Local Power Analysis Research Articles

A conditional distribution function-based measure for independence and [formula omitted]-sample tests in multivariate data

We introduce a new index to measure the degree of dependence and test for independence between two random vectors. The index is obtained by generalizing the Cramér-von Mises distances between the conditional and marginal distribution functions via the projection-averaging technique. If one of the random vectors is categorical with K categories, we propose slicing estimators to estimate our index. We conduct an asymptotic analysis for the slicing estimators, considering both situations where K is fixed and where K is allowed to increase with the sample size. When both random vectors are continuous, we introduce a kernel regression estimator for the proposed index, demonstrating that its asymptotic null distribution follows a normal distribution and conducting a local power analysis for the kernel estimator-based independence test. The proposed tests are studied via simulation, with a real data application presented to illustrate our methods.

A NOVEL APPROACH TO PREDICTIVE ACCURACY TESTING IN NESTED ENVIRONMENTS

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g., stationary and local to unit root). A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.

A Novel Approach to Predictive Accuracy Testing in Nested Environments

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample MSE loss differentials between the two competing models, leads to nuisance parameter free Gaussian asymptotics and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g. stationary and local to unit root). A local power analysis also establishes its ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.

On universally consistent and fully distribution-free rank tests of vector independence

Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent tests of independence between pairs of random variables. Using ranks is especially appealing for continuous data as tests become distribution-free. However, the traditional concept of ranks relies on ordering data and is, thus, tied to univariate observations. As a result, it has long remained unclear how one may construct distribution-free yet consistent tests of independence between random vectors. This is the problem addressed in this paper, in which we lay out a general framework for designing dependence measures that give tests of multivariate independence that are not only consistent and distribution-free but which we also prove to be statistically efficient. Our framework leverages the recently introduced concept of center-outward ranks and signs, a multivariate generalization of traditional ranks, and adopts a common standard form for dependence measures that encompasses many popular examples. In a unified study, we derive a general asymptotic representation of center-outward rank-based test statistics under independence, extending to the multivariate setting the classical Hájek asymptotic representation results. This representation permits direct calculation of limiting null distributions and facilitates a local power analysis that provides strong support for the center-outward approach by establishing, for the first time, the nontrivial power of center-outward rank-based tests over root-n neighborhoods within the class of quadratic mean differentiable alternatives.

Specification Tests for Families of Discrete Distributions with Applications to Insurance Claims Data

Families of distributions are commonly used to model insurance claims data that require flexible distributional forms in a satisfactory manner, but the specification problem to assess the goodness-of-fit of the hypothesized model can sometimes be a challenge due to the complexity of the likelihood function of the family of distributions involved. The previous work shows that these specification problems can be attacked by means of semi-parametric tests based on generalized method of moment (GMM) estimators. While the approach can be directly applied to both discrete and continuous families of distributions, the paper focuses on developing a testing strategy within a framework of discrete families of distributions. Both the local power analysis and the approximate slope method demonstrate the excellent performance of these tests. The finite-sample performance of the tests, based on both asymptotic and bootstrap critical values, are also discussed and are compared with established methods that require the complete specification of likelihood functions.

Semi-parametric homogeneity test and sample size calculation for a two-sample problem under an inequality constraint

In medical researches such as case-control studies with contaminated controls, frequently encountered is a particular two-sample testing problem in which one sample has a mixture structure. It is a very common case that the exposure in a case-control study may have a positive (or negative) effect on the response variable if the effect exists. This is often ignored by existing tests, which would lead to potentially power loss. Meanwhile, it is of much practical importance to determine a minimal sample size to reach a target power. Based on empirical likelihood and density ratio model, we develop a new EM-test by incorporating the inequality information in the alternative. We show that the proposed EM-test has a mixture of zero and χ12 limiting distribution under the null hypothesis. Its local power analysis and sample size calculations are also investigated. A simulation study and two real data analyses are provided to illustrate the proposed EM-test and sample size formula.

Estimation of heterogeneous panels with systematic slope variations

We analyse estimation procedures for the panel data models with heterogeneous slopes. Specifically we take into account a possible dependence between regressors and heterogeneous slope coefficients, which is referred to as systematic variation. It is shown that under relevant forms of systematic slope variations (i) the pooled OLS estimator is severely biased, (ii) Swamy’s GLS estimator is inconsistent if the number of time periods T is fixed, whereas (iii) the mean-group estimator always provides consistent estimators at the risk of high variances. Following Mundlak (1978) we propose an augmentated regression which results in a simple and robust version of the pooled estimator. The latter approach avoids the risk of large standard errors of the mean-group estimator, whenever T is small. We also propose two test statistics for systematic slope variation using the Lagrange multiplier and Hausman principles. We derive their asymptotic properties and provide a local power analysis of both test statistics. Monte Carlo experiments corroborate our theoretical findings and show that for all combinations of N and T the Mundlak-type GLS estimator outperform all other estimators.

