Modified Robust Second-Order Slope-Rotatable Designs

Generally it is very difficult to construct robust slope-rotatable designs along axial directions. Present paper focuses on modified second-order slope-rotatable designs (SOSRDs) with correlated errors. Modified robust second-order slope-rotatability conditions are derived for a general variance–covariance structure of errors. These conditions get simplified for intraclass correlation structure. A few robust second-order slope-rotatable designs (over all directions, or with equal maximum directional variance slope, or D-optimal slope) are examined with respect to modified robust slope-rotatability. It is observed that robust second-order slope-rotatable designs over all directions, or with equal maximum directional variance slope, or D-optimal slope are not generally modified robust second-order slope-rotatable designs.     

The Melancholic Name

How to think the gift of the name that announces the finitude of the named and the name itself, insofar as finitude is not reducible to the negativity of the concept and sense, a Gift to the other insofar as the other concerns us with his finitude? There is, as it were, a note of melancholy that adheres our finite existence, which also intimates the very gift that is given to the other. The whole question of the ethico‐political, understood here as being‐towards‐others, is at stake here. The article reads Schelling, Heidegger and Benjamin to think anew the place of language as gift and its concern with the thoughts of the political.     

“When will They Ever Learn”? Selective Discrimination in Provision of Schooling Facilities in Muslim Majority Areas: A Case Study of Murshidabad District of West Bengal,India

Inequality in educational attainment among various religious communities in India has come to light in the public domain only after the publication of Sachar Committee Report. The committee opined that selective discrimination of schooling facilities in Muslim concentrated areas is one of the major reasons behind the low educational attainment of that community. The present study aims at understanding the disparities in the provision of schooling facilities in Muslim-dominated and non-Muslim-dominated regions of West Bengal considering Murshidabad district as the study area. The present study constructed an Educational Development Index by considering 11 socioeconomic indicators and using the principal component analysis method, applied it to the study population. It has been found that the blocks having a higher share of Muslim population registered lower levels of educational development. It has also been found that most of the deprived schools located in the Muslim-dominated areas and within the non-Muslim-dominated areas the schools having higher share of Muslim pupil are mostly deprived.     

Robust first-order rotatable lifetime improvement experimental designs

Experimental designs are widely used in predicting the optimal operating conditions of the process parameters in lifetime improvement experiments. The most commonly observed lifetime distributions are log-normal, exponential, gamma and Weibull. In the present article, invariant robust first-order rotatable designs are derived for autocorrelated lifetime responses having log-normal, exponential, gamma and Weibull distributions. In the process, robust first-order D-optimal and rotatable conditions have been derived under these situations. For these lifetime distributions with correlated errors, it is shown that robust first-order D-optimal designs are always robust rotatable but the converse is not true. Moreover, it is observed that robust first-order D-optimal and rotatable designs depend on the respective error variance–covariance structure but are independent from these considered lifetime response distributions.     

Two Non-Negative Estimators for the Model With a Common Mean

Recently C. R. Rao (1984) suggested two modifications to the MINQUE, called MINQUE(S.D.) and MINQUE(C.P.), for estimating the variance components in a linear model. These modifications provide non-negative estimates unlike the MINQUE. In this article we shall compare the performance of these two estimators with some of the other existing modifications of MINQUE in terms of standard criteria such as the mean squared error and total squared bias.     

Designs Robust Against the Presence of an Aberration in a Diallel Cross Design Setup

In this article, we find designs insensitive to the presence of an outlier in a diallel cross design setup for estimating a complete set of orthonormal contrasts among the effects of the general combining abilities of a set of parental lines. The criterion of robustness, suggested by Mandal (1989 Mandal , N. K. ( 1989 ). On robust designs . Cal. Stat. Assoc. Bull. 38 : 115 – 119 . [Google Scholar]) in block design setup and used by Biswas (2012 Biswas , A. ( 2012 ). Block designs robust against the presence of an aberration in a treatment-control setup . Commun. Statist. Theor. Meth. 41 : 920 – 933 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in treatment-control setup, is adapted here. Complete diallel cross designs, suggested by Gupta and Kageyama (1994 Gupta , S. , Kageyama , S. ( 1994 ). Optimal complete diallel crosses . Biometrika 81 : 420 – 424 .[Crossref], [Web of Science ®] , [Google Scholar]), and partial diallel cross designs, suggested by Gupta et al. (1995 Gupta , S. , Das , A. , Kageyama , S. ( 1995 ). Single replicate orthogonal block designs for circulant partial diallel crosses . Commun. Statist. A 24 : 2601 – 2607 .[Taylor & Francis Online] , [Google Scholar]) and Mukerjee (1997 Mukerjee , R. ( 1997 ). Optimal partial diallel crosses . Biometrika 84 : 939 – 948 .[Crossref], [Web of Science ®] , [Google Scholar]), are found to be robust under certain conditions.     

Optimum covariate designs in split-plot and strip-plot design set-ups

The problem considered is that of finding optimum covariate designs for estimation of covariate parameters in standard split-plot and strip-plot design set-ups with the levels of the whole-plot factor in r randomised blocks. Also an extended version of a mixed orthogonal array has been introduced, which is used to construct such optimum covariate designs. Hadamard matrices, as usual, play the key role for such construction.     

Bias correction in logistic regression with missing categorical covariates

Logistic regression plays an important role in many fields. In practice, we often encounter missing covariates in different applied sectors, particularly in biomedical sciences. Ibrahim (1990) proposed a method to handle missing covariates in generalized linear model (GLM) setup. It is well known that logistic regression estimates using small or medium sized missing data are biased. Considering the missing data that are missing at random, in this paper we have reduced the bias by two methods; first we have derived a closed form bias expression using Cox and Snell (1968), and second we have used likelihood based modification similar to Firth (1993). Here we have analytically shown that the Firth type likelihood modification in Ibrahim led to the second order bias reduction. The proposed methods are simple to apply on an existing method, need no analytical work, with the exception of a little change in the optimization function. We have carried out extensive simulation studies comparing the methods, and our simulation results are also supported by a real world data.