Density estimation in the uniform deconvolution model

We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data.     

控制费用为“取最大”形式的可控排序问题

本文讨论了一类新的加工时间可控的单机排序问题,其目标函数为正则函数与最大不满意程度函数之和,不满意函数刻划了对工件实际加工时间偏离其额定加工时间不满意的程度,本文对这类问题提出了几个多项式算法。     

Modeling Conditional Yield Densities

Given the increasing interest in agricultural risk, many have sought improved methods to characterize conditional crop-yield densities. While most have postulated the Beta as a flexible alternative to the Normal, others have chosen nonparametric methods. Unfortunately, yield data tends not to be sufficiently abundant to invalidate many reasonable parametric models. This is problematic because conclusions from economic analyses, which require estimated conditional yield densities, tend not to be invariant to the modeling assumption. We propose a semiparametric estimator that, because of its theoretical properties and our simulation results, enables one to empirically proceed with a higher degree of confidence.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 1

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and, in a sequel to this paper, prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

Likelihood-based specification analysis of continuous-time models of the short-term interest rate

An extensive collection of continuous-time models of the short-term interest rate is evaluated over data sets that have appeared previously in the literature. The analysis, which uses the simulated maximum likelihood procedure proposed by Durham and Gallant (2002), provides new insights regarding several previously unresolved questions. For single factor models, I find that the volatility, not the drift, is the critical component in model specification. Allowing for additional flexibility beyond a constant term in the drift provides negligible benefit. While constant drift would appear to imply that the short rate is nonstationary, in fact, stationarity is volatility-induced. The simple constant elasticity of volatility model fits weekly observations of the three-month Treasury bill rate remarkably well but is easily rejected when compared with more flexible volatility specifications over daily data. The methodology of Durham and Gallant can also be used to estimate stochastic volatility models. While adding the latent volatility component provides a large improvement in the likelihood for the physical process, it does little to improve bond-pricing performance.     

Robustness issues in multilevel regression analysis

A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.     

Progressive stress accelerated life tests under finite mixture models

In this paper, progressive stress accelerated life tests are considered when the lifetime of a product under use condition follows a finite mixture of distributions. The experiment is performed when each of the components in the mixture follows a general class of distributions which includes, among others, the Weibull, compound Weibull, power function, Gompertz and compound Gompertz distributions. It is assumed that the scale parameter of each component satisfies the inverse power low, the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Based on type-I censoring, the maximum likelihood estimates (MLEs) of the parameters under consideration are obtained. A special attention is paid to a mixture of two Rayleigh components. Simulation results are carried out to study the precision of the MLEs and to obtain confidence intervals for the parameters involved.     

On estimating the mean of the selected normal population under the LINEX loss function

Following Parsian and Farsipour (1999), we consider the problem of estimating the mean of the selected normal population, from two normal populations with unknown means and common known variance, under the LINEX loss function. Some admissibility results for a subclass of equivariant estimators are derived and a sufficient condition for the inadmissibility of an arbitrary equivariant estimator is provided. As a consequence, several of the estimators proposed by Parsian and Farsipour (1999) are shown to be inadmissible and better estimators are obtained. Received January 2001/Revised May 2002     

Pitfalls of Normal-Gamma Stochastic Frontier Models

Although conceptually pleasing, normal-gamma frontier models lead to difficult estimation problems. It is shown here that unless the sample size reaches several thousands of observations the shape parameter of the gamma density is hard to estimate, and that this carries over to estimates of the stochastic frontier, the individual inefficiencies, and the allocation of the overall variance to the stochastic frontier and to the inefficiencies.     

Nonparametric efficiency analysis: A multivariate conditional quantile approach

This paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup (multiple inputs and multiple outputs). It introduces α-quantile efficiency scores. A nonparametric estimator is proposed achieving strong consistency and asymptotic normality. Then if α increases to one as a function of the sample size we recover the properties of the FDH estimator. But our estimator is more robust to the perturbations in data, since it attains a finite gross-error sensitivity. Environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed. Numerical examples illustrate the usefulness of the approach.