Contributions to the Theory of Optimal Tests

This paper considers tests which maximize the weighted average power (WAP). The focus is on determining WAP tests subject to an uncountable number of equalities and/or inequalities. The unifying theory allows us to obtain tests with correct size, similar tests, and unbiased tests, among others. A WAP test may be randomized and its characterization is not always possible. We show how to approximate the power of the optimal test by sequences of nonrandomized tests. Two alternative approximations are considered. The rst approach considers a sequence of similar tests for an increasing number of boundary conditions. This discretization allows us to implement the WAP tests in practice. The second method nds a sequence of tests which approximate the WAP test uniformly. This approximation allows us to show that WAP similar tests are admissible. The theoretical framework is readily applicable to several econometric models, including the important class of the curved-exponential family. In this paper, we consider the instrumental variable model with heteroskedastic and autocorrelated errors (HAC-IV) and the nearly integrated regressor model. In both models, we nd WAP similar and (locally) unbiased tests which dominate other available tests.

Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors

This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the nite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We introduce two weights which are invariant to orthogonal transformations of the instruments; e.g., changing the order in which the instruments appear. While tests using the MM1 weight can be severely biased, optimal tests based on the MM2 weight are naturally two-sided when errors are homoskedastic. We propose two boundary conditions that yield two-sided tests whether errors are homoskedastic or not. The locally unbiased (LU) condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness. The strongly unbiased (SU) condition is more restrictive than LU, but the associated WAP tests are easier to implement. Several tests are SU in nite samples or asymptotically, including tests robust to weak IV (such as the Anderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews' (2015) PI-CLC tests) and two-sided tests which are optimal when the sample size is large and instruments are strong. We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests. Dropping the restrictive assumptions of normality and known variance, the theory is shown to remain valid at the cost of asymptotic approximations. The MM2-SU test is optimal under the strong IV asymptotics, and outperforms other existing tests under the weak IV asymptotics.

GLS Detrending, Efficient Unit Root Tests and Structural Change

We extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we consider two models : one allowing for a change in slope and the other for both a change in intercept and slope. We derive the asymptotic distribution of the tests as well as that of the feasible point optimal tests PT(GLS) suggested by ERS. The asymptotic critical values of the tests are tabulated. Also, we compute the non-centrality parameter used for the local GLS detrending that permits the tests to have 50% asymptotic power at that value. We show that the M(GLS) and PT(GLS) tests have an asymptotic power function close to the power envelope. An extensive simulation study analyzes the size and power in finite samples under various methods to select the truncation lag for the autoregressive spectral density estimator. An empirical application is also provided.

Wald tests for IV regression with weak instruments

This dissertation deals with the problem of making inference when there is weak identification in models of instrumental variables regression. More specifically we are interested in one-sided hypothesis testing for the coefficient of the endogenous variable when the instruments are weak. The focus is on the conditional tests based on likelihood ratio, score and Wald statistics. Theoretical and numerical work shows that the conditional t-test based on the two-stage least square (2SLS) estimator performs well even when instruments are weakly correlated with the endogenous variable. The conditional approach correct uniformly its size and when the population F-statistic is as small as two, its power is near the power envelopes for similar and non-similar tests. This finding is surprising considering the bad performance of the two-sided conditional t-tests found in Andrews, Moreira and Stock (2007). Given this counter intuitive result, we propose novel two-sided t-tests which are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test of Moreira (2003).

Invariant tests in an instrumental variables model with unknown data generating process

In this work we focus on tests for the parameter of an endogenous variable in a weakly identi ed instrumental variable regressionmodel. We propose a new unbiasedness restriction for weighted average power (WAP) tests introduced by Moreira and Moreira (2013). This new boundary condition is motivated by the score e ciency under strong identi cation. It allows reducing computational costs of WAP tests by replacing the strongly unbiased condition. This latter restriction imposes, under the null hypothesis, the test to be uncorrelated to a given statistic with dimension given by the number of instruments. The new proposed boundary condition only imposes the test to be uncorrelated to a linear combination of the statistic. WAP tests under both restrictions to perform similarly numerically. We apply the di erent tests discussed to an empirical example. Using data from Yogo (2004), we assess the e ect of weak instruments on the estimation of the elasticity of inter-temporal substitution of a CCAPM model.

