Estimators for a simultaneous equation model with lagged endogenous variables and autocorrelated errors

Two full information estimators and a limited information estimator for the simultaneous equation model with autocorrelated errors are studies by the Monte Carlo method.The estimators share features of the two-step Gauss-Newton procedure and of Aitken generalized least squares.One full information method generates the estimated endogenous variables used in the later stages of computation from the unrestricted reduced form while the other uses a restricted reduced form.The observed small sample behavior was close to that suggested by asymptotic theory.     

Conditionally gaussian distributions and an application to kalman filtering with stochastic regressors

The work reviews theory of conditionally Gaussian distributions, especially so called theorems on normal correlation. Three theorems are given: the basic, the recursive, and the conditional theorem on normal correlation. They assume that (a,y), (a,x,y), or (a,y,z) has a Gaussian distribution, ussert that (a,y), (a,x,y), and (a,y,z), respectively, are Gaussian, and give formulas for the corresponding conditional mean vectors and variance covariance matrices. A proof is presented for the recursive and the conditional theorem.     

Applications and asymptotic power of marginal-free tests of stochastic vectorial independence

Fully nonparametric tests for the independence between random vectors are studied in this paper. The test statistics are functionals of an empirical process defined as the difference between the joint empirical copula and the product of the empirical copulas associated to the vectors that are suspected to be independent. The validity of a weighted bootstrap procedure is established, which allows for a quick computation of p-values. A special attention is given to the asymptotic behavior of the tests under contiguous sequences of distributions. Finally, a characteristic of the copulas in the Archimedean class in terms of independence of vectors is exploited in order to propose a new goodness-of-fit procedure.     

Bias correction through filtering omitted variables and instruments

This paper proposes a combination of the particle-filter-based method and the expectation-maximization algorithm (PFEM), in order to filter unobservable variables and hence, to reduce the omitted variables bias. Furthermore, I consider as an unobservable variable, an exogenous one that can be used as an instrument in the instrumental variable (IV) methodology. The aim is to show that the PFEM is able to eliminate or reduce both the omitted variable bias and the simultaneous equation bias by filtering the omitted variable and the unobserved instrument, respectively. In other words, the procedure provides (at least approximately) consistent estimates, without using additional information embedded in the omitted variable or in the instruments, since they are filtered by the observable variables. The validity of the procedure is shown both through simulations and through a comparison to an IV analysis which appeared in an important previous publication. As regards the latter point, I demonstrate that the procedure developed in this article yields similar results to those of the original IV analysis.     

Stability in distribution of Markov-modulated stochastic differential delay equations with reflection

In this paper, we discuss Markov-modulated stochastic differential delay equations with reflection. The aim of this paper is to extend the stability criterion in distribution as in [Systems and Control Letters Vol 50 (2003) 195–207] to the equations with reflection. Interesting examples are provided to demonstrate not only our theory, but also the importance of Markov-modulating.     

Critical values of some nonparametric statistics used for tests of total stochastic independence

The problem of testing for total independence of the variates of a stochastic p(≧3) component vector using rank correlation statistics is considered. Two distribution free statistics are considered, one based on the determinant of the matrix of rank correlation statistics, the second on their sum of squares. Tables of critical values are given for p=3,4 for the cases when (a) ranks, and (b) exponential scores are used to replace the ordered observations within each variate. Some approximations to the critical values are proposed and evaluated.     

A note on reflecting boundaries for solutions of stochastic differential equations

In this note, sufficient conditions are given for a function g(t) to be a reflecting barrier for the sample paths of a solution process X(t) of a stochastic differential equation.     

On similarity and independence properties of composite edf goodness-of-fit tests

Many test statistics for classical simple goodness-of-fit hypothesis testing problems are distancemeasures between the distribution function of the null hypothesis distributipn and the empirical distribution function sometimes called EDF tests. If a composite parametric null hypothesis is considered in place of the simple null hypothesis, then a test statistic can be obtained from each EDF test by replacing the known distribution function of the simple problem by the Rao-Blackwell estimating distribution function. In this note we use known results to show that these Rao-Blackwell-EDF test statistics have distributions that do not depend upon parameter values, and hence that these tests are independent of a complete sufficient statistic for the parameters.     

