We derive the exact Bahadur slopes of studentized score tests for a simple null hypothesis in a one-parameter family of distributions. The Student's t-test is included as a special case for which a recent result of Rukhin (1993, Sankhy Ser. A, 55, 159–163) was improved upon. It is shown that locally optimal Bahadur efficiency for one-sample location models with a known or estimated scale parameter is attained within the class of studentized score tests. The studentized test has an asymptotic null distribution free of the scale parameter, and the optimality of likelihood scores does not depend on the existence of a moment generating function. We also consider the influence function and breakdown point of such tests as part of our robustness investigation. The influence of any studentized score test is bounded from above, indicating certain degree of robustness of validity, but a bounded score function is needed to cap the influence from below and to ensure a high power breakdown point. We find that the standard Huber-type score tests are not only locally minimax in Bahadur efficiency, but also very competitive in global efficiency at a variety of location models. 相似文献
A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.
A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.
This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.
We show for the first time that a classical Hookean viscoelastic constitutive law for rubbery materials can predict the impact forces and deflections measured with a commercial drop tester when a mass, or tup with a flat impacting surface is dropped onto a flat pad of commercial impact-absorbing rubber. The viscoelastic properties of the rubber, namely the relaxation times and strengths, are obtained by a standard rheological linear-oscillatory test, and the equation of momentum transfer is then solved, using these measured parameters, assuming a uniaxial deflection of the pad during the impact. Good agreement between measured and predicted forces and deflections is obtained for a series of various drop heights, tup masses, impact areas, and pad thicknesses, as long as the deflection of the pad relative to its thickness is small or modest (<50% or so), and as long as the area of the pad is less than or equal to that of the tup. When the pad area is greater than the tup, forces are higher than predicted, unless an empirical factor is introduced to account for the nonuniaxial stretching of the ring of material that extends outside of the impact area. These results imply that the impact-absorbing properties of a rubbery polymeric material can be assessed by simply examining the material's linear viscoelastic spectrum. 相似文献
In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3. 相似文献
This article presents a new method to generate test patterns for multiple stuck-at faults in combinational circuits. We assume the presence of all multiple faults of all multiplicities and we do not resort to their explicit enumeration: the target fault is a single component of possibly several multiple faults. New line and gate models are introduced to handle multiple fault effect propagation through the circuits. The method tries to generate test conditions that propagate the effect of the target fault to primary outputs. When these conditions are fulfilled, the input vector is a test for the target fault and it is guaranteed that all multiple faults of all multiplicities containing the target fault as component are also detected. The method uses similar techniques to those in FAN and SOCRATES algorithms to guide the search part of the algorithm, and includes several new heuristics to enhance the performance and fault detection capability. Experiments performed on the ISCAS'85 benchmark circuits show that test sets for multiple faults can be generated with high fault coverage and a reasonable increase in cost over test generation for single stuck-at faults. 相似文献
A new and highly sensitive spectrophotometric method is developed for the determination of sub ppm levels of the widely used organophosphorus insecticide dichlorvos. The method is based on alkaline hydrolysis of dichlorvos to dichloroacetaldehyde followed by coupling with diphenyl semicarbazide (DPC) in alkaline medium. The absorption maxima of the wine red dye compound formed is measured at 490 nm. Beer's law is obeyed over the concentration range of 4.3 to 34 μg in a final solution volume of 25 mL (0.18–1.36 ppm). The molar absorptivity, Sandell's sensitivity and correlation coefficient were found to be 2.9 × 105 l mole?1 cm?1, 0.013 μg cm?2 and 0.9999, respectively. The standard deviation and relative standard deviation were found to be ± 0.007 and 1.90%, respectively. The lower limit of detection is 0.04 μg. The method is simple, sensitive and free from interferences of other pesticides and diverse ions. Other organophosphorous pesticides do not interfere with the proposed method. The method has been satisfactorily applied to the determination of dichlorvos in environmental and agricultural samples. 相似文献
A spot test was implemented in a flow-injection system for the spectrophotometric determination of zinc in digests of plant materials. It is based on the influence of Zn2+ on the oxidation rate of 1-naphthylethylenediamine (NED) by hexacyanoferrate(III) under acidic conditions. In order to control the precipitate formation and to maintain the resulting suspension, a micellar medium was established by adding Triton X-100. The proposed system handles about 65 samples per hour, meaning 72 μg NED and 9.0 mg K3[Fe(CN)6] per determination. Baseline drift is usually <0.01 absorbance per hour and the analytical signals for 0.5-2.5 mg l−1 Zn range within ca. 0.07-0.45 absorbance. Linearity of the analytical curve is fair (r>0.999, n=6) and detection limit was estimated as 0.2 mg l−1 Zn. Results are precise (R.S.D.<1%, n=10) and in agreement with flame atomic absorption spectrometry and with certified values of standard reference materials. 相似文献