Oracle model selection for correlated data via residuals

This paper concerns model selection for autoregressive time series when the observations are contaminated with trend. We propose an adaptive least absolute shrinkage and selection operator (LASSO) type model selection method, in which the trend is estimated by B-splines, the detrended residuals are calculated, and then the residuals are used as if they were observations to optimize an adaptive LASSO type objective function. The oracle properties of such an adaptive LASSO model selection procedure are established; that is, the proposed method can identify the true model with probability approaching one as the sample size increases, and the asymptotic properties of estimators are not affected by the replacement of observations with detrended residuals. The intensive simulation studies of several constrained and unconstrained autoregressive models also confirm the theoretical results. The method is illustrated by two time series data sets, the annual U.S. tobacco production and annual tree ring width measurements.     

Estimation of parameters in logistic and log-logistic distribution with grouped data

In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study.     

Least Squares Model Averaging

This paper considers the problem of selection of weights for averaging across least squares estimates obtained from a set of models. Existing model average methods are based on exponential Akaike information criterion (AIC) and Bayesian information criterion (BIC) weights. In distinction, this paper proposes selecting the weights by minimizing a Mallows criterion, the latter an estimate of the average squared error from the model average fit. We show that our new Mallows model average (MMA) estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators. In a simulation experiment we show that the MMA estimator compares favorably with those based on AIC and BIC weights. The proof of the main result is an application of the work of Li (1987).     

Testing Parameters in GMM Without Assuming that They Are Identified

We propose a generalized method of moments (GMM) Lagrange multiplier statistic, i.e., the K statistic, that uses a Jacobian estimator based on the continuous updating estimator that is asymptotically uncorrelated with the sample average of the moments. Its asymptotic χ² distribution therefore holds under a wider set of circumstances, like weak instruments, than the standard full rank case for the expected Jacobian under which the asymptotic χ² distributions of the traditional statistics are valid. The behavior of the K statistic can be spurious around inflection points and maxima of the objective function. This inadequacy is overcome by combining the K statistic with a statistic that tests the validity of the moment equations and by an extension of Moreira's (2003) conditional likelihood ratio statistic toward GMM. We conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series.     

岭型主成分估计在降维估计类中的最优性

研究岭型主成分估计在岭型降维估计类中的性质 ,在不同的条件下 ,证明了岭型主成分估计有某些最优性质     

Correction locale de l'estimateur à noyau de la densité d'une loi de probabilité

The standard Parzen-Rosenblatt kernel density estimator is known to systematically deviate from the true value near critical points of the density curve. To overcome this difficulty, we extend the Rao-Blackwell method by using locally sufficient statistics: we define a new estimator and study its asymptotic behaviour. The interest of the method is shown by means of simulations.     

Confidence limits for estimates of totals from stratified samples, with application to medicare Part B overpayment audits

Superpopulation models are proposed that should be appropriate for modelling sample-based audits of Medicare payments and other overpayment situations. Simulations are used to estimate the coverage probabilities of confidence intervals formed using the standard Stratified Expansion and Combined Ratio estimators of the total. Despite severe departures from the usual model of normal deviations, these methods have actual coverage probabilities reasonably close to the nominal level specified by the US government's sampling guidelines. An exception occurs when all claims from a single sampling unit are either completely allowed, or completely denied, and for this situation an alternative is explored. A balanced sampling design is also examined, but shown to make no improvement over ordinary stratified samples used in conjunction with ratio estimates.     

Comparison of some linear calibration estimators

In this article, we consider a family of linear calibration estimators arising from inverse estimator and analyze its properties employing the small disturbance asymptotic theory. The asymptotic approximations for bias and mean squared error of this family are compared with the corresponding results for classical and inverse estimators, whose properties are also compared.     

Choosing between two unknown intervals: an empirical bayes testing approach to a classification problem

Let X₁,X₂…be i.i.d. observations from a mixture density. The support of the unknown prior distribution is the union of two unknown intervals. The paper deals with an empirical Bayes testing approach (?≤ c against>c where c is an unknown parameter to be estimated) in order to classify the observed variables as coming from one population or the other as ? belongs to one or the other unknown interval. Two methods are proposed in which asymptotically optimal decision rules are constructed avoiding the estimation of the unknown prior. The first method deals with the case of exponential families and is a generalization of the method of Johns and Van Ryzin (1971, 1972) whereas the second one deals with families that are closed under convolution and is a Fourier method. The application of the Fourier method to some densities (i.e. contaminated Gaussian distributions, exponential distribution, double-exponential distribution) which are interesting in view of applications and which cannot be studied by means of the direct method, is also considered herein.     

Testing the equality of variance-covariance matrices the robust way

The robust statistic T² _Dproposed by Tiku and Singh (1982) for testing the equality of mean vectors of two mu1 t ivariate populations is modified to test the equality of variance-covariance matrices.