On the joint distribution of placement statistics under progressive censoring and applications to precedence test

In reliability and survival analysis, comparison of two or more populations is an important problem. For example, while comparing a treatment group with a control group, one may be interested in determining whether the observations in the treatment group have a longer lifetime than those from the control group, that is, whether the treatment is effective or not. In such a study, it would be extremely valuable to make a decision based on early failures. In this paper, we consider independent progressively Type-II censored random samples from two populations with cumulative distribution function's (cdf) F(·)$F(·)$ and G(·)$G(·)$ respectively, and discuss a precedence test for testing the equality of the two distributions based on placements. For this purpose, we derive the joint distribution of the first l   placement statistics from the progressively censored sample from F(·)$F(·)$. We then derive the exact null distribution of the precedence test statistic which is simply the sum of the placements. We provide the rejection regions for fixed levels of significance and various sample sizes and different progressive censoring schemes.     

The asymptotic distribution of numbers of observations near order statistics

In this paper, we discuss the limiting behavior of numbers of observations near an order statistic. We then derive an expression for the joint distribution of the numbers of observations that fall into the open right a-vicinity and left b-vicinity of k  th and (n-r)$(n-r)$th order statistics, respectively, from a sample of size n and establish the result that they are asymptotically independent under suitable conditions.     

Estimation of the exponential mean time to failure under a weighted balanced loss function

This paper considers estimation of a exponential mean time to failure using a loss function that reflects both goodness of fit and precision of estimation. The admissibility and inadmissibility of a class of linear estimators of the form are studied.     

Estimating the grid of time-points for the piecewise exponential model

One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.     

Modeling interest rate cycles in India

The present study tries to examine the behaviour of various Indian interest rates such as call money rate, and yields on secondary market securities with maturity periods of 15–91 days, 1-year, 5-years and 10-years. In the first stage, the study investigates the determinants of interest rates and finds that although the interest rates depend on some domestic macroeconomic variables such as yield spread and expected exchange rate, they are mainly affected by the movements of international interest rates, although with some lags. The policy variables such as Bank Rate and Federal Funds Rate did not show any significant impact on any of the interest rates. Further, it was found that the interest rates in the very recent period show some cyclical movements similar to that of the developed countries. Future behaviour of interest rates show that the present cycle of each interest rate would peak at different time points. This expected behaviour in domestic interest rates could be due to the integration of the domestic economy with the international money and financial market. This trend may be same in most of the emerging economies of Asia.     

HOW LARGE ARE SEARCH FRICTIONS?

This paper shows that we can normalize job and worker characteristics so that, without frictions, there exists a linear relationship between wages on the one hand and worker and job type indices on the other. However, for five European countries and the United States we find strong evidence for a systematic concave relationship. An assignment model with search frictions provides a parsimonious explanation for our findings. This model yields two restrictions on the coefficients that fit the data well. Allowing for unobserved heterogeneity and measurement error, we find that reservation wages are 25% lower than they would be in a frictionless world. Our results relate to the literature on industry wage differentials and on structural identification in hedonic models. (JEL: J210, J300, J600, J230)     

Tests for assessment of agreement using probability criteria

For the assessment of agreement using probability criteria, we obtain an exact test, and for sample sizes exceeding 30, we give a bootstrap-t$t$ test that is remarkably accurate. We show that for assessing agreement, the total deviation index approach of Lin [2000. Total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence. Statist. Med. 19, 255–270] is not consistent and may not preserve its asymptotic nominal level, and that the coverage probability approach of Lin et al. [2002. Statistical methods in assessing agreement: models, issues and tools. J. Amer. Statist. Assoc. 97, 257–270] is overly conservative for moderate sample sizes. We also show that the nearly unbiased test of Wang and Hwang [2001. A nearly unbiased test for individual bioequivalence problems using probability criteria. J. Statist. Plann. Inference 99, 41–58] may be liberal for large sample sizes, and suggest a minor modification that gives numerically equivalent approximation to the exact test for sample sizes 30 or less. We present a simple and accurate sample size formula for planning studies on assessing agreement, and illustrate our methodology with a real data set from the literature.     

DIALOGUES OF THE NATIONS: Revisiting Visions and Its Critics

Critics of Visions in this symposium raise three general questions. The question of inclusiveness is addressed by linking pertinent criteria to the book's aims; that of justifying national traditions by reviewing pertinent evidence; and that of the viability of dialogue by arguing that responsive communication does not entail full agreement. A number of particular issues the critics raise are addressed by the book's arguments regarding the relation of the discipline of sociology to its philosophical background, the international setting of early sociology, Durkheim's individualism, Weber's distinction between naturalism and interpretability, Marx's treatment of Feuerbach and of nationalism, and the relation between power and knowledge. This response concludes by explicating the proposal that the time may be ripe to rejoin a number of the elements of Aristotelian social science that had been delegated to various national traditions of social theory in the modern era.     

Designing and integrating composite networks for monitoring multivariate gaussian pollution fields

Networks of ambient monitoring stations are used to monitor environmental pollution fields such as those for acid rain and air pollution. Such stations provide regular measurements of pollutant concentrations. The networks are established for a variety of purposes at various times so often several stations measuring different subsets of pollutant concentrations can be found in compact geographical regions. The problem of statistically combining these disparate information sources into a single 'network' then arises. Capitalizing on the efficiencies so achieved can then lead to the secondary problem of extending this network. The subject of this paper is a set of 31 air pollution monitoring stations in southern Ontario. Each of these regularly measures a particular subset of ionic sulphate, sulphite, nitrite and ozone. However, this subset varies from station to station. For example only two stations measure all four. Some measure just one. We describe a Bayesian framework for integrating the measurements of these stations to yield a spatial predictive distribution for unmonitored sites and unmeasured concentrations at existing stations. Furthermore we show how this network can be extended by using an entropy maximization criterion. The methods assume that the multivariate response field being measured has a joint Gaussian distribution conditional on its mean and covariance function. A conjugate prior is used for these parameters, some of its hyperparameters being fitted empirically.     

Factors influencing Soay sheep survival

We present a survival analysis of Soay sheep mark recapture and recovery data. Unlike previous conditional analyses, it is not necessary to assume equality of recovery and recapture probabilities; instead these are estimated by maximum likelihood. Male and female sheep are treated separately, with the higher numbers and survival probabilities of the females resulting in a more complex model than that used for the males. In both cases, however, age and time aspects need to be included and there is a strong indication of a reduction in survival for sheep aged 7 years or more. Time variation in survival is related to the size of the population and selected weather variables, by using logistic regression. The size of the population significantly affects the survival probabilities of male and female lambs, and of female sheep aged 7 or more years. March rainfall and a measure of the North Atlantic oscillation are found to influence survival significantly for all age groups considered, for both males and females. Either of these weather variables can be used in a model. Several phenotypic and genotypic individual covariates are also fitted. The only covariate which is found to influence survival significantly is the type of horn of first-year female sheep. There is a substantial variation in the recovery probabilities over time, reflecting in part the increased effort when a population crash was expected. The goodness of fit of the model is checked by using graphical procedures.