EM-test for homogeneity in a two-sample problem with a mixture structure

ABSTRACTIn many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials, a two-sample problem with one of the samples having a mixture structure often arises. Due to the importance and wide applications of scale mixtures and location mixtures, we consider in this paper the case that the component densities differ only in scale parameters and the case that the component densities differ only in location parameters, and further construct an EM-test for the two-sample problem under each case. We show that both the EM-tests possess a chi-squared null limiting distribution. The local power analysis and sample size calculations are also investigated. Finally, the simulation studies and real data analysis demonstrate that the proposed EM-tests have better performance than the existing methods.

Long-range functional coupling predicts performance: Oscillatory EEG networks in multisensory processing

The integration of sensory signals from different modalities requires flexible interaction of remote brain areas. One candidate mechanism to establish communication in the brain is transient synchronization of oscillatory neural signals. Although there is abundant evidence for the involvement of cortical oscillations in brain functions based on the analysis of local power, assessment of the phase dynamics among spatially distributed neuronal populations and their relevance for behavior is still sparse. In the present study, we investigated the interaction between remote brain areas by analyzing high-density electroencephalogram (EEG) data obtained from human participants engaged in a visuotactile pattern matching task. We deployed an approach for purely data-driven clustering of neuronal phase coupling in source space, which allowed imaging of large-scale functional networks in space, time and frequency without defining a priori constraints. Based on the phase coupling results, we further explored how brain areas interacted across frequencies by computing phase-amplitude coupling. Several networks of interacting sources were identified with our approach, synchronizing their activity within and across the theta (∼5 Hz), alpha (∼10 Hz), and beta (∼20 Hz) frequency bands and involving multiple brain areas that have previously been associated with attention and motor control. We demonstrate the functional relevance of these networks by showing that phase delays – in contrast to spectral power – were predictive of task performance. The data-driven analysis approach employed in the current study allowed an unbiased examination of functional brain networks based on EEG source level connectivity data. Showcased for multisensory processing, our results provide evidence that large-scale neuronal coupling is vital to long-range communication in the human brain and relevant for the behavioral outcome in a cognitive task.

CUMULATED SUM OF SQUARES STATISTICS FOR NONLINEAR AND NONSTATIONARY REGRESSIONS

We show that the cumulated sum of squares statistic has a standard Brownian bridge–type asymptotic distribution in nonlinear regression models with (possibly) nonstationary regressors. This contrasts with cumulated sum statistics which have been previously studied and whose asymptotic distribution has been shown to depend on the functional form and the stochastic properties, such as persistence and stationarity, of the regressors. A recursive version of the test is also considered. A local power analysis is provided, and through simulations, we show that the test has good size and power properties across a variety of situations.

Alternative over-identifying restriction test in the GMM estimation of panel data models

A new over-identifying restriction test in the generalized method of moments (GMM) estimation of panel data models is proposed. In contrast to the conventional over-identifying restriction test, where the sample covariance matrix of the moment conditions is used in the weighting matrix, the proposed test uses a block diagonal weighting matrix constructed from the efficient optimal weighting matrix. It is shown that the proposed test statistic asymptotically follows the weighted sum of the chi-square distribution with one degree of freedom. A detailed local power analysis is provided for dynamic panel data models, and it is demonstrated that the new test has a comparable power to the conventional J test in many cases. The Monte Carlo simulations reveal that the proposed test has a substantially better size property than the conventional test does.

Movimentos sociais e a formação política de mulheres na luta por creches: a experiência do “Artcreche” em São Gonçalo

O artigo objetiva inventariar e atualizar a luta de Movimentos Sociais urbanos, em especial do Movimento de Articulação das Creches de São Gonçalo (ArtCreche) que desde 1980 vem construindo uma pauta coletiva de demandas e lutas junto ao poder público e Sociedade civil em São Gonçalo. Do ponto de vista teórico-conceitual, enfocamos a luta do ArtCreche a partir do diálogo com autores/as que fazem alusão à eclosão dos movimentos populares na década de 1980, bem como ao seu refluxo no período de pós-democratização brasileira, e que remetem ao contexto de mudanças frente aos paradigmas clássicos e contemporâneos de participação popular. No artigo investigamos a luta de mulheres pelo direito à creche a partir de uma pesquisa qualitativa, de cunho participante, que intenciona investigar o trabalho cotidiano e as lutas de um grupo de educadoras populares do Movimento ARTCreche, a partir da realização de entrevistas semi-estruturadas, priorizando uma análise do poder local em diálogo com lutas contemporâneas pelo direito à creche nas periferias urbanas.

