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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.

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.