Estimation of a Gamma Scale Parameter Under Asymmetric Squared Log Error Loss

Abstract

Estimation of scale parameter under the squared log error loss function is considered with restriction to the principle of invariance and risk unbiasedness. An explicit form of minimum risk scale-equivariant estimator under this loss is obtained. The admissibility and inadmissibility of a class of linear estimators of the form (cT + d) are considered, where T follows a gamma distribution with an unknown scale parameter η and a known shape parameter ν. This includes the admissibility of the minimum risk equivariant estimator on η (MRE).     

Model-based confidence bands for survival functions

This paper focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model-based, relying on a parametric model for the conditional expectation of the censoring indicator given the observed minimum, and derives its strength from easy access to a good-fitting model among a plethora of choices available for binary response data. The substantive methodological contribution is in exploiting a semiparametric estimator of the survival function to produce improved simultaneous confidence bands. To obtain critical values for computing the confidence bands, a two-stage bootstrap approach that combines the classical bootstrap with the more recent model-based regeneration of censoring indicators is proposed and a justification of its asymptotic validity is also provided. Several different confidence bands are studied using the proposed approach. Numerical studies, including robustness of the proposed bands to misspecification, are carried out to check efficacy. The method is illustrated using two lung cancer data sets.     

Using Bayesian Techniques for Data Pooling in Regional Payroll Forecasting

This article adapts to the regional level a multicountry technique recently used by Garcia-Ferrer, Highfield, Palm, and Zellner (1987) and extended by Zellner and Hong (1987) to forecast the growth rates in gross national product across nine countries. This forecasting methodology is applied to the regional level by modeling payroll formation in seven Ohio metropolitan areas. We compare the forecasting performance of these procedures with that of a ridge estimator and find that the ridge estimator produces forecasts equal to or better than those from the newly proposed estimators. We conclude that the ridge estimator, which does not reference the pooled data information introduced by the newly proposed techniques, may serve as a benchmark against which to judge the relative importance of this kind of information in improving forecasts.     

Some Observations,a Suggestion,and Some Comments on the Conway-Roberts Article

This article provides new tools for the evaluation of dynamic stochastic general equilibrium (DSGE) models and applies them to a large-scale new Keynesian model. We approximate the DSGE model by a vector autoregression, and then systematically relax the implied cross-equation restrictions and document how the model fit changes. We also compare the DSGE model's impulse responses to structural shocks with those obtained after relaxing its restrictions. We find that the degree of misspecification in this large-scale DSGE model is no longer so large as to prevent its use in day-to-day policy analysis, yet is not small enough to be ignored.     

Estimation of Parameters of Mixed Failure Time Distribution Based on an Extended Modified Sampling Scheme

Abstract

The problem of estimation of parameters of a mixture of degenerate (at zero) and exponential distribution is considered by Dixit and Prasad [Dixit, V. U. (Nee: Jayade, V. D.), Prasad, M. S. (1990 Dixit, V. U. and Prasad, M. S. 1990. Estimation of parameters of mixed failure time distribution. Commun.in Statist.-Theory Meth, 19(12): 4667–4678. (Nee: Jayade, V. D.) [Google Scholar]). Estimation of parameters of mixed failure time distribution. Commun.in Statist.-Theory Meth., 19(12):4667–4678]. The sampling scheme proposed in it is extended to k positive observations in Dixit [Dixit, V. U. (1993 Dixit, V. U. 1993. “Statistical Inference for AR (1) Process with Mixed Errors”. Kolhapur, , India: Shivaji University. Unpublished Ph.D. thesis [Google Scholar]). Statistical Inference for AR (1) Process with Mixed Errors. Unpublished Ph.D. thesis, Shivaji University Kolhapur, India] and moment estimator, MLE and UMVUE based on it are obtained and their finite sample and asymptotic properties are studied. These results are presented in this paper. It is interesting to mention that the sampling scheme proposed by Shinde and Shanubhogue [Shinde, R. L., Shanubhogue, A. (2000 Shinde, R. L. and Shanubhogue, A. 2000. Estimation of parameters and the mean life of a mixed failure time distribution. Commun. Statist.-Theory Meth, 29(11): 2621–2642. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Estimation of parameters and the mean life of a mixed failure time distribution. Commun. Statist.-Theory Meth. 29(11):2621–2642] is a particular case of the sampling scheme proposed in Dixit [Dixit, V. U. (1993 Dixit, V. U. 1993. “Statistical Inference for AR (1) Process with Mixed Errors”. Kolhapur, , India: Shivaji University. Unpublished Ph.D. thesis [Google Scholar]). Statistical Inference for AR (1) Process with Mixed Errors. Unpublished Ph.D. thesis, Shivaji University Kolhapur, India] for n = k.     

