Nonparametric tests for left-truncated and interval-censored data

This paper considers two-sample nonparametric comparison of survival function when data are subject to left truncation and interval censoring. We propose a class of rank-based tests, which are generalization of weighted log-rank tests for right-censored data. Simulation studies indicate that the proposed tests are appropriate for practical use.     

On exact confidence intervals in a competing risks model with generalized hybrid type-I censored exponential data

In a recent paper by Mao, Shi and Sun that appeared in Journal of Statistical Computation and Simulation, the authors discuss, among other approaches, the construction of exact confidence intervals for the underlying parameters by ‘pivoting the cumulative distribution functions’ of the corresponding maximum likelihood estimators (MLEs). The authors assume that this method is applicable without providing the appropriate justification. In this short note the two requirements for the applicability of this method are discussed, namely, the stochastic monotonicity of the MLEs and the existence of solutions to the equations defining the exact confidence interval's endpoints.     

Quantile regression based on a weighted approach under semi-competing risks data

In this article, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. Due to the dependent censoring, the estimation of quantile regression coefficients on the non-terminal event becomes difficult. In order to handle this problem, we assume Archimedean Copula to specify the dependence of the non-terminal event and the terminal event. Portnoy [Censored regression quantiles. J Amer Statist Assoc. 2003;98:1001–1012] considered the quantile regression model under right-censoring data. We extend his approach to construct a weight function, and then impose the weight function to estimate the quantile regression parameter for the non-terminal event under semi-competing risks data. We also prove the consistency and asymptotic properties for the proposed estimator. According to the simulation studies, the performance of our proposed method is good. We also apply our suggested approach to analyse a real data.     

Point predictors of the latent failure times of censored units in progressively Type-II censored competing risks data from the exponential distributions

In this paper, we discuss the problem of predicting times to the latent failures of units censored in multiple stages in a progressively Type-II censored competing risks model. It is assumed that the lifetime distribution of the latent failure times are independent and exponential-distributed with the different scale parameters. Several classical point predictors such as the maximum likelihood predictor, the best unbiased predictor, the best linear unbiased predictor, the median unbiased predictor and the conditional median predictor are obtained. The Bayesian point predictors are derived under squared error loss criterion. Moreover, the point estimators of the unknown parameters are obtained using the observed data and different point predictors of the latent failure times. Finally, Monte-Carlo simulations are carried out to compare the performances of the different methods of prediction and estimation and one real data is used to illustrate the proposed procedures.     

Bias corrected MLEs under progressive type-II censoring scheme

ABSTRACT

Censoring frequently occurs in survival analysis but naturally observed lifetimes are not of a large size. Thus, inferences based on the popular maximum likelihood (ML) estimation which often give biased estimates should be corrected in the sense of bias. Here, we investigate the biases of ML estimates under the progressive type-II censoring scheme (pIIcs). We use a method proposed in Efron and Johnstone [Fisher's information in terms of the hazard rate. Technical Report No. 264, January 1987, Stanford University, Stanford, California; 1987] to derive general expressions for bias corrected ML estimates under the pIIcs. This requires derivation of the Fisher information matrix under the pIIcs. As an application, exact expressions are given for bias corrected ML estimates of the Weibull distribution under the pIIcs. The performance of the bias corrected ML estimates and ML estimates are compared by simulations and a real data application.     

All‐Pay Contests

This paper studies a class of games, “all‐pay contests,” which capture general asymmetries and sunk investments inherent in scenarios such as lobbying, competition for market power, labor‐market tournaments, and R&D races. Players compete for one of several identical prizes by choosing a score. Conditional on winning or losing, it is weakly better to do so with a lower score. This formulation allows for differing production technologies, costs of capital, prior investments, attitudes toward risk, and conditional and unconditional investments, among others. I provide a closed‐form formula for players' equilibrium payoffs and analyze player participation. A special case of contests is multiprize, complete‐information all‐pay auctions.     

Nonparametric Instrumental Regression

The focus of this paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model E[Y−ϕ(Z)|W]=0, and involve endogenous variables Y and Z and instruments W. The function ϕ is the solution of an ill‐posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.     

Real‐Time Delay Estimation Based on Delay History in Many‐Server Service Systems with Time‐Varying Arrivals

Motivated by interest in making delay announcements in service systems, we study real‐time delay estimators in many‐server service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time‐varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time‐varying arrival rates can introduce significant estimation bias in delay‐history‐based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delay‐history estimators that effectively cope with time‐varying arrival rates together with non‐exponential service‐time and abandonment‐time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.     

Pool‐Point Distribution of Zero‐Inventory Products

We study zero‐inventory production‐distribution systems under pool‐point delivery. The zero‐inventory production and distribution paradigm is supported in a variety of industries in which a product cannot be inventoried because of its short shelf life. The advantages of pool‐point (or hub‐and‐spoke) distribution, explored extensively in the literature, include the efficient use of transportation resources and effective day‐to‐day management of operations. The setting of our analysis is as follows: A production facility (plant) with a finite production rate distributes its single product, which cannot be inventoried, to several pool points. Each pool point may require multiple truckloads to satisfy its customers' demand. A third‐party logistics provider then transports the product to individual customers surrounding each pool point. The production rate can be increased up to a certain limit by incurring additional cost. The delivery of the product is done by identical trucks, each having limited capacity and non‐negligible traveling time between the plant and the pool points. Our objective is to coordinate the production and transportation operations so that the total cost of production and distribution is minimized, while respecting the product lifetime and the delivery capacity constraints. This study attempts to develop intuition into zero‐inventory production‐distribution systems under pool‐point delivery by considering several variants of the above setting. These include multiple trucks, a modifiable production rate, and alternative objectives. Using a combination of theoretical analysis and computational experiments, we gain insights into optimizing the total cost of a production‐delivery plan by understanding the trade‐off between production and transportation.