Optimal Test for Parameter Instability When the Unstable Process and the Error Distribution are Unknown

This paper proposes asymptotically optimal tests for unstable parameter process under the feasible circumstance that the researcher has little information about the unstable parameter process and the error distribution, and suggests conditions under which the knowledge of those processes does not provide asymptotic power gains. I first derive a test under known error distribution, which is asymptotically equivalent to LR tests for correctly identified unstable parameter processes under suitable conditions. The conditions are weak enough to cover a wide range of unstable processes such as various types of structural breaks and time varying parameter processes. The test is then extended to semiparametric models in which the underlying distribution in unknown but treated as unknown infinite dimensional nuisance parameter. The semiparametric test is adaptive in the sense that its asymptotic power function is equivalent to the power envelope under known error distribution.

Cost effectiveness of OptiMal (R) rapid diagnostic test for malaria in remote areas of the Amazon Region, Brazil

Background: In areas with limited structure in place for microscopy diagnosis, rapid diagnostic tests (RDT) have been demonstrated to be effective. Method: The cost-effectiveness of the Optimal (R) and thick smear microscopy was estimated and compared. Data were collected on remote areas of 12 municipalities in the Brazilian Amazon. Data sources included the National Malaria Control Programme of the Ministry of Health, the National Healthcare System reimbursement table, hospitalization records, primary data collected from the municipalities, and scientific literature. The perspective was that of the Brazilian public health system, the analytical horizon was from the start of fever until the diagnostic results provided to patient and the temporal reference was that of year 2006. The results were expressed in costs per adequately diagnosed cases in 2006 U. S. dollars. Sensitivity analysis was performed considering key model parameters. Results: In the case base scenario, considering 92% and 95% sensitivity for thick smear microscopy to Plasmodium falciparum and Plasmodium vivax, respectively, and 100% specificity for both species, thick smear microscopy is more costly and more effective, with an incremental cost estimated at US$ 549.9 per adequately diagnosed case. In sensitivity analysis, when sensitivity and specificity of microscopy for P. vivax were 0.90 and 0.98, respectively, and when its sensitivity for P. falciparum was 0.83, the RDT was more cost-effective than microscopy. Conclusion: Microscopy is more cost-effective than OptiMal (R) in these remote areas if high accuracy of microscopy is maintained in the field. Decision regarding use of rapid tests for diagnosis of malaria in these areas depends on current microscopy accuracy in the field.

Optimal conditions for the wetting balance test

Wetting balance tests of copper sheets submerged in tin solder baths were carried out in a completely automatic wetting balance. Wetting curves were examined for three different values of sheet thickness and four different solder bath temperatures. Most of the wetting curves showed a distorted shape relative to that of a standard curve, preventing calculation of important wetting parameters, such as the wetting rate and the wetting force. The wetting tests showed that the distortion increased for a thicker sheet thickness and a lower solder bath temperature, being the result of solder bath solidification around the submerged sheet substrate. (C) 2008 Elsevier B.V. All rights reserved.

A Bayesian approach to fuzzy hypotheses testing for the estimation of optimal age for vaccination against measles

Fuzzy Bayesian tests were performed to evaluate whether the mother`s seroprevalence and children`s seroconversion to measles vaccine could be considered as ""high"" or ""low"". The results of the tests were aggregated into a fuzzy rule-based model structure, which would allow an expert to influence the model results. The linguistic model was developed considering four input variables. As the model output, we obtain the recommended age-specific vaccine coverage. The inputs of the fuzzy rules are fuzzy sets and the outputs are constant functions, performing the simplest Takagi-Sugeno-Kang model. This fuzzy approach is compared to a classical one, where the classical Bayes test was performed. Although the fuzzy and classical performances were similar, the fuzzy approach was more detailed and revealed important differences. In addition to taking into account subjective information in the form of fuzzy hypotheses it can be intuitively grasped by the decision maker. Finally, we show that the Bayesian test of fuzzy hypotheses is an interesting approach from the theoretical point of view, in the sense that it combines two complementary areas of investigation, normally seen as competitive. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Diagnostic performance of Antineutrophil Cytoplasmic Antibody tests for Idiopathic Vasculitides: Metaanalysis with a focus on antimyeloperoxidase antibodies

