An approximation for analyzing a broad class of implicitly and explicitly defined estimators

An approximation is presented that can be used to gain insight into the characteristics – such as outlier sensitivity, bias, and variability – of a wide class of estimators, including maximum likelihood and least squares. The approximation relies on a convenient form for an arbitrary order Taylor expansion in a multivariate setting. The implicit function theorem can be used to construct the expansion when the estimator is not defined in closed form. We present several finite-sample and asymptotic properties of such Taylor expansions, which are useful in characterizing the difference between the estimator and the expansion.     

Statistical analysis of a two-unit dependent repairable system

Maximum likelihood estimators are investigated a for lr-out-of 2:G repairable system when failures and repairs are statistically dependent. Under two censoring schemes Accelerated Life Testing Procedure (ALTP) is used to obtain the estimates. Information matrices are supplied and a special case when the failure and repair phenomenon are independent of each other is considered.     

Estimation of the parameters of a regression model with a multivariate t error variable

This paper deals with a regression model for several vari¬ables under the assumption that the errors have a multivariate t-distribution. The parameters of the model, the regression parameters, as well as the scale parameters and the degress of freedom of the error variable are estimated and the estimation procedure is illustrated by a numerical example, Also, the prop¬erties of the estimators and tests for the regression parameters are discussed.     

First‐order bias correction for fractionally integrated time series

Most of the long memory estimators for stationary fractionally integrated time series models are known to experience non‐negligible bias in small and finite samples. Simple moment estimators are also vulnerable to such bias, but can easily be corrected. In this article, the authors propose bias reduction methods for a lag‐one sample autocorrelation‐based moment estimator. In order to reduce the bias of the moment estimator, the authors explicitly obtain the exact bias of lag‐one sample autocorrelation up to the order n⁻¹. An example where the exact first‐order bias can be noticeably more accurate than its asymptotic counterpart, even for large samples, is presented. The authors show via a simulation study that the proposed methods are promising and effective in reducing the bias of the moment estimator with minimal variance inflation. The proposed methods are applied to the northern hemisphere data. The Canadian Journal of Statistics 37: 476–493; 2009 © 2009 Statistical Society of Canada     

Influence analysis in multivariate linear general models

In this paper we obtain several influence measures for the multivariate linear general model through the approach proposed by Muñoz-Pichardo et al. (1995), which is based on the concept of conditional bias. An interesting charasteristic of this approach is that it does not require any distributional hypothesis. Appling the obtained results to the multivariate regression model, we obtain some measures proposed by other authors. Nevertheless, on the results obtained in this paper, we emphasize two aspects. First, they provide a theoretical foundation for measures proposed by other authors for the mul¬tivariate regression model. Second, they can be applied to any linear model that can be formulated as a particular case of the multivariate linear general model. In particular, we carry out an application to the multivariate analysis of covariance.     

Smoothing Splines with Boundary Correction

Regular smoothing splines are known to have a type of boundary bias problem that can reduce their estimation efficiency. In this paper, a boundary corrected smoothing spline with general order is designed in a way that the risk will decay at an optimal rate. An O(n) algorithm is also developed to compute the resultant estimator efficiently.     

A Bivariate Distribution for the Reliability Analysis of Failure Data in Presence of a Forewarning or Primer Event

This article presents a bivariate distribution for analyzing the failure data of mechanical and electrical components in presence of a forewarning or primer event whose occurrence denotes the inception of the failure mechanism that will cause the component failure after an additional random time. The characteristics of the proposed distribution are discussed and several point estimators of parameters are illustrated and compared, in case of complete sampling, via a large Monte Carlo simulation study. Confidence intervals based on asymptotic results are derived, as well as procedures are given for testing the independence between the occurrence time of the forewarning event and the additional time to failure. Numerical applications based on failure data of cable insulation specimens and of two-component parallel systems are illustrated.     

Finite Sample Modifications of the Granger Non Causality Test in Cointegrated Vector Autoregressions

This article deals with the Granger non causality test in cointegrated vector autoregressive processes. We propose a new testing procedure that yields an asymptotically standard distribution and performs well in small samples by combining the standard Wald test and the generalized inverse procedure. We also propose a few simple modifications to the test statistics in order to help our procedure perform better in finite samples. Monte Carlo simulations show that our procedure works better than the conventional approach.     

An improved estimator of omission rate for census count: With particular reference to India

ABSTRACT

Every large census operation should undergo evaluation programs to find the sources and extent of inherent coverage errors. In this article, we briefly discuss the statistical methodology to estimate the omission rate in Indian census using dual-system estimation (DSE) technique. We have explicitly studied the correlation bias factor involved in the estimate, its extent, and consequences. A new potential source of bias in the estimate is identified and discussed. During the survey, more efficient enumerators compared to the census operations are appointed, and this fact may inflate the dependency between two lists and lead to a significant bias. Some examples are given to demonstrate this argument in various plausible situations. We have suggested one simple and flexible approach which can control this bias. Our proposed estimator can efficiently overcome the potential bias by achieving the desired degree of accuracy (almost unbiased) with relatively higher efficiency. Overall improvements in the results are explored through simulation study on different populations.