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The author develops and extends the asymptotic F- and t-test theory in linear regression models where the regressors could be deterministic trends, unit-root processes, near-unit-root processes, among others. The author considers both the exogenous case where the regressors and the regression error are independent and the endogenous case where they are correlated. In the former case, the author designs a new set of basis functions that are invariant to the parameter estimation uncertainty and uses them to construct a new series long-run variance estimator. The author shows that the F-test version of the Wald statistic and the t-statistic are asymptotically F and t distributed, respectively. In the latter case, the author shows that the asymptotic F and t theory is still possible, but one has to develop it in a pseudo-frequency domain. The F and t approximations are more accurate than the more commonly used chi-squared and normal approximations. The resulting F and t tests are also easy to implement – they can be implemented in exactly the same way as the F and t tests in a classical normal linear regression.

New asymptotic approximations are established for the Wald and t statistics in the presence of unknown but strong autocorrelation. The asymptotic theory extends the usual fixed-smoothing asymptotics under weak dependence to allow for near-unit-root and weak-unit-root processes. As the locality parameter that characterizes the neighborhood of the autoregressive root increases from zero to infinity, the new fixed-smoothing asymptotic distribution changes smoothly from the unit-root fixed-smoothing asymptotics to the usual fixed-smoothing asymptotics under weak dependence. Simulations show that the new approximation is more accurate than the usual fixed-smoothing approximation.

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n = 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

The paper aims to present acceptance sampling plans based on failure‐censored step‐stress accelerated life tests for items having Weibull lives.

The model parameters are estimated by the method of maximum likelihood. Based on asymptotic distribution theory, the sample size and the acceptability constant are determined satisfying the producer's and consumer's risks. The step‐stress accelerated life test is optimized to have a minimum sample size by minimizing the asymptotic variance of test statistic. Two modes of step‐stress accelerated life test are considered, and a comparison between them is made. The proposed sampling plans are compared with the sampling plans based on constant stress accelerated life tests.

Asymptotic variance is a dominating factor in determining the sample size required for a sampling plan to determine the acceptability of a lot. The sample size is minimized by optimally designing a step‐stress accelerated life test so that the asymptotic variance is minimized.

The sampling plans presented in this paper are particularly useful when items to be tested are so reliable and are useful to reliability engineers and life test planners.

Acceptance sampling plans are designed to decide about acceptance or rejection of a lot of products on the basis of sample drawn from it. Accelerating the life test helps in obtaining information about the lifetimes of high reliability products quickly. The purpose of this paper is to formulate an optimum time censored acceptance sampling plan based on ramp-stress accelerated life test (ALT) for items having log-logistic life distribution. The log-logistic life distribution has been found appropriate for highly reliable components such as power system components and insulating materials.

The inverse power relationship has been used to model stress-life relationship. It is meant for analyzing data for which the accelerated stress is nonthermal in nature, and frequently used as an accelerating stress for products such as capacitors, transformers, and insulators. The method of maximum likelihood is used for estimating design parameters. The optimal test plan is obtained by minimizing variance of test-statistic that decides on acceptability or rejectibility of lot. The optimal test plan finds optimal sample size, stress rates, sample proportion allocated to each stress and lot acceptability constant such that producer’s risk and consumer’s risk is satisfied.

Asymptotic variance plays a pivotal role in determining the sample size required for a sampling plan for deciding the acceptance/rejection of a lot. The sample size is minimized by optimally designing a ramp-stress ALT so that the asymptotic variance is minimized.

The model suggested is of use to quality control and reliability engineers dealing with highly reliable items.

In this paper we use Monte Carlo sampling experiments to examine the properties of pretest estimators in the random parameters logit (RPL) model. The pretests are for the presence of random parameters. We study the Lagrange multiplier (LM), likelihood ratio (LR), and Wald tests, using conditional logit as the restricted model. The LM test is the fastest test to implement among these three test procedures since it only uses restricted, conditional logit, estimates. However, the LM-based pretest estimator has poor risk properties. The ratio of LM-based pretest estimator root mean squared error (RMSE) to the random parameters logit model estimator RMSE diverges from one with increases in the standard deviation of the parameter distribution. The LR and Wald tests exhibit properties of consistent tests, with the power approaching one as the specification error increases, so that the pretest estimator is consistent. We explore the power of these three tests for the random parameters by calculating the empirical percentile values, size, and rejection rates of the test statistics. We find the power of LR and Wald tests decreases with increases in the mean of the coefficient distribution. The LM test has the weakest power for presence of the random coefficient in the RPL model.

This study aims to render a fundamental assessment of the Basel II internal ratings-based (IRB) approach by taking readings of the Australian banking sector since the implementation of Basel II and comparing them with signals from macroeconomic indicators, financial statistics and external credit ratings. The IRB approach to capital adequacy for credit risk, which implements an asymptotic single risk factor (ASRF) model, plays an important role in protecting the Australian banking sector against insolvency.

Realisations of the single systematic risk factor, interpreted as describing the prevailing state of the Australian economy, are recovered from the ASRF model and compared with macroeconomic indicators. Similarly, estimates of distance-to-default, reflecting the capacity of the Australian banking sector to absorb credit losses, are recovered from the ASRF model and compared with financial statistics and external credit ratings. With the implementation of Basel II preceding the time when the effect of the financial crisis of 2007-2009 was most acutely felt, the authors measure the impact of the crisis on the Australian banking sector.

Measurements from the ASRF model find general agreement with signals from macroeconomic indicators, financial statistics and external credit ratings. This leads to a favourable assessment of the ASRF model for the purposes of capital allocation, performance attribution and risk monitoring. The empirical analysis used in this paper reveals that the recent crisis imparted a mild stress on the Australian banking sector.

Given the range of economic conditions, from mild contraction to moderate expansion, experienced in Australia since the implementation of Basel II, the authors cannot attest to the validity of the model specification of the IRB approach for its intended purpose of solvency assessment.

Access to internal bank data collected by the prudential regulator distinguishes this paper from other empirical studies on the IRB approach and financial crisis of 2007-2009. The authors are not the first to attempt to measure the effects of the recent crisis, but they believe that they are the first to do so using regulatory data.

This article uses a Value‐at‐Risk approach to derive an estimator of the failure probability of a financial institution. The proposed approach can be applied to any profit/loss distribution, although Extreme Value (EV) theory also tells us that the most appropriate distributions are EV. The estimator suggested here is superior to the “Z” indicator of failure risk, which is sometimes used in the literature. Illustrative results confirm that the distribution selected makes a considerable difference to the results, and that estimates of failure probabilities based on the assumption of normality are too low to be valid.