Objective. The diagnostic value of tests for antimyeloperoxidase antibodies (anti-MPO) for systemic vasculitis is less established than that for cytoplasmic antineutrophil cytoplasmic antibody (cANCA)/antiproteinase 3 antibodies (anti-PR3). Controversy exists regarding the optimal utilization of indirect immunofluorescence (IIF) ANCA testing versus antigen-specific ANCA testing. To summarize the pertinent data, we conducted a metaanalysis examining the diagnostic value of ANCA testing systems that include assays for anti-MPO. Methods. We performed a structured Medline search and reference list review. Target articles in the search strategy were those reporting the diagnostic value of immunoassays for anti-MPO for the spectrum of systemic necrotizing vasculitides that includes Wegener's granulomatosis, microscopic polyangiitis, the Churg-Strauss syndrome, and isolated pauci-immune necrotizing or crescentic glomerulonephritis, regardless of other types of ANCA tests. Inclusion criteria required specification of a consecutive or random patient selection method and the use of acceptable criteria for the diagnosis of vasculitis exclusive of ANCA test results. Weighted pooled summary estimates of sensitivity and specificity were calculated for anti-MPO alone, anti-MPO + perinuclear ANCA (pANCA), and anti-MPO/pANCA + anti-PR3/cANCA. Results. Of 457 articles reviewed, only 7 met the selection criteria. Summary estimates of sensitivity and specificity (against disease controls only) of assays for anti-MPO for the diagnosis of systemic necrotizing vasculitides were 37.1% (confidence interval 26.6% to 47.6%) and 96.3% (CI 94.1% to 98.5%), respectively. When the pANCA pattern by IIF was combined with anti-MPO testing, the specificity improved to 99.4%, with a lower sensitivity, 31.5%. The combined ANCA testing system (anti-PR3/cANCA + anti-MPO/pANCA) increased the sensitivity to 85.5% with a specificity of 98.6%. Conclusion. These results suggest that while anti-MPO is relatively specific for the diagnosis of systemic vasculitis, the combination system of immunoassays for anti-MPO and IIF for pANCA is highly specific and both tests should be used together given the high diagnostic precision required for these conditions. Because patients with ANCA associated vasculitis have either anti-MPO with pANCA or anti-PR3 with cANCA, and rarely both, a combined ANCA testing system including anti-PR3/cANCA and anti-MPO/pANCA is recommended to optimize the diagnostic performance of ANCA testing. (J Rheumatol 2001;28:1584-90)

Optimal patch-leaving behaviour: a case study using the parasitoid Cotesia rubecular

1. Parasitoids are predicted to spend longer in patches with more hosts, but previous work on Cotesia rubecula (Marshall) has not upheld this prediction, Tests of theoretical predictions may be affected by the definition of patch leaving behaviour, which is often ambiguous. 2. In this study whole plants were considered as patches and assumed that wasps move within patches by means of walking or flying. Within-patch and between-patch flights were distinguished based on flight distance. The quality of this classification was tested statistically by examination of log-survivor curves of flight times. 3. Wasps remained longer in patches with higher host densities, which is consistent with predictions of the marginal value theorem (Charnov 1976). tinder the assumption that each flight indicates a patch departure, there is no relationship between host density and leaving tendency. 4. Oviposition influences the patch leaving behaviour of wasps in a count down fashion (Driessen et al. 1995), as predicted by an optimal foraging model (Tenhumberg, Keller & Possingham 2001). 5. Wasps spend significantly longer in the first patch encountered following release, resulting in an increased rate of superparasitism.

A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

The Emperor Has New Clothes: Empirical Tests of Mainstream Theories of Economic Growth

Modern macroeconomic theory utilises optimal control techniques to model the maximisation of individual well-being using a lifetime utility function. Agents face choices over current and future consumption (with resultant implied savings decisions) seeking to maximise the present value of current plus future well-being. However, such inter-temporal welfare-maximising assumptions remain empirically untested. In the work presented here we test whether welfare was in (historical) fact maximised in the US between 1870-2000 and find empirical support for the optimising basis of growth theory, but only once a comprehensive view of what constitutes a country’s wealth or capital is taken into account.

