Mean squared error of empirical predictor

The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases

Decentralised bilateral trading in a market with incomplete information

types: ArticleDiscussion paperWe study a model of decentralised bilateral interactions in a small market where one of the sellers has private information about her value. There are two identical buyers and another seller, whose valuation is commonly known to be in between the two possible valuations of the informed seller. We consider two in nite horizon games, with public and private simultaneous one-sided o¤ers respectively and simultaneous responses. We show that there is a stationary perfect Bayes equilibrium for both models such that prices in all transactions converge to the same value as the discount factor goes to 1

Inferences for Joint Modelling of Repeated Ordinal Scores and Time to Event Data

In clinical trials and other follow-up studies, it is natural that a response variable is repeatedly measured during follow-up and the occurrence of some key event is also monitored. There has been a considerable study on the joint modelling these measures together with information on covariates. But most of the studies are related to continuous outcomes. In many situations instead of observing continuous outcomes, repeated ordinal outcomes are recorded over time. The joint modelling of such serial outcomes and the time to event data then becomes a bit complicated. In this article we have attempted to analyse such models through a latent variable model. In view of the longitudinal variation on the ordinal outcome measure, it is desirable to account for the dependence between ordered categorical responses and survival time for different causes due to unobserved factors. A flexible Monte Carlo EM (MCEM) method based on exact likelihood is proposed that can simultaneously handle the longitudinal ordinal data and also the censored time to event data. A computationally more efficient MCEM method based on approximation of the likelihood is also proposed. The method is applied to a number of ordinal scores and survival data from trials of a treatment for children suffering from Duchenne Muscular Dystrophy. Finally, a simulation study is conducted to examine the finite sample properties of the proposed estimators in the joint model under two different methods

Caste in/as Humanities:: Unsettling the Politics of Suffering

  From the time of early travel narratives on South Asia by western tradesmen, orientalist scholars like William Jones, Max Muller, narratives written by Christian missionaries like Mead or Caldwell or the denigrators of ‘oriental societies’ like G.W. F. Hegel and concerned critics like Karl Marx to much of our postcolonial socio-political struggles, ‘caste’ has been perceived as either an elusive, resilient hydra-headed monster or a unique feature of the Hindu society that pre-empts competition that western modernity brings about. However, caste could be read both diachronically as well as synchronically, as a historical formation as well as a structural imperative. This makes any easy understanding of the question of caste impossible. Textual evidences are not enough, neither are the various archaeological resources, as we know that each historical moment is also constituted by the logic of synchronicity and structure which produces its own form of aphasia and silence. This introduction to the Special Issue of Sanglap on ‘Caste in Humanities’ would show how question of caste is also about silence and therefore requires incessant and seamless re-textualization

Likelihood-based missing data analysis in multivariate crossover trials

For gene expression data measured in a crossover trial, a multivariate mixed-effects model seems to be most appropriate. Standard statistical inference fails to provide reliable results when some responses are missing. Particularly for crossover studies, missingness is a serious concern as the trial requires a small number of participants. A Monte Carlo EM (MCEM) based technique has been adopted to deal with this situation. Along with estimation, a MCEM likelihood ratio test (LRTs) is developed for testing the fixed effects in such a multivariate crossover model with missing data. Intensive simulation studies have been carried out prior to the analysis of the gene expression data

Improved Rejection Penalty Algorithm with Multiprocessor Rejection Technique

This paper deals with multiprocessor scheduling with rejection technique where each job is provided with processing time and a given penalty cost. If the job satisfies the acceptance condition, it will schedule in the least loaded identical parallel machine else job is rejected. In this way its penalty cost is calculated. Our objective is to minimize the makespan of the scheduled job and to minimize the sum of the penalties of rejected jobs. We have merged ‘CHOOSE ‘and ‘REJECTION PENALTY’ algorithm to reduce the sum of penalties cost and makespan. Our proposed ‘Improved Reject penalty algorithm’ reduce competitive ratio, which in turn enhances the efficiency of the on-line algorithm. By applying our new on-line technique, we got the lower bound of our algorithm is is 1.286 which is far better from the existing algorithms whose competitive ratio is at 1.819. In our approach we have consider non-preemption scheduling technique