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.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Locally Efficient Estimation with Current Status Data and High Dimensional Covariates

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed monitoring time, then the data is described by the well known singly-censored current status model, also known as interval censored data, case I. We extend this current status model by allowing the presence of a time-dependent process, which is partly observed and allowing C to depend on T through the observed part of this time-dependent process. Because of the high dimension of the covariate process, no globally efficient estimators exist with a good practical performance at moderate sample sizes. We follow the approach of Robins and Rotnitzky (1992) by modeling the censoring variable, given the time-variable and the covariate-process, i.e., the missingness process, under the restriction that it satisfied coarsening at random. We propose a generalization of the simple current status estimator of the distribution of T and of smooth functionals of the distribution of T, which is based on an estimate of the missingness. In this estimator the covariates enter only through the estimate of the missingness process. Due to the coarsening at random assumption, the estimator has the interesting property that if we estimate the missingness process more nonparametrically, then we improve its efficiency. We show that by local estimation of an optimal model or optimal function of the covariates for the missingness process, the generalized current status estimator for smooth functionals become locally efficient; meaning it is efficient if the right model or covariate is consistently estimated and it is consistent and asymptotically normal in general. Estimation of the optimal model requires estimation of the conditional distribution of T, given the covariates. Any (prior) knowledge of this conditional distribution can be used at this stage without any risk of losing root-n consistency. We also propose locally efficient one step estimators. Finally, we show some simulation results.

Trends and outcomes in the use of surgery and radiation for the treatment of locally advanced esophageal cancer: a propensity score adjusted analysis of the surveillance, epidemiology, and end results registry from 1998 to 2008

We examined outcomes and trends in surgery and radiation use for patients with locally advanced esophageal cancer, for whom optimal treatment isn't clear. Trends in surgery and radiation for patients with T1-T3N1M0 squamous cell or adenocarcinoma of the mid or distal esophagus in the Surveillance, Epidemiology, and End Results database from 1998 to 2008 were analyzed using generalized linear models including year as predictor; Surveillance, Epidemiology, and End Results doesn't record chemotherapy data. Local treatment was unimodal if patients had only surgery or radiation and bimodal if they had both. Five-year cancer-specific survival (CSS) and overall survival (OS) were analyzed using propensity-score adjusted Cox proportional-hazard models. Overall 5-year survival for the 3295 patients identified (mean age 65.1 years, standard deviation 11.0) was 18.9% (95% confidence interval: 17.3-20.7). Local treatment was bimodal for 1274 (38.7%) and unimodal for 2021 (61.3%) patients; 1325 (40.2%) had radiation alone and 696 (21.1%) underwent only surgery. The use of bimodal therapy (32.8-42.5%, P = 0.01) and radiation alone (29.3-44.5%, P < 0.001) increased significantly from 1998 to 2008. Bimodal therapy predicted improved CSS (hazard ratios [HR]: 0.68, P < 0.001) and OS (HR: 0.58, P < 0.001) compared with unimodal therapy. For the first 7 months (before survival curve crossing), CSS after radiation therapy alone was similar to surgery alone (HR: 0.86, P = 0.12) while OS was worse for surgery only (HR: 0.70, P = 0.001). However, worse CSS (HR: 1.43, P < 0.001) and OS (HR: 1.46, P < 0.001) after that initial timeframe were found for radiation therapy only. The use of radiation to treat locally advanced mid and distal esophageal cancers increased from 1998 to 2008. Survival was best when both surgery and radiation were used.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Acceptability of short term neo-adjuvant androgen deprivation in patients with locally advanced prostate cancer

Purpose: To determine the acceptability of short term neo-adjuvant maximal androgen deprivation (MAD) to patients treated with external beam radiation for locally advanced prostate cancer. Methods: Between 1996 and 2000, 818 patients with locally advanced, but non-metastatic, prostate cancer were entered into a randomised clinical trial (TROG 96.01), which compared radiation treatment alone with the same radiation treatment and 3 or 6 months neo-adjuvant MAD with goserelin and flutamide. Relevant symptoms, and how troublesome they were to the patient, were scored using a self-assessment questionnaire. This was completed by the patient at registration, and at specified times during and after treatment. Patients taking flutamide had liver function tests checked at regular intervals. Results: All patients have completed at least 12 months follow-up after treatment. Nearly all patients completed planned treatment with goserelin, but 27% of patients in the 6-month MAD treatment arm, and 20% in the 3-month arm, had to stop flutamide early. This was mainly due to altered liver function (up to 17% patients) and bowel side effects (up to 8% patients). However, although flutamide resulted in more bowel symptoms for patients on MAD, there was significant reduction in some urinary symptoms on this treatment. Acute bowel and urinary side effects at the end of radiation treatment were similar in all treatment arms. Side effect severity was unrelated to radiation target volume size, which was reduced by MAD, but symptomatology prior to any treatment was a powerful predictor. Of the 36% of patients who were sexually active before any treatment, the majority became inactive whilst on MAD. However, sexual activity at 12 months after radiation treatment was similar in all treatment arms, indicating that the effects of short term MAD on sexual function are reversible. Conclusion: Despite temporary effects on sexual activity, and compliance difficulties with flutamide, short-term neo-adjuvant MAD was not perceived by patients to be a major inconvenience. If neo-adjuvant MAD in the way tested can be demonstrated to lead to improved biochemical control and/or survival, then patients would view these therapeutic gains as worthwhile. Compliance with short-term goserelin was excellent, confirming that LH-RH analogues have a potential role in more long-term adjuvant treatment. However, for more protracted androgen deprivation, survival advantages and deleterious effects need to be assessed in parallel, in order to determine the optimal duration of treatment. (C) 2003 Elsevier Ireland Ltd. All fights reserved.

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed quantum nonlocality without entanglement. We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.

Entry, reforms complementarity and performance:a tale of two Indian manufacturing sectors

In this paper, we use plant-level data from two Indian industries, namely, electrical machinery and textiles, to examine the empirical relationship between structural reforms like abandonment of entry restrictions to the product market, competition and firm-level productivity and efficiency. These industries have faced different sets of policies since Independence but both were restricted in the adoption of technology and in the development of optimal scales of production. They also belonged to the first set of industries that benefited from the liberalization process started in the 1980s. Our results suggest that both the industries have improved their efficiency and scales of operation by the turn of the century. However, the process of adjustment seems to have been worked out more fully for electrical machinery. We also find evidence of spatial fragmentation of the market as late as 2000–2001. Gains in labour productivity were much more evident in states that either have a strong history of industrial activity or those that have experienced significant improvements in business environment since 1991.