Semiparametric estimation of employment duration models

There are a variety of economic areas, such as studies of employment duration and of the durability of capital goods, in which data on important variables typically are censored. The standard techinques for estimating a model from censored data require the distributions of unobservable random components of the model to be specified a priori up to a finite set of parameters, and misspecification of these distributions usually leads to inconsistent parameter estimates. However, economic theory rarely gives guidance about distributions and the standard estimation techniques do not provide convenient methods for identifying distributions from censored data. Recently, several distribution-free or semiparametric methods for estimating censored regression models have been developed. This paper presents the results of using two such methods to estimate a model of employment duration. The paper reports the operating characteristics of the semiparametric estimators and compares the semiparametric estimates with those obtained from a standard parametric model.     

Efficient estimation of non parametric simultaneous equations models

This paper defines a new procedure to efficiently estimate non parametric simultaneous equations models. The proposed estimation procedure exploits the additive structure and achieves oracle efficiency without the knowledge of unobserved error terms. Furthermore, simulation results show that our new estimator outperforms the existing estimator in terms of mean squared error.     

On admissible estimation for parametric functions in linear models

This paper deals with the linear model Ey∈K, Cov y∈V. The question is investigated when a parametric function (a,y) is an admissible or inadmissible estimator of some parametric function (p,Ey). It is also discussed when a linear mapping C:K→K has the property that (a,cy) is an admissible estimator of ((Ey),a) for all a∈K. Finall the question is raised how inadmissible estimators (a,y) can be replaced by admissible estimators superior to (a,y).     

Bayesian estimation of reliability using time-to-failure distribution of parametric degradation models

This paper focusses on computing the Bayesian reliability of components whose performance characteristics (degradation – fatigue and cracks) are observed during a specified period of time. Depending upon the nature of degradation data collected, we fit a monotone increasing or decreasing function for the data. Since the components are supposed to have different lifetimes, the rate of degradation is assumed to be a random variable. At a critical level of degradation, the time to failure distribution is obtained. The exponential and power degradation models are studied and exponential density function is assumed for the random variable representing the rate of degradation. The maximum likelihood estimator and Bayesian estimator of the parameter of exponential density function, predictive distribution, hierarchical Bayes approach and robustness of the posterior mean are presented. The Gibbs sampling algorithm is used to obtain the Bayesian estimates of the parameter. Illustrations are provided for the train wheel degradation data.     

Asymptotic results for parametric estimation in inadequate two phases regression models

We study the asymptotic properties, consistency, asymptotic normality, of the least squares estimator in a non linear regression problem. The model uses a parametric class Л of functions, but we do not assume that the unknown function belongs to that class. Л is here a class of continuous functions with a discontinuity in the first derivative. The problem of making a choice between two classes of that type is also studied.     

Structural duration models

In this paper we discuss structural duration models, which arise from a dynamic optimization decision of an individual: for example, the decision of an unemployed worker to accept or reject a wage offer, or the decision of a plant manager to shut down the plant for inspection or repair. Starting from well-known simple models, we move on to more complex and new models, such as monitor-repair models and bivariate duration models. For each model we indicate a solution of the Bellman equation and derive the likelihood function of a typical event history.     

Identification of parametric Rasch-type models

In modern Item Response Theory, the Rasch model is viewed as a Generalized Linear Mixed Model, where the item parameters correspond to the fixed-effects, whereas the person specific parameters are the random-effects. The statistical model, bearing on the observable variables only, is obtained after integrating out the random-effects. Although it is widely accepted that the parameters of this model are identified, it is hard to find a correct justification. Furthermore, the meaning of the parameters of the Rasch model – as well as of its extensions – is typically based on the fixed-effects specification of the model, that is, when the person specific parameters are also treated as fixed-effects. The contribution of this paper is to provide an explicit proof of the identification of the random-effects Rasch model. The proof is valid for a large class of Rasch-type models. It is also shown that such a proof can be applied to analyze the identification of Explanatory Rasch Models. Finally, the meaning of the parameters of interest with respect to the different data generating process is discussed.     