On periodic autoregressive stochastic volatility models: structure and estimation

To capture both the volatility evolution and the periodicity feature in the autocorrelation structure exhibited by many nonlinear time series, a Periodic AutoRegressive Stochastic Volatility (PAR-SV ) model is proposed. Some probabilistic properties, namely the strict and second-order periodic stationarity, are provided. Furthermore, conditions for the existence of higher-order moments are established. The autocovariance structure of the squares and higher order powers of the PAR-SV process is studied. Its dynamic properties are shown to be consistent with financial time series empirical findings. Ways in which the model may be estimated are discussed. Finally, a simulation study of the performance of the proposed estimation methods is provided and the PAR-SV is applied to model the spot rates of the euro and US dollar both against the Algerian dinar. The empirical analysis shows that the proposed PAR-SV model can be considered as a viable alternative to the periodic generalized autoregressive conditionally heteroscedastic (PGARCH) model.     

Estimation of nonseparable models with censored dependent variables and endogenous regressors

In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719.[Crossref], [Web of Science ®] , [Google Scholar]), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging.     

Robust estimators and robust tests for the slightly contaminated stochastic logistic population models

This article introduces the robust indirect technique for the slightly contaminated stochastic logistic population models. Based on discrete sampled data with a fixed unit of time between two consecutive observations, we not only construct the robust indirect inference generalized method of moments (GMM) estimator for the model parameters, but also propose a likelihood-ratio-type indirect statistic and a robust indirect GMM saddle-point statistic for testing the parameters of interest. In addition, we develop the robust exponential tilting estimator and the robust exponential tilting test to improve their small sample performances. Finally, their finite-sample properties are studied through Monte Carlo experiments.     

On stochastic behaviors of load-sharing parallel systems

Abstract

This paper mainly investigates a general load-sharing parallel system having two units. First, we construct some comparisons among a load standby system, a warm standby system, a hot standby system and a cold standby system. Moreover, some stochastic comparisons between the load-sharing parallel system and one of its two components are obtained in the sense of the usual stochastic order. Finally, the residual life of this system and its properties are examined.     

Instrument endogeneity and identification-robust tests: Some analytical results

When some explanatory variables in a regression are correlated with the disturbance term, instrumental variable methods are typically employed to make reliable inferences. Furthermore, to avoid difficulties associated with weak instruments, identification-robust methods are often proposed. However, it is hard to assess whether an instrumental variable is valid in practice because instrument validity is based on the questionable assumption that some of them are exogenous. In this paper, we focus on structural models and analyze the effects of instrument endogeneity on two identification-robust procedures, the Anderson–Rubin (1949, AR) and the Kleibergen (2002, K) tests, with or without weak instruments. Two main setups are considered: (1) the level of “instrument” endogeneity is fixed (does not depend on the sample size) and (2) the instruments are locally exogenous, i.e. the parameter which controls instrument endogeneity approaches zero as the sample size increases. In the first setup, we show that both test procedures are in general consistent against the presence of invalid instruments (hence asymptotically invalid for the hypothesis of interest), whether the instruments are “strong” or “weak”. We also describe cases where test consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. These include, in particular, cases where the 2SLS estimator remains consistent, but the AR and K tests are asymptotically invalid. In the second setup, we find (non-degenerate) asymptotic non-central chi-square distributions in all cases, and describe cases where the non-centrality parameter is zero and the asymptotic distribution remains the same as in the case of valid instruments (despite the presence of invalid instruments). Overall, our results underscore the importance of checking for the presence of possibly invalid instruments when applying “identification-robust” tests.     

Empirical bayes approach to parameter identification in linear stochastic difference equations

Empirical Bayesian parameter estimators and predictors for linear stochastic difference equations are constructed and discussed. Some properties as consistency and asymptotic optimality are investigated. The given methods are illustrated by the example of a univariate first order autoregressive process.     

