Empirical Bayes regression analysis with many regressors but fewer observations

In this paper, we consider the prediction problem in multiple linear regression model in which the number of predictor variables, p, is extremely large compared to the number of available observations, n  . The least-squares predictor based on a generalized inverse is not efficient. We propose six empirical Bayes estimators of the regression parameters. Three of them are shown to have uniformly lower prediction error than the least-squares predictors when the vector of regressor variables are assumed to be random with mean vector zero and the covariance matrix (1/n)X^tX$(1/n){\mathit{X}}^{\mathrm{t}}\mathit{X}$ where X^t=(_x1,…,_xn)${\mathit{X}}^{\mathrm{t}}=({\mathit{x}}_1,\dots ,{\mathit{x}}_n)$ is the p×n$p\times n$ matrix of observations on the regressor vector centered from their sample means. For other estimators, we use simulation to show its superiority over the least-squares predictor.     

Testing equality of mean vectors in a one-way MANOVA with monotone missing data

In this study, testing the equality of mean vectors in a one-way multivariate analysis of variance (MANOVA) is considered when each dataset has a monotone pattern of missing observations. The likelihood ratio test (LRT) statistic in a one-way MANOVA with monotone missing data is given. Furthermore, the modified test (MT) statistic based on likelihood ratio (LR) and the modified LRT (MLRT) statistic with monotone missing data are proposed using the decomposition of the LR and an asymptotic expansion for each decomposed LR. The accuracy of the approximation for the Chi-square distribution is investigated using a Monte Carlo simulation. Finally, an example is given to illustrate the methods.     

Efficient use of multi-auxiliary information in search of good rotation patterns in successive sampling

This article considers the problem of estimating the population mean on the current (second) occasion using multi-auxiliary information in successive sampling over two occasions. A general class of estimators is proposed for estimating population mean on the current occasion and expressions for bias and mean square error for these estimators are obtained up to first degree of approximation. The minimum variance bound estimator in the proposed class is discussed. Many popular estimators have been shown to belong to this class. Optimum replacement policy is also discussed. Finally, the superiority of the proposed class of estimators over multivariate version of chain type ratio estimator envisaged by Singh (2005 Singh, G.N. (2005). On the use of chain type ratio estimator in successive sampling. Stat Transition 7:21–26. [Google Scholar]) is established empirically.     

Traffic engineering of tunnel-based networks with class specific diversity requirements

Tunnel-based networks such as Multi-protocol Label switching (MPLS) are suitable for providing diversity guarantees to different service classes or customers. Based on the number of active tunnels to handle, router capabilities can be taxed due to the limited amount of memory and/or processing power of these routers. In this paper, we present a mixed-integer linear program formulation for a traffic engineering problem where such tunnel restrictions are taken into account in addition to standard capacity constraints while addressing diversity requirement of services. Due to large size of the formulation, we also present an accompanied solution approach based on Lagrangian relaxation and sub-gradient optimization. We then present results towards impact of diversity constraint upon the tunneling and capacity restrictions. We observed that the networks having higher amounts of capacity and demands with higher level of survivability are much more sensitive to number of allowed tunnels in the network. The impact is even more prominent for sparsely-connected, large-sized networks.     

Evaluation of a synthetic method of estimation for small areas

A synthetic estimator is one of the simplest estimators for a small area, and it has several variants. In this paper, a ratio-synthetic estimator is proposed and compared with the existing synthetic estimator (Ghangurde & Singh, 1977) and it is observed that the gain due to stratification in the case of a synthetic estimator reduces proportional to the domain coverage.     

A two-stage procedure for estimating a linear function of K multinormal mean vectors when covariance matrices are unknown

We consider the problem of constructing a fixed-size confidence region for a linear function of mean vectors of k multinormal populations, where all covariance matrices are completely unknown. A two-stage procedure is proposed to construct such a confidence region. It is shown that the proposed two-stage procedure is consistent and its asymptotic property for the expected sample size is also given. A Monte Carlo simulation study is given for an illustration.     

Asymptotic non-null distribution for the locally most powerful invariant test for sphericity

The asymptotic non-null distribution of the locally most powerful invariant test for sphericity is derived under local alternatives and the power is compared with that of the likelihood ratio test, which is admissible (Kiefe and Schwartz (1965)) and has a monotone power function (Carter and Srivastava (1977)). Up to 0(n ^-3/2) the powers are essentially the same.     

A comparison of bootstrap method and Edgeworth expansion in approximating the distribution of sample variance — one sample and two sample cases

The performance of the bootstrap method and the Edgeworth expansion in approximating the distribution of sample variance are compared when the data are from a non-normal population. Both approximations are very good. so long as the parent population is close to normal.     

Cusum procedure for monitoring variability

In this paper, a CUSUM procedure is given for monitoring for a decrease in the variance (process improvement) as well as a two-sided CUSUM which monitors for both increases and decreases in the variance. The observations are assumed to be independent and normally distributed. The procedure is based on the log¬arithm of the likelihood ratio of the probability density functions under the two competing hypotheses. Formulae that approximate the average run length of the CUSUM procedure for detecting an increase (or decrease) in the variance of a normal distribution are given. These formulae, when corrected for the overshoot from the boundary, provide a very accurate approximation