Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.     

The Determinants of Lottery Sales in Portugal

In sum, this paper examines the core determinants of lottery sales in Portugal. With panel data analysis covering 18 Portuguese districts and 5 years, this study explains the variations in a district’s per-capita lottery sales in terms of key theoretical hypotheses such as per capita district income, age, education index, gender and religion. This paper concludes that the richer Portuguese districts spend more than the poorer districts and there is an inverted-U relationship between lottery sales and per capita income. The paper also concludes that married Catholic citizens spend more on lottery products than others and that the level of education returns a negative effect on lottery spending.     

On Optimal Estimating Functions in the Presence of Nuisance Parameters

When there is only one interesting parameter θ₁ and one nuisance parameter θ₂, Godambe and Thompson (1974 Godambe , V. P. , Thompson , M. E. ( 1974 ). Estimating equations in the presence of a nuisance parameter . Ann. Statist. 2 : 568 – 571 .[Crossref], [Web of Science ®] , [Google Scholar]) showed that the optimal estimating function for θ₁ essentially is a linear function of the θ₁-score, the square of the θ₂-score, and the derivative of θ₂-score with respect to θ₂. Mukhopadhyay (2000b) generalized this result to m nuisance parameters. Mukhopadhyay (2000 Mukhopadhyay , P. ( 2000 ). On some lower bounds for the variance of an estimating function . Int. J. Math. Statist. Sci. 9 ( 2 ). [Google Scholar] 2002a Mukhopadhyay , P. ( 2002a ). On estimating functions in the presence of a nuisance parameter . Commun. Statist. Theor. Mem. 31 ( 1 ): 31 – 36 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar] b Mukhopadhyay , P. ( 2002b ): Some lower bounds on variance of estimating functions . J. Statist. Res. 36 ( 2 ): 189 – 197 . [Google Scholar]) obtained lower bounds to the variance of regular estimating functions in the presence of nuisance parameters. Taking cues from these results we propose a method of finding optimal estimating function for θ₁ by taking the multiple regression equation on θ₁ score and Bhattacharyya's (1946 Bhattacharyya , A. ( 1946 ). On some analogues of the amount of information and their use in statistical estimation . Sankhya A 8 : 1 – 14 . [Google Scholar]) scores with respect to θ₂. The result is extended to the case of m nuisance parameters.     

Renaissance of a rural artifact in a city with a million people: biodiversity responses to an agro-forestry restoration in a large urban traditional fruit orchard

The rural landscapes surrounding large cities are rapidly becoming incorporated into the urban environment. The most conspicuous changes involve green spaces, such as former agro-forestry systems like fruit orchards. In this paper, we assess the influence on biodiversity of restoring a large urban traditional fruit orchard as reflected by six selected taxa: plants, lichens, butterflies, beetles, orthopteroids and birds. The study was performed in Prague, which is the capital city of the Czech Republic and has more than a million inhabitants. We studied the effect of orchard renewal in 45 patches (15 for birds and 30 for other taxa). The majority of taxa responded positively to the restoration. The restoration had a significant positive effect on the species richness of lichens, butterflies and beetles. All taxa showed significantly altered species compositions, and the number of red-listed species increased. Orchards have a high potential for multi-functional use. Orchards are productive agro-forestry systems and host numerous possible human activities. Therefore, orchard restoration also has a social aspect. Moreover, our research in this artificial ecosystem revealed that its restoration increased the biodiversity and conservation potential of the associated areas.

     

Factors Influencing Family Business Continuity in Indian Small and Medium Enterprises (SMEs)

Most of the research on family business continuity is based in the western world. Continuity of family business is affected by social and cultural factors on one hand and on the stage of growth of the economy on the other. This paper focuses on the continuity concerns with reference to (1) the Eastern context and (2) the developing economy’s context, by studying Indian family businesses, with (3) specific focus on Small and Medium Enterprises (SMEs). Data were collected from SME business families using a questionnaire. The impact of various factors was examined on the family, the business and the inductee. This empirical study validates some of the drivers of effective succession identified so far in the literature. It sharply identifies the variables that can be more relevant and can directly affect the outcome in terms of positive impact on the business, family and the inductee. The findings of the study will be of great help in successful succession planning for the growth and development of SMEs that contribute significantly to economic growth.     

Suitability of biodiversity-area and biodiversity-perimeter relationships in ecology: a case study of urban ecosystems

Urban areas are probably the most fragmented environments with respect to the presence of semi-natural habitats and shape of these habitats may be significantly affected by urbanization. Patch perimeter in landscape or habitat studies is much less popular to study than patch area. The studied sites were situated in the industrial city of Pardubice, which is one of the ten largest cities in the Czech Republic with nearly 100,000 inhabitants. In total, 40 grasslands were studied within a circular area of 314 km². Butterflies and beetles with diurnal activity were studied during timed survey walks. A Simultaneous autoregressive model was used for test of the effect of biodiversity-area and biodiversity-perimeter relationships and for exclusion of potential bias caused by spatial autocorrelation. The models including patch perimeter performed better than those using patch area in explaining species richness, abundance and diversity of investigated organisms and were less influenced by spatial autocorrelation. The main conclusion and recommendation of the present study is that researchers should pay more attention to the possible influence of the patch perimeter as a potential predictor or co-predictor for landscape and habitat studies – especially in urban areas, where the negative effects of fragmentation might be much higher than in rural or more natural landscapes. Performing preliminary tests on comparisons between area and perimeter is highly recommended.     

Note on umvsu-estimation under randomized response model

Considering a class ofs randomized response trials for eliciting sensitive information from a sample survey and a class of ordered sampling designs, a uniformly minimum variance unbiased estimator of population variance (of the sensitive character) has been obtained. This note indicates that a theorem (theorem 3.9) of Cassel, Sarndal and Wretman (1977) and the results in the present note can be extended to estimation of any symmetric function of population values in the field of direct response surveys and randomized response surveys respectively.     

SAVE: Robust or not?

Abstract

Sliced average variance estimation (SAVE) is one of the best methods for estimating central dimension-reduction subspace in semi parametric regression models when covariates are normal. In recent days SAVE is being used to analyze DNA microarray data especially in tumor classification but most important drawback is normality of covariates. In this article, the asymptotic behavior of estimates of CDR space under varying slice size is studied through simulation studies when covariates are non normal but follows linearity condition as well as when covariates slightly perturbed from normal distribution and we observed that serious error may occur under violation normality assumption.     

Committee Decisions with Partisans and Side-Transfers

A dichotomous decision-making context in committees is considered where potential partisan members with predetermined votes can generate inefficient decisions and buy neutral votes. The optimal voting rule minimizing the expected costs of inefficient decisions for the case of a three-member committee is analyzed. It is shown that the optimal voting rule can be non-monotonic with respect to side-transfers: in the symmetric case, majority voting is optimal under either zero, mild or full side-transfer possibilities, whereas unanimity voting may be optimal under an intermediate side-transfer possibility. The side-transfer possibilities depend on the power of partisans (their ability or willingness to pay for neutral votes) relative to the corruptibility of neutral members (personal cost of deliberately casting a `wrong' vote).