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.

A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Computer simulation of the stochastic transport equation

Trabalho apresentado no 37th Conference on Stochastic Processes and their Applications - July 28 - August 01, 2014 -Universidad de Buenos Aires

Numerical integration of coupled stochastic oscillators driven by Random Forces

Trabalho apresentado no International Conference on Scientific Computation And Differential Equations 2015

Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Stochastic discount factor bounds and rare events: a review

We aim to provide a review of the stochastic discount factor bounds usually applied to diagnose asset pricing models. In particular, we mainly discuss the bounds used to analyze the disaster model of Barro (2006). Our attention is focused in this disaster model since the stochastic discount factor bounds that are applied to study the performance of disaster models usually consider the approach of Barro (2006). We first present the entropy bounds that provide a diagnosis of the analyzed disaster model which are the methods of Almeida and Garcia (2012, 2016); Ghosh et al. (2016). Then, we discuss how their results according to the disaster model are related to each other and also present the findings of other methodologies that are similar to these bounds but provide different evidence about the performance of the framework developed by Barro (2006).

Assessing global economic activity linkages: an empirical exercise based on global autoregressive regression

Economic performance increasingly relies on global economic environment due to the growing importance of trade and nancial links among countries. Literature on growth spillovers shows various gains obtained by this interaction. This work aims at analyzing the possible e ects of a potential economic growth downturn in China, Germany and United States on the growth of other economies. We use global autoregressive regression approach to assess interdependence among countries. Two types of phenomena are simulated. The rst one is a one time shock that hit these economies. Our simulations use a large shock of -2.5 standard deviations, a gure very similar to what we saw back in the 2008 crises. The second experiment simulate the e ect of a hypothetical downturn of the aforementioned economies. Our results suggest that the United States play the role of a global economy a ecting countries across the globe whereas Germany and China play a regional role.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimation of genetic parameters for partial egg production periods by means of random regression models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Morphological Aspects and Storage of Dypsis leptocheilos (Hodel) Beentje & J. Dransf. (Arecaceae) Seeds

Dypsis leptocheilos (Hodel) Beentje & J. Dransf. palms are widely used in landscaping, however there is a lack of studies about its biology, especially on the morphology of its seedling disseminules and the ideal seed storage time without loss of viability. The objectives of this work were to describe the morphological aspects and to study the storage effect on the germination of D. leptocheilos seeds. The experiments were performed at FCAV/UNESP, Jaboticabal Campus, São Paulo State, Brazil. In order to obtain a morphology description 100 disseminules were sowed in vermiculite. The external and internal sides of the disseminules as well as the representative phases of the germination process were sketched with the help of a light chamber attached to a stereomicroscope. Five treatments were arranged in order to study the storage effects on the seeds (four months of storage and straight after harvest), with four replicates with 25 disseminules each (seeds with attached endocarp) in a completely randomized design. The germination test was conducted over a 140 days period and noted every two days. In order to calculate the germination percentage (% G) and the Germination Speed Index (GSI), the seeds were considered germinated when the germinative button appeared. The data were submitted to a polynomial regression analysis to verify the behavior of the variables over the storage period. The D. leptocheilos seeds have rounded shape, ruminate endosperm and hard consistency. The embryo is lateral, peripheral and relatively undifferentiated, with approximately 3 mm long and conical shape. The germination percentage increased from 17% for seeds sowed straight after harvest to 73% for those stored over a three-month period. For the GSI the increase was about 0.85%. It was concluded that the germination of D. leptocheilos is of an adjacent ligulate type. Furthermore, the seeds stored for 3 months at 14 degrees C showed both higher percentage and germination speed.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimates of genetic parameters for scrotal circumference using random regression models in Nelore cattle

A total of 15,901 scrotal circumference (SC) records from 5300 Nelore bulls, ranging from 229 to 560 days of age, were used with the objective of estimating (co)variance functions for SC, using random regression models. Models included the fixed effects of contemporary group and age of dam at calving as covariable (linear and quadratic effects). To model the population mean trend, a third order Legendre polynomial on animal age was utilized. The direct additive genetic and animal permanent environmental random effects were modeled by Legendre polynomials on animal age, with orders of fit ranging from 1 to 5. Residual variances were modeled considering 1 (homogeneity of variance) or 4 age classes. Results obtained with the random regression models were compared to multi-trait analysis. (Co)variance estimates using multi-trait and random regression models were similar. The model considering a third- and fifth-order Legendre polynomials for additive genetic and animal permanent environmental effects, respectively, was the most adequate to model changes in variance of SC with age. Heritability estimates for SC ranged from 0.24 (229 days of age) to 0.47 (300 days of age), remained almost constant until 500 days of age (0.52), decreasing thereafter (0.44). In general, the genetic correlations between measures of scrotal circumference obtained from 229 to 560 days of age decreased with increasing distance between ages. For genetic evaluation scrotal circumference could be measured between 400 and 500 days of age. (C) 2010 Elsevier B.V. All rights reserved.