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.     

Uncertainty Analysis Based on Probability Bounds (P-Box) Approach in Probabilistic Safety Assessment

A wide range of uncertainties will be introduced inevitably during the process of performing a safety assessment of engineering systems. The impact of all these uncertainties must be addressed if the analysis is to serve as a tool in the decision-making process. Uncertainties present in the components (input parameters of model or basic events) of model output are propagated to quantify its impact in the final results. There are several methods available in the literature, namely, method of moments, discrete probability analysis, Monte Carlo simulation, fuzzy arithmetic, and Dempster-Shafer theory. All the methods are different in terms of characterizing at the component level and also in propagating to the system level. All these methods have different desirable and undesirable features, making them more or less useful in different situations. In the probabilistic framework, which is most widely used, probability distribution is used to characterize uncertainty. However, in situations in which one cannot specify (1) parameter values for input distributions, (2) precise probability distributions (shape), and (3) dependencies between input parameters, these methods have limitations and are found to be not effective. In order to address some of these limitations, the article presents uncertainty analysis in the context of level-1 probabilistic safety assessment (PSA) based on a probability bounds (PB) approach. PB analysis combines probability theory and interval arithmetic to produce probability boxes (p-boxes), structures that allow the comprehensive propagation through calculation in a rigorous way. A practical case study is also carried out with the developed code based on the PB approach and compared with the two-phase Monte Carlo simulation results.     

Urban Aboriginal use of fringe financial institutions: Survey evidence from Prince George, British Columbia

This paper analyses the use of fringe financial institutions (FFIs), such as payday loan and check cashing providers, by urban Aboriginal people based on a survey undertaken in Prince George, British Columbia. We found that 60% of FFIs’ clients surveyed self-identified as Aboriginal. Their characteristics, compared to the non-Aboriginal FFI clients, included having lower average incomes, lower levels of education, more likely to be female, a higher incidence of being unemployed, higher levels of financial exclusion, and less satisfaction with the service provided by FFIs. We find that government policy towards regulating the FFI industry is inadequate for meeting the basic financial needs of urban Aboriginal people.     

Pension reform, the stock market, capital formation and economic growth: A critical commentary on the World Bank's proposals

Proposing far-reaching reforms to pension systems, the World Bank has recently suggested that the existing pay-as-you-go systems in many rich as well as poor countries should be replaced by fully funded, mandatory, preferably private pensions, as the main pillars of the new system. It argues that these reforms will not only benefit pensioners but also enhance savings, and promote capital formation and economic development. This paper provides a critical examination of the Bank's theses and concludes that it has adopted a one-sided view of the relationships between the key critical variables. The proposed reform may therefore neither protect the old nor achieve faster economic growth.     

Multi-stage estimation of the common location parameter of several exponential distributions

The problem of constructing a confidence interval of ‘preassigned width and coverage probability’ considered by Costanza/ Hamdy and Son(1986) is further analyzed. Several multi-stage estimation procedures [ like, purely sequential, accelerated sequential and three-stage procedures ] are utilized to deal with the same estimation problem. The relative advantages and disadvantages of these procedures are discussed.     

Household wealth and the measurement of economic well-being in the United States

We analyze the level and distribution of economic well-being in the United States during the 1980s and 1990s based on the standard measure of money income and a measure in which income from wealth is calculated as the sum of lifetime annuity from nonhome wealth and imputed rental-equivalent for owner-occupied homes. Over the 1982–2000 period, median well-being increases faster when these adjustments are made than when standard money income is used. This adjustment also widens the income gap between African-Americans and whites but increases the relative well-being of the elderly. Adding imputed rent and annuities from household wealth to household income considerably increases measured inequality and the share of income from wealth in inequality. However, both measures show about the same rise in inequality over the period. We also find an increasing share of wage and salary income in our expanded definition of income among the richest 1% over the period but do not find that the “working rich” have largely replaced rentiers at the top of the economic ladder.      

A Two-stage minimax procedure with screening for selecting the largest normal mean

The problem of selecting the normal population with the largest population mean when the populations have a common known variance is considered. A two-stage procedure is proposed which guarantees the same probability requirement using the indifference-zone approach as does the single-stage procedure of Bechhofer (1954). The two-stage procedure has the highly desirable property that the expected total number of observations required by the procedure is always less than the total number of observations required by the corresponding single-stage procedure, regardless of the configuration of the population means. The saving in expected total number of observations can be substantial, particularly when the configuration of the population means is favorable to the experimenter. The saving is accomplished by screening out “non-contending” populations in the first stage, and concentrating sampling only on “contending” populations in the second stage.

The two-stage procedure can be regarded as a composite one which uses a screening subset-type approach (Gupta (1956), (1965)) in the first stage, and an indifference-zone approach (Bechhofer (1954)) applied to all populations retained in the selected sub-set in the second stage. Constants to implement the procedure for various k and P? are provided, as are calculations giving the saving in expected total sample size if the two-stage procedure is used in place of the corresponding single-stage procedure.