A model of the Canadian global exchange rate: A test of the 1970s

This comment points out some methodological weaknesses in the Canadian global exchange rate model and the associated efficiency tests of Marwah and Bodkin. The model is found to be inadequate for policy analysis.     

Kernel naive Bayes discrimination for high‐dimensional pattern recognition

Kernel discriminant analysis translates the original classification problem into feature space and solves the problem with dimension and sample size interchanged. In high‐dimension low sample size (HDLSS) settings, this reduces the ‘dimension’ to that of the sample size. For HDLSS two‐class problems we modify Mika's kernel Fisher discriminant function which – in general – remains ill‐posed even in a kernel setting; see Mika et al. (1999). We propose a kernel naive Bayes discriminant function and its smoothed version, using first‐ and second‐degree polynomial kernels. For fixed sample size and increasing dimension, we present asymptotic expressions for the kernel discriminant functions, discriminant directions and for the error probability of our kernel discriminant functions. The theoretical calculations are complemented by simulations which show the convergence of the estimators to the population quantities as the dimension grows. We illustrate the performance of the new discriminant rules, which are easy to implement, on real HDLSS data. For such data, our results clearly demonstrate the superior performance of the new discriminant rules, and especially their smoothed versions, over Mika's kernel Fisher version, and typically also over the commonly used naive Bayes discriminant rule.     

High dimensional asymptotics for the naive Hotelling T2 statistic in pattern recognition

Abstract

This paper examines the high dimensional asymptotics of the naive Hotelling T² statistic. Naive Bayes has been utilized in high dimensional pattern recognition as a method to avoid singularities in the estimated covariance matrix. The naive Hotelling T² statistic, which is equivalent to the estimator of the naive canonical correlation, is a statistically important quantity in naive Bayes and its high dimensional behavior has been studied under several conditions. In this paper, asymptotic normality of the naive Hotelling T² statistic under a high dimension low sample size setting is developed using the central limit theorem of a martingale difference sequence.     

Tibetans in South Asia: a research note

The research note provides an overview of Tibetan refugee settlements in South Asia, viz. in India, Nepal and Bhutan. The note focuses on the residential status of Tibetans and their life and livelihood. Tibetan refugees are viewed as representatives of Tibetan culture and religion in these countries.     

Promissory Capital: State Legitimacy among Women Community Health Workers in India

Qualitative Sociology - Despite public sector working conditions that are increasingly precarious, how does the state manage to attract and retain its workers? I draw on 14 months of ethnographic...     

Asymptotics for penalised splines in generalised additive models

This paper discusses asymptotic theory for penalised spline estimators in generalised additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the ridge-corrected penalised spline estimator. Furthermore, the asymptotics for the penalised quasi-likelihood fit in mixed models are also discussed.     

Asymptotic theory for local estimators based on Bregman divergence

This article is concerned with asymptotic theory for local estimators based on Bregman divergence. We consider a localized version of Bregman divergence induced by a kernel weight and minimize it to obtain the local estimator. We provide a rigorous proof for the asymptotic consistency of the local estimator in a situation where both the sample size and the bandwidth involved in the kernel weight increase. Asymptotic normality of the local estimator is also developed under the same asymptotic scenario. Monte Carlo simulations are also performed to confirm the theoretical results. The Canadian Journal of Statistics 47: 628–652; 2019 © 2019 Statistical Society of Canada     

A model of the Canadian global exchange rate: A test of the 1970s

A review of the literature indicates that no single exchange rate model has been able to track successfully the movements of the Canadian dollar for both the 1970–1976 period and the period thereafter. The purchasing power parity model, irrespective of whether based on relative wholesale prices, unit labor costs, GNP deflators, or export prices performs very poorly; the monetarist models collapse because of their strict adherence to the purchasing power parity and interest rate parity assumptions; the portfolio demand models require a significant adjustment for the post-1976 period. This paper presents a medium-term eclectic model of the global exchange rate of the Canadian dollar and examines a spectrum of broad issues that reflect on the efficiency of the foreign exchange market of Canada. These issues are basically related to the interest parity assumption, the role of speculation, and the test of rational expectations. The global exchange rate is defined as the value of the Canadian dollar measured in terms of a unit of basket of currencies comprising currencies of France, West Germany, Japan, the U.K., and the USA. The model belongs to the same genre of balance of payments structural models that explain the exchange rates by balancing demand and supply of foreign currencies. The model simultaneously explains both spot and forward rates, and it has been estimated and tested by using the quarterly data for 1971–1981.     

Estimating the common hazard rate of several exponential distributions

Abstract

In the present communication, we consider the estimation of the common hazard rate of several exponential distributions with unknown and unequal location parameters with a common scale parameter under a general class of bowl-shaped scale invariant loss functions. We have shown that the best affine equivariant estimator (BAEE) is inadmissible by deriving a non smooth improved estimator. Further, we have obtained a smooth estimator which improves upon the BAEE. As an application, we have obtained explicit expressions of improved estimators for special loss functions. Finally, a simulation study is carried out for numerically comparing the risk performance of various estimators.