Second-Order Approximations to Two Classes of Sequential Estimation Procedures

For the model considered by Chaturvedi, Pandey and Gupta (1991), two classes of sequential procedures are developed to construct confidence regions (which may be interval, ellipsoidal or spherical) of ‘pre-assigned width and coverage probability’ for the parameters of interest and for the minimum risk point estimation (taking loss to be quadratic plus linear cost of sampling) of the nuisance parameter. Second-Order approximations are derived for the expected sample size, coverage probability and ‘regret’ associated with the two classes of sequential procedures. A simple and direct method of obtaining the asymptotic distribution of the stopping time is provided. By means of examples, it is illustrated that several estimation problems can be tackled with the help of proposed classes of sequential procedures.     

Weighted bivariate logarithmic series distributions

In this paper, we are interested in the weighted distributions of a bivariate three parameter logarithmic series distribution studied by Kocherlakota and Kocherlakota (1990). The weighted versions of the model are derived with weight W(x,y) = x^[r] y^[s]. Explicit expressions for the probability mass function and probability generating functions are derived in the case r = s = l. The marginal and conditional distributions are derived in the general case. The maximum likelihood estimation of the parameters, in both two parameter and three parameter cases, is studied. A procedure for computer generation of bivariate data from a discrete distribution is described. This enables us to present two examples, in order to illustrate the methods developed, for finding the maximum likelihood estimates.     

Elliptically contoured model and factorization of wllks1 A

In a series of papers, Kshirsagar (1964, 1971) and McHenry and Kshirsagar (1977), factorize Wilks' A into a number of factors and find the independent null multivariate beta densities of these factors. These factors are the likelihood ratio test criteria for testing the goodness of fit of certain assigned discriminant functions or canonical variables either in the space of independent or dependent variables. Essentially the factors of Wilks' A are the factors of certain multivariate beta distributed matrix or its determinant. The Bartlett decomposition of the underlying multivariate beta distribution into independent factors determines the distribution of these factors. The present paper generalizes Kshirsagar's (1971) normal theory to the elliptically contoured model, and shows that his results are null robust for the elliptically contoured model.     

THE U.S. PRODUCTIVITY SLOWDOWN: A PEAK THROUGH THE STRUCTURAL BREAK WINDOW

This paper provides a formal test of the null hypothesis of a unit root in the log-level of labor productivity against the alternative of linear trend stationarity with a one-time structural break in the level and slope of the trend at an a priori unknown date. Using some newly developed time series tests, we show that the log-level of productivity is more accurately modeled as following a deterministic trend with a regime shift rather than as a unit root process. Some implications of the results for detrending and for testing cointegration relationships between productivity and other variables are discussed. ( JEL C22. O40)     

Habitat selection by an avian top predator in the tropical megacity of Delhi: human activities and socio-religious practices as prey-facilitating tools

Research in urban ecology is growing rapidly in response to the exponential growth of the urban environment. However, few studies have focused on tropical megacities, and on the interplay between predators’ habitat selection and human socio-economic aspects, which may mediate their resilience and coexistence with humans. We examined mechanisms of breeding habitat selection by a synanthropic raptor, the Black Kite Milvus migrans, in Delhi (India) where kites mainly subsist on: (1) human refuse and its associated prey-fauna, and (2) ritualised feeding of kites, particularly practised by Muslims. We used mixed effects models to test the effect of urban habitat configuration and human practices on habitat selection, site occupancy and breeding success. Kite habitat decisions, territory occupancy and breeding success were tightly enmeshed with human activities: kites preferred areas with high human density, poor waste management and a road configuration that facilitated better access to resources provided by humans, in particular to Muslim colonies that provided ritual subsidies. Furthermore, kites bred at ‘clean’ sites with less human refuse only when close to Muslim colonies, suggesting that the proximity to ritual-feeding sites modulated the suitability of other habitats. Rather than a nuisance to avoid, as previously portrayed, humans were a keenly-targeted foraging resource, which tied a predator’s distribution to human activities, politics, history, socio-economics and urban planning at multiple spatio-temporal scales. Many synurbic species may exploit humans in more subtle and direct ways than was previously assumed, but uncovering them will require greater integration of human socio-cultural estimates in urban ecological research.

     

A new approach to statistical efficiency of weighted least squares fitting algorithms for reparameterization of nonlinear regression models

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao-Cramer lower bound) in the limit of small noise.     

The Kumaraswamy skew-t distribution and its related properties

Skew normal distribution is an alternative distribution to the normal distribution to accommodate asymmetry. Since then extensive studies have been done on applying Azzalini’s skewness mechanism to other well-known distributions, such as skew-t distribution, which is more flexible and can better accommodate long tailed data than the skew normal one. The Kumaraswamy generalized distribution (Kw ? F) is another new class of distribution which is capable of fitting skewed data that can not be fitted well by existing distributions. Such a distribution has been widely studied and various versions of generalization of this distribution family have been introduced. In this article, we introduce a new generalization of the skew-t distribution based on the Kumaraswamy generalized distribution. The new class of distribution, which we call the Kumaraswamy skew-t (KwST) has the ability of fitting skewed, long, and heavy-tailed data and is more flexible than the skew-t distribution as it contains the skew-t distribution as a special case. Related properties of this distribution family such as mathematical properties, moments, and order statistics are discussed. The proposed distribution is applied to a real dataset to illustrate the estimation procedure.