On identifiability of parametric statistical models

Summary This is a review article on statistical identifiability. Besides the definition of the main concepts, we deal with several questions relevant to the statistician: parallelism between parametric identifiability and sample sufficiency; relationship of identifiability with measures of sample information and with the inferential concept of estimability; several strategies of making inferences in unidentifiable models with emphasis on the distinct behaviour of the classical and Bayesian approaches. The concepts, ideas and methods discussed are illustrated with simple examples of statistical models. Centro de Análise e Processamento de Sinais da UTL     

Non-identifiable parametric probability models and reparametrization

Identifiability is a primary assumption in virtually all classical statistical theory. However, such an assumption may be violated in a variety of statistical models. We consider parametric models where the assumption of identifiability is violated, but otherwise satisfy standard assumptions. We propose an analytic method for constructing new parameters under which the model will be at least locally identifiable. This method is based on solving a system of linear partial differential equations involving the Fisher information matrix. Some consequences and valid inference procedures under non-identifiability have been discussed. The method of reparametrization is illustrated with an example.     

Steady-state ranked set sampling and parametric estimation

Ranked set sampling (RSS) was first used to obtain a more efficient estimator of the population mean, as compared to the one based on simple random sampling. This technique is useful when judgment ordering of a simple random sample (SRS) of small size can be done easily and fairly accurately, but exact measurement of an observation is difficult and expensive. It is noted that, due to the complicated likelihood, parametric estimation with RSS is difficult. In this article, the notion of steady-state RSS is introduced, its relation to stratified sampling is established, and its possible use in parametric estimation is explored and put forward for further investigations.     

A geometrically motivated parametric model in manifold estimation

The general aim of manifold estimation is reconstructing, by statistical methods, an m-dimensional compact manifold S on ^d (with m≤d) or estimating some relevant quantities related to the geometric properties of S. Focussing on the cases d=2 and d=3, with m=d or m=d?1, we will assume that the data are given by the distances to S from points randomly chosen on a band surrounding S. The aim of this paper is to show that, if S belongs to a wide class of compact sets (which we call sets with polynomial volume), the proposed statistical model leads to a relatively simple parametric formulation. In this setup, standard methodologies (method of moments, maximum likelihood) can be used to estimate some interesting geometric parameters, including curvatures and Euler characteristic. We will particularly focus on the estimation of the (d?1)-dimensional boundary measure (in Minkowski's sense) of S. It turns out, however, that the estimation problem is not straightforward since the standard estimators show a remarkably pathological behaviour: while they are consistent and asymptotically normal, their expectations are infinite. The theoretical and practical consequences of this fact are discussed in some detail.     

Earthquakes occurrences estimation through a parametric semi-Markov approach

The estimation of earthquakes’ occurrences prediction in seismic areas is a challenging problem in seismology and earthquake engineering. Indeed, the prevention and the quantification of possible damage provoked by destructive earthquakes are directly linked to this kind of prevision. In our paper, we adopt a parametric semi-Markov approach. This model assumes that a sequence of earthquakes is seen as a Markov process and besides it permits to take into consideration the more realistic assumption of events’ dependence in space and time. The elapsed time between two consecutive events is modeled as a general Weibull distribution. We determine then the transition probabilities and the so-called crossing states probabilities. We conclude then with a Monte Carlo simulation and the model is validated through a large database containing real data.     

Perfect linear models and perfect parametric functions

General linear models with a common design matrix and with various structures of the variance–covariance matrix are considered. We say that a model is perfect for a linearly estimable parametric function, or the function is perfect in the model, if there exists the best linear unbiased estimator. All perfect models for a given function and all perfect functions in a given model are characterized.     

Penalized proportion estimation for non parametric mixture of regressions

Abstract

In this article, we propose a penalized local log-likelihood method to locally select the number of components in non parametric finite mixture of regression models via proportion shrinkage method. Mean functions and variance functions are estimated simultaneously. We show that the number of components can be estimated consistently, and further establish asymptotic normality of functional estimates. We use a modified EM algorithm to estimate the unknown functions. Simulations are conducted to demonstrate the performance of the proposed method. We illustrate our method via an empirical analysis of the housing price index data of United States.