Statistical inference for start-up demonstration tests with rejection of units upon observing d failures

In this paper, we consider the statistical inference for the success probability in the case of start-up demonstration tests in which rejection of units is possible when a pre-fixed number of failures is observed before the required number of consecutive successes are achieved for acceptance of the unit. Since the expected value of the stopping time is not a monotone function of the unknown parameter, the method of moments is not useful in this situation. Therefore, we discuss two estimation methods for the success probability: (1) the maximum likelihood estimation (MLE) via the expectation-maximization (EM) algorithm and (2) Bayesian estimation with a beta prior. We examine the small-sample properties of the MLE and Bayesian estimator. Finally, we present an example to illustrate the method of inference discussed here.     

Ordered ranked set samples and applications to inference

Ranked set sampling (RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian J. Agricultural Res. 3, 385–390] as an effective way to estimate the unknown population mean. Chuiv and Sinha [1998. On some aspects of ranked set sampling in parametric estimation. In: Balakrishnan, N., Rao, C.R. (Eds.), Handbook of Statistics, vol. 17. Elsevier, Amsterdam, pp. 337–377] and Chen et al. [2004. Ranked Set Sampling—Theory and Application. Lecture Notes in Statistics, vol. 176. Springer, New York] have provided excellent surveys of RSS and various inferential results based on RSS. In this paper, we use the idea of order statistics from independent and non-identically distributed (INID) random variables to propose ordered ranked set sampling (ORSS) and then develop optimal linear inference based on ORSS. We determine the best linear unbiased estimators based on ORSS (BLUE-ORSS) and show that they are more efficient than BLUE-RSS for the two-parameter exponential, normal and logistic distributions. Although this is not the case for the one-parameter exponential distribution, the relative efficiency of the BLUE-ORSS (to BLUE-RSS) is very close to 1. Furthermore, we compare both BLUE-ORSS and BLUE-RSS with the BLUE based on order statistics from a simple random sample (BLUE-OS). We show that BLUE-ORSS is uniformly better than BLUE-OS, while BLUE-RSS is not as efficient as BLUE-OS for small sample sizes (n<5$n<5$).     

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.