Optimal 3-T MRI for depiction of the finger A2 pulley: comparison between T1-weighted, fat-saturated T2-weighted and gadolinium-enhanced fat-saturated T1-weighted sequences

OBJECTIVE: To compare three spin-echo sequences, transverse T1-weighted (T1WI), transverse fat-saturated (FS) T2-weighted (T2WI), and transverse gadolinium-enhanced (Gd) FS T1WI, for the visualisation of normal and abnormal finger A2 pulley with magnetic resonance (MR) imaging at 3 tesla (T). MATERIALS AND METHODS: Sixty-three fingers from 21 patients were consecutively investigated. Two musculoskeletal radiologists retrospectively compared all sequences to assess the visibility of normal and abnormal A2 pulleys and the presence of motion or ghost artefacts. RESULTS: Normal and abnormal A2 pulleys were visible in 94% (59/63) and 95% (60/63) on T1WI sequences, in 63% (40/63) and 60% (38/63) on FS T2WI sequences, and in 87% (55/63) and 73% (46/63) on Gd FS T1WI sequences when read by the first and second observer, respectively. Motion and ghost artefacts were higher on FS T2WI sequences. Seven among eight abnormal A2 pulleys were detected, and were best depicted with Gd FS T1WI sequences in 71% (5/7) and 86% (6/7) by the first and the second observer, respectively. CONCLUSION: In 3-T MRI, the comparison between transverse T1WI, FS T2WI, and Gd FS T1WI sequences shows that transverse T1WI allows excellent depiction of the A2 pulley, that FS T2WI suffers from a higher rate of motion and ghost artefacts, and transverse Gd FS T1WI is the best sequence for the depiction of abnormal A2 pulley.

Is PaCO2 management optimal under controlled mechanical ventilation (CMV) during neuro-resuscitation?

INTRODUCTION. Both hypocapnia and hypercapnia can be deleterious to brain injured patients. Strict PaCO2 control is difficult to achieve because of patient's instability and unpredictable effects of ventilator settings changes. OBJECTIVE. The aim of this study was to evaluate our ability to comply with a protocol of controlled mechanical ventilation (CMV) aiming at a PaCO2 between 35 and 40 mmHg in patients requiring neuro-resuscitation. METHODS. Retrospective analysis of consecutive patients (2005-2011) requiring intracranial pressure (ICP) monitoring for traumatic brain injury (TBI), subarachnoid haemorrhage (SAH), intracranial haemorrhage (ICH) or ischemic stroke (IS). Demographic data, GCS, SAPS II, hospital mortality, PaCO2 and ICP values were recorded. During CMV in the first 48 h after admission, we analyzed the time spent within the PaCO2 target in relation to the presence or absence of intracranial hypertension (ICP[20 mmHg, by periods of 30 min) (Table 1). We also compared the fraction of time (determined by linear interpolation) spent with normal, low or high PaCO2 in hospital survivors and non-survivors (Wilcoxon, Bonferroni correction, p\0.05) (Table 2). PaCO2 samples collected during and after apnoea tests were excluded. Results given as median [IQR]. RESULTS. 436 patients were included (TBI: 51.2 %, SAH: 20.6 %, ICH: 23.2 %, IS: 5.0 %), age: 54 [39-64], SAPS II score: 52 [41-62], GCS: 5 [3-8]. 8744 PaCO2 samples were collected during 150611 h of CMV. CONCLUSIONS. Despite a high number of PaCO2 samples collected (in average one sample every 107 min), our results show that patients undergoing CMV for neuro- resuscitation spent less than half of the time within the pre-defined PaCO2 range. During documented intracranial hypertension, hypercapnia was observed in 17.4 % of the time. Since non-survivors spent more time with hypocapnia, further analysis is required to determine whether hypocapnia was detrimental per se, or merely reflects increased severity of brain insult.