MAKE MOST OF THE KNOWLEDGE NETWORK, JOIN ACADEMIC RESEARCH FOUNDATION

We study the consistency of the semi-parametric maximum likelihood estimator (SMLE) of the Lehmann family (Lehmann (1959)) with rightcensored data. The Lehmann family is a class of survival functions of the form (So(t))exp(x0b), where So(
) is a survival function and x is a pdimensional vector. It is the same as Cox’s regression model iff So is absolutely continuous. The Lehmann family and Cox’s model are both popular semi-parametric regression models in survival analysis. Consistency proofs of an estimator under various semi-parametric set-ups are often based on additional regularity conditions. We establish the consistency of the SMLE of the Lehmann family without any additional assumption.

JEL Codes: N01 and G08

Keywords: Lehmann family, Cox’s model, Semi-parametric Maximum likelihood estimator, consistency, Kullback-Leibler Inequality.

Mortality projection is a pivotal topic in the diverse branches related to insurance, demography, and public policy. Motivated by the thread of Lee-Carter related models, we propose a Bayesian model to estimate and predict mortality rates for multi-population. This new model features in information borrowing among populations and properly reflecting variations of data. It also provides a solution to a long-time overlooked problem: model selection for dependence structures of population-specific time parameters. By introducing a novel dirac spike function that hierarchically follows the conditional autoregressive model via the probit link, simultaneous model selection and estimation for population-specific time effects can be achieved without much extra computational cost. Additionally, this selection procedure can leverage spatial information to inform about the geographic proximity in adjacent areas. Via the Brook’s lemma and data augmentation steps, a computationally efficient MCMC sampling algorithm is also developed. We use the Japanese mortality data sets from Human Mortality Database to illustrate the desirable properties of our model.

An efficient design that can analyze high dimensional simulation model by using fewer runs as compared with other second-order designs is needed in a complex system. In this paper, a new class of designs called spacefilling orthogonal-array based composite designs was proposed using the centered l2-discrepancy and maximin distance. The proposed designs were constructed and compared with other existing composite designs such as orthogonal-array based composite designs, centered composite designs and small composite designs based on relative D-efficiency and Ds-optimality criterion for full model, linear, quadratic and bilinear terms respectively. The results from the comparison show that the space-filling orthogonal-array based composite designs are better in terms of efficiency and run sizes for some cases especially as the number of factors increases.

Influential observations in data (both multivariate and univariate) can alter the estimates of the regression coefficients subjectively such that the underlying statistical relationships particularly in a least square estimation are rendered meaningless. Our objective is to examine the effects of extreme influential observations on model coefficients by comparing the classical OLS estimators with the more robust least square of maximum likelihood-like plus scale estimators such as MM-estimators. In order to achieve this set objective, the authors postulated an exchange rate regression model in the presence of extreme influential observations. Four major macroeconomic variables were included in the study as regressors. These regressors comprise foreign external reserve, foreign direct investment inflow, crude oil price and credit to private sector. The analysis showed that the standard errors and p-values of the model coefficients for the robust least square are smaller than the classical OLS method largely due to detection and handling of the influential observations. Furthermore, the forecast values from the robust MM-estimation indicate that the model slightly provide more precise estimates than the OLS.

In many cases, parameter estimation results in limiting normality. This allows for approximate confidence intervals and significance tests. Often, one wishes to bound the length of confidence intervals and to guarantee a certain power for tests. These issues depend on the sam-ple size: How large does it have to be? We provide simple formulae answering this question. Numerical examples show that reasonably reliable inference requires in some cases rather large samples.

This paper reviewed many papers and provided more than 100 different available estimators for estimating the ridge or shrinkage parameter k for the Gaussian linear regression model. These estimators may be used for generalized linear regression models, namely, Poisson regression, Logistic regression, Beta regression, Gamma regression, zero inflated Poisson regression, negative binomial (NB) regression, zero inflated NB, Bell regression and inverse Gaussian regression models among others. It is expected that this paper will bring a lot of attention among the researchers and will be used as a reference paper in the area of ridge regression, which is mainly used to solve the multicollinearity problems.

Keywords: Generalized Linear Regression; Linear Regression; OLS; MSE; Multicollinearity; Ridge Regression; Shrinkage parameters.

In this paper, it is argued that for the detection of a stochastic trend in a time series it is advisable to use the detrended series rather than the original series or the differenced series. While the examination of the original series is clearly impaired by the possible presence of a deterministic trend and dealing with the differenced series comes along with an increased variability, trend removal is a data dependent transformation and is prone to overfitting. However, it is shown that the latter disadvantage can be overcome by simply omitting the lowest Fourier frequency when the analysis is carried out in the frequency domain. This issue is illustrated using climatological, macroeconomic and financial time series. The results of an extensive simulation corroborate the usefulness of this approach for different sample sizes and different types of long-term dependence and short-term dependence.     

Saha and Ghosh (2013) (The Quarterly Review of Historical Studies, LIII (1&2):30-44) extensively studied the history of migration of both the districts of Jalpaiguri and Darjeeling in North Bengal during the colonial and post-colonial periods from 1869 to 1971.  Human migration is a fundamental social science research problem that is an interdisciplinary research topic. Researchers from different branches such as Demography, Mathematics, Statistics, Social Studies and History are currently working on migration history.  History of migration always searches for the basic five problems such as who changes places, when do they change of place, what are the social/political/historical events related with the change of place, why do they change of place, what are the social impacts when they settle there. The present article focuses a comparative study of migration history of both the districts of Jalpaiguri and Darjeeling based on the above basic migration problems, using census data, and adopting parametric gamma model and non-parametric cubic spline method.  It is derived herein that both the mean and variance trend equations are different for two districts.  In addition, all the above basic five migration problems are different in both the districts even though both the districts are located adjacent to each other.