Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Improving small area estimation by combining surveys: new perspectives in regional statistics

A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey (EPA) and the Barometer in Spain for our study.

A general theory of rank testing

This paper develops an approach to rank testing that nests all existing rank tests andsimplifies their asymptotics. The approach is based on the fact that implicit in every ranktest there are estimators of the null spaces of the matrix in question. The approach yieldsmany new insights about the behavior of rank testing statistics under the null as well as localand global alternatives in both the standard and the cointegration setting. The approach alsosuggests many new rank tests based on alternative estimates of the null spaces as well as thenew fixed-b theory. A brief Monte Carlo study illustrates the results.

Testing Normality : A GMM Approach

In this paper, we consider testing marginal normal distributional assumptions. More precisely, we propose tests based on moment conditions implied by normality. These moment conditions are known as the Stein (1972) equations. They coincide with the first class of moment conditions derived by Hansen and Scheinkman (1995) when the random variable of interest is a scalar diffusion. Among other examples, Stein equation implies that the mean of Hermite polynomials is zero. The GMM approach we adopted is well suited for two reasons. It allows us to study in detail the parameter uncertainty problem, i.e., when the tests depend on unknown parameters that have to be estimated. In particular, we characterize the moment conditions that are robust against parameter uncertainty and show that Hermite polynomials are special examples. This is the main contribution of the paper. The second reason for using GMM is that our tests are also valid for time series. In this case, we adopt a Heteroskedastic-Autocorrelation-Consistent approach to estimate the weighting matrix when the dependence of the data is unspecified. We also make a theoretical comparison of our tests with Jarque and Bera (1980) and OPG regression tests of Davidson and MacKinnon (1993). Finite sample properties of our tests are derived through a comprehensive Monte Carlo study. Finally, three applications to GARCH and realized volatility models are presented.

A jackknife variance estimator for unequal probability sampling

The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs.We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.

Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Finite sample weighting of recursive forecast errors

This paper proposes and tests a new framework for weighting recursive out-of-sample prediction errors according to their corresponding levels of in-sample estimation uncertainty. In essence, we show how to use the maximum possible amount of information from the sample in the evaluation of the prediction accuracy, by commencing the forecasts at the earliest opportunity and weighting the prediction errors. Via a Monte Carlo study, we demonstrate that the proposed framework selects the correct model from a set of candidate models considerably more often than the existing standard approach when only a small sample is available. We also show that the proposed weighting approaches result in tests of equal predictive accuracy that have much better sizes than the standard approach. An application to an exchange rate dataset highlights relevant differences in the results of tests of predictive accuracy based on the standard approach versus the framework proposed in this paper.

Infant mortality model for lifetime data

In this paper we introduce a parametric model for handling lifetime data where an early lifetime can be related to the infant-mortality failure or to the wear processes but we do not know which risk is responsible for the failure. The maximum likelihood approach and the sampling-based approach are used to get the inferences of interest. Some special cases of the proposed model are studied via Monte Carlo methods for size and power of hypothesis tests. To illustrate the proposed methodology, we introduce an example consisting of a real data set.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. A Monte Carlo study explores the finite sample performance of this procedure and evaluates the forecasting accuracy of models selected by this procedure. Two empirical applications confirm the usefulness of the model selection procedure proposed here for forecasting.

The NINJA-2 project: detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave (GW) astrophysics communities. The purpose of NINJA is to study the ability to detect GWs emitted from merging binary black holes (BBH) and recover their parameters with next-generation GW observatories. We report here on the results of the second NINJA project, NINJA-2, which employs 60 complete BBH hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. In a 'blind injection challenge' similar to that conducted in recent Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo science runs, we added seven hybrid waveforms to two months of data recoloured to predictions of Advanced LIGO (aLIGO) and Advanced Virgo (AdV) sensitivity curves during their first observing runs. The resulting data was analysed by GW detection algorithms and 6 of the waveforms were recovered with false alarm rates smaller than 1 in a thousand years. Parameter-estimation algorithms were run on each of these waveforms to explore the ability to constrain the masses, component angular momenta and sky position of these waveforms. We find that the strong degeneracy between the mass ratio and the BHs' angular momenta will make it difficult to precisely estimate these parameters with aLIGO and AdV. We also perform a large-scale Monte Carlo study to assess the ability to recover each of the 60 hybrid waveforms with early aLIGO and AdV sensitivity curves. Our results predict that early aLIGO and AdV will have a volume-weighted average sensitive distance of 300 Mpc (1 Gpc) for 10M circle dot + 10M circle dot (50M circle dot + 50M circle dot) BBH coalescences. We demonstrate that neglecting the component angular momenta in the waveform models used in matched-filtering will result in a reduction in sensitivity for systems with large component angular momenta. This reduction is estimated to be up to similar to 15% for 50M circle dot + 50M circle dot BBH coalescences with almost maximal angular momenta aligned with the orbit when using early aLIGO and AdV sensitivity curves.

Consistent estimation of the fixed effects ordered logit model

The paper considers panel data methods for estimating ordered logit models with individual-specific correlated unobserved heterogeneity. We show that a popular approach is inconsistent, whereas some consistent and efficient estimators are available, including minimum distance and generalized method-of-moment estimators. A Monte Carlo study reveals the good properties of an alternative estimator that has not been considered in econometric applications before, is simple to implement and almost as efficient. An illustrative application based on data from the German Socio-Economic Panel confirms the large negative effect of unemployment on life satisfaction that has been found in the previous literature.

Semiparametric smooth-coefficient stoachastic frontier model

This paper proposes a semiparametric smooth-coefficient stochastic production frontier model where all the coefficients are expressed as some unknown functions of environmental factors. The inefficiency term is multiplicatively decomposed into a scaling function of the environmental factors and a standard truncated normal random variable. A testing procedure is suggested for the relevance of the environmental factors. Monte Carlo study shows plausible ¯nite sample behavior of our proposed estimation and inference procedure. An empirical example is given, where both the semiparametric and standard parametric models are estimated and results are compared.