Hypothesis testing of multiple inequalities: the method of constraint chaining

Econometric inequality hypotheses arise in diverse ways. Examples include concavity restrictions on technological and behavioural functions, monotonicity and dominance relations, one-sided constraints on conditional moments in GMM estimation, bounds on parameters which are only partially identified, and orderings of predictive performance measures for competing models. In this paper we set forth four key properties which tests of multiple inequality constraints should ideally satisfy. These are (1) (asymptotic) exactness, (2) (asymptotic)similarity on the boundary, (3) absence of nuisance parameters from the asymptotic null distribution of the test statistic, (4) low computational complexity and boostrapping cost. We observe that the predominant tests currently used in econometrics do not appear to enjoy all these properties simultaneously. We therefore ask the question : Does there exist any nontrivial test which, as a mathematical fact, satisfies the first three properties and, by any reasonable measure, satisfies the fourth ? Remarkably the answer is affirmative. The paper demonstrates this constructively. We introduce a method of test construction called chaining which begins by writing multiple inequalities as a single equality using zero-one indicator functions. We then smooth the indicator functions. The approximate equality thus obtained is the basis of a well-behaved test. This test may be considered as the baseline of a wider class of tests. A full asymptotic theory is provided for the baseline. Simulation results show that the finite-sample performance of the test matches the theory quite well

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

The two-parameter Birnbaum-Saunders distribution has been used succesfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Three empirical applications are presented.Comment: Submitted for publicatio

Fretting wear of TiN PVD coating under variable relative humidity conditions – development of a “composite” wear law

Fretting is defined as a small oscillatory displacement between two contacting bodies. The interface is damaged by debris generation and its ejection from the contact area. The application of hard coatings is an established solution to protect against fretting wear. For this study the TiN hard coating manufactured by a PVD method has been selected, and tested against a polycrystalline alumina smooth ball. A fretting test programme has been carried out at a frequency of 5 Hz, 100 N normal load, 100 μm displacement amplitude and at five values of relative humidity: 10, 30, 50, 70 and 90% at a temperature of 296 K. The intensity of the wear process is shown to be significantly dependent on the environmental conditions. A dissipated energy approach has been employed in this study to quantify wear rates of the hard coating. The approach predicts wear kinetics under constant medium relative humidity in a stable manner. It has been shown that an increase of relative humidity promotes the formation of hydrate structures at the interface and modifies the third body rheology. This phenomenon has been characterised by the evolution of wear kinetics associated with a significant variation of the corresponding energy wear coefficient. Hence, a ‘composite’ wear law, integrating the energy wear coefficient as a function of relative humidity, is introduced. It permits a prediction of wear under variable relative humidity conditions from 10 to 90% within a single fretting test. The stability of this approach is demonstrated by comparing various variable relative humidity sequences