differe...