Large sample tests for testing symmetry and independence in some bivariate exponential models

Bivariate Exponential Distribution (BVED) were introduced by Freund (1961), Marshall and Olkin (1967) and Block and Basu (1974) as models for the distributions of (X,Y) the failure times of dependent components (C₁,C₂). We study the structure of these models and observe that Freund model leads to a regular exponential family with a four dimensional orthogonal parameter. Marshall-Olkin model involving three parameters leads to a conditional or piece wise exponential family and Block-Basu model which also depends on three parameters is a sub-model of the Freund model and is a curved exponential family. We obtain a large sample tests for symmetry as well as independence of (X,Y) in each of these models by using the Generalized Likelihood Ratio Tests (GLRT) or tests basesd on MLE of the parameters and root n consistent estimators of their variance-covariance matrices.     

On two conjectures about perturbations of the stochastic growth rate

The stochastic growth rate describes long-run growth of a population that lives in a fluctuating environment. Perturbation analysis of the stochastic growth rate provides crucial information for population managers, ecologists and evolutionary biologists. This analysis quantifies the response of the stochastic growth rate to changes in demographic parameters. A form of this analysis deals with changes that only occur in some environmental states. Caswell put forth two conjectures about environment-specific perturbations of the stochastic growth rate. The conjectures link the stationary distribution of the stochastic environmental process with the magnitude of some environment-specific perturbations. This note disproves one conjecture and proves the other.     

C337. Misspecified location and scale. 11. independence of and s2

A hierarchical Bayesian approach to the problem of estimating the largest normal mean is considered. Calculation of the posterior mean and the posterior variance involves, at worst, 3-dimensional numerical integration, for which an efficient Monte Carlo method of evaluation is given. An example is presented to illustrate the methodology. In the two populations case, computation of the posterior estimates can be substantially simplified and in special cases can actually be performed using closed form solutions. A simulation study has been done to compare mean square errors of some hierarchical Bayesian estimators that are expressed in closed forms and several existing estimators of the larger mean.     

Preservation properties of stochastic orders by transformation to the transmuted-G model

Abstract

The transmuted-G model is a useful technique to construct some new distributions by adding a parameter. This paper considers stochastic comparisons in the transmuted-G family with different parameters and different baseline distributions in the sense of the usual stochastic, shifted stochastic, proportional stochastic and shifted proportional stochastic orders. Also, we present a necessary and sufficient condition for existence of the moments of the transmuted-G model and then we obtain some bounds for the survival and aging intensity functions of the transmuted-G model conditioned on its parameter and its baseline distribution.     

On testing for independence between the innovations of several time series

Test statistics for checking the independence between the innovations of several time series are developed. The time series models considered allow for general specifications for the conditional mean and variance functions that could depend on common explanatory variables. In testing for independence between more than two time series, checking pairwise independence does not lead to consistent procedures. Thus a finite family of empirical processes relying on multivariate lagged residuals are constructed, and we derive their asymptotic distributions. In order to obtain simple asymptotic covariance structures, Möbius transformations of the empirical processes are studied, and simplifications occur. Under the null hypothesis of independence, we show that these transformed processes are asymptotically Gaussian, independent, and with tractable covariance functions not depending on the estimated parameters. Various procedures are discussed, including Cramér–von Mises test statistics and tests based on non‐parametric measures. The ranks of the residuals are considered in the new methods, giving test statistics which are asymptotically margin‐free. Generalized cross‐correlations are introduced, extending the concept of cross‐correlation to an arbitrary number of time series; portmanteau procedures based on them are discussed. In order to detect the dependence visually, graphical devices are proposed. Simulations are conducted to explore the finite sample properties of the methodology, which is found to be powerful against various types of alternatives when the independence is tested between two and three time series. An application is considered, using the daily log‐returns of Apple, Intel and Hewlett‐Packard traded on the Nasdaq financial market. The Canadian Journal of Statistics 40: 447–479; 2012 © 2012 Statistical Society of Canada