Optimal Binary Prediction for Group Decision Making

We address the problem of optimally forecasting a binary variable for a heterogeneous group of decision makers facing various (binary) decision problems that are tied together only by the unknown outcome. A typical example is a weather forecaster who needs to estimate the probability of rain tomorrow and then report it to the public. Given a conditional probability model for the outcome of interest (e.g., logit or probit), we introduce the idea of maximum welfare estimation and derive conditions under which traditional estimators, such as maximum likelihood or (nonlinear) least squares, are asymptotically socially optimal even when the underlying model is misspecified.     

基于季报数据的收入公告后漂移现象研究

利用收入指标对股票超额收益率进行解释构成了理解"定价异常"的重要方面。为此,基于盈余公告后漂移的理论分析框架,以上证A股2008年1季度至2011年4季度的相关数据为基础,利用标准化预期外收入估计量(SURE)和分类检验模型方法对中国股票市场公告期内股票价格的收入公告后漂移现象进行实证检验,研究发现:在盈余公告期内,预期外收入与股票超额收益率呈现出负相关或是不显著的关系,即中国股票市场的收入公告后漂移效应不显著。之后的稳健性分析也同样证实了负相关或是不显著关系的存在,而这种异常可能与中国股市的弱有效率相关。     

Dirichlet Processes in Nonlinear Mixed Effects Models

In this article, we use two efficient approaches to deal with the difficulty in computing the intractable integrals when implementing Gibbs sampling in the nonlinear mixed effects model (NLMM) based on Dirichlet processes (DP). In the first approach, we compute the Laplace's approximation to the integral for its high accuracy, low cost, and ease of implementation. The second approach uses the no-gaps algorithm of MacEachern and Müller (1998 MacEachern , S. , Müller , P. ( 1998 ). Estimating mixtures of Dirichlet process models . Journal of Computational and Graphical Statistics 7 : 223 – 238 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) to perform Gibbs sampling without evaluating the difficult integral. We apply both approaches to real problems and simulations. Results show that both approaches perform well in density estimation and prediction and are superior to the parametric analysis in that they can detect important model features, such as skewness, long tails, and multimodality, whereas the parametric analysis cannot.     

On the Preliminary Test Backfitting and Speckman Estimators in Partially Linear Models and Numerical Comparisons

Przystalski and Krajewski (2007 Przystalski , M. , Krajewski , P. ( 2007 ). Constrained estimators of treatment parameters in semiparametric models . Statist. Probab. Lett. 77 : 914 – 919 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed the restricted backfitting (RBCF) estimator and restricted Speckman (RSPC) estimator for the treatment effects in a partially linear model when some additional exact linear restrictions are assumed to hold. In this article, we introduce the preliminary test backfitting (PTBCF) estimator and preliminary test Speckman (PTSPC) estimator when the validity of the restrictions is suspected. Performances of the proposed estimators are examined with respect to the mean squared error (MSE) criterion. In addition, numerical behaviors of the proposed estimators are illustrated and compared via a Monte Carlo simulation study.     

Computational Method for Jackknifed Generalized Ridge Tuning Parameter based on Generalized Maximum Entropy

In this article, a new method to estimate the Jackknifed generalized ridge tuning parameter, based on the Jackknifed Ridge-trace and an analytical method borrowed from generalized maximum entropy, is presented. The ideas in the article are illustrated and evaluated using to the well-known Portland cement data set and simulations.