Testing for Money Illusion Hypothesis in Aggregate Consumption Function: Mixed Data Sampling Approach

Testing for the money illusion hypothesis in aggregate consumption function generally involves a regression model that projects real consumption onto nominal income and a consumer price index. While consumption and income data are typically sampled at a quarterly level, price data are often available at a monthly level. This paper takes advantage of mixed data sampling (MIDAS) techniques in order to exploit monthly price data. We show via local power analysis and Monte Carlo simulations that our approach yields deeper economic insights and higher statistical precision than the previous single-frequency approach that aggregates price data into a quarterly level. In particular, the MIDAS approach allows for heterogeneous effects of monthly prices on real consumption within each quarter. In empirical applications we find that the heterogeneous effects indeed exist in Japan and the U.S.

Alternative Over-Identifying Restriction Test in GMM Estimation of Panel Data Models

This paper proposes a new over-identifying restriction test called the diagonal J test in the generalized method of moments (GMM) framework. Different from the conventional over-identifying restriction test, where the sample covariance matrix of moment conditions is used in the weighting matrix, the proposed test uses a block diagonal weighting matrix constructed from the efficient optimal weighting matrix. We show that the proposed test statistic asymptotically follows a weighted sum of chi-square distributions with one degree of freedom. Since we need to decompose the moment conditions into groups when implementing the proposed test, we propose two methods to split the moment conditions. The first is to use K-means method that is widely used in the cluster analysis. The second is to utilize the special structure of moment conditions where they are available sequentially. Such a case typically appears in the panel data models. We also conduct a local power analysis of the diagonal J test in the context of dynamic panel data models, and show that the proposed test has almost the same power as the standard J test in some specific cases. Monte Carlo simulation reveals that the proposed test has substantially better size property than the standard test does, while having almost no power loss in comparison to the standard test when it has no size distortions.

Using the Sun to estimate Earth-like planets detection capabilities

Context. Radial velocity (RV) time series are strongly impacted by the presence of stellar activity. In a series of papers, we have reconstructed solar RV variations over a full solar cycle from observed solar structures (spots and plages) and studied their impact on the detectability of an Earth-mass planet in the habitable zone of the Sun as seen edge-on from a neighbour star in several typical cases. We found that the convective contribution dominates the RV times series.Aims. The objective of this paper is twofold: to determine detection limits on a Sun-like star seen edge-on with different levels of convection and to estimate the performance of the activity correction using a Ca index.Methods. We apply two methods to compute the detection limits: a correlation-based method and a local power analysis method, which both take into account the temporal structure of the observations. Furthermore, we test two methods using a Ca index to correct for the convective contribution to the RV: a sinusoidal fit to the Ca variations and a linear fit to the RV-Ca relation. In both cases, we use observed Ca and reconstructed Ca to study the various effects and limitations of our estimations.Results. We confirm that an excellent sampling is necessary to have detection limits below 1 M Earth (e.g. 0.2−0.3 M Earth ) when there is no convection and a low RV noise. With convection, the detection limit is always above 7 M Earth . The two correction methods perform similarly when the Ca time series are noisy, leading to a significant improvement (down to a few M Earth ), which is above the 1 M Earth limit. With a very good Ca noise (signal to noise ratio, S/N, around 130), the sinusoidal method does not get significantly better because it is dominated by the fact that the solar cycle is not sinusoidal, but the RV-Ca method can reach the 1 M Earth for an excellent Ca noise level.Conclusions. For Sun-like conditions and under the simplifying assumptions considered, we first conclude that the detection limit of a few M Earth planet can be reached providing good sampling and Ca noise. The detection of a 1 M Earth may be possible, but only with an excellent temporal sampling and an excellent Ca index noise level: we estimate that a probability larger than 50% to detect a 1 M Earth at 1.2 AU requires more than 1000 well-sampled observations and a Ca S/N larger than 130.

Comparison of different exoplanet mass detection limit methods using a sample of main-sequence intermediate-type stars

The radial velocity (RV) technique is a powerful tool for detecting extrasolar planets and deriving mass detection limits that are useful for constraining planet pulsations and formation models. Detection limit methods must take into account the temporal distribution of power of various origins in the stellar signal. These methods must also be able to be applied to large samples of stellar RV time series We describe new methods for providing detection limits. We compute the detection limits for a sample of ten main sequence stars, which are of G-F-A type, in general active, and/or with detected planets, and various properties. We use them to compare the performances of these methods with those of two other methods used in the litterature. We obtained detection limits in the 2-1000 day period range for ten stars. Two of the proposed methods, based on the correlation between periodograms and the power in the periodogram of the RV time series in specific period ranges, are robust and represent a significant improvement compared to a method based on the root mean square of the RV signal. We conclude that two of the new methods (correlation-based method and local power analysis, i.e. LPA, method) provide robust detection limits, which are better than those provided by methods that do not take into account the temporal sampling.

The power of unit root tests against nonlinear local alternatives

This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and tests built specifically against stationary nonlinear models. In particular, we focus on the popular test proposed by Kapetanios et al. (2003, Journal of Econometrics 112, 359–379) in comparison to the linear Dickey–Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behaviour of the tests in the nonlinear case; the reason for such behaviour is the interplay of non‐stationarity and nonlinearity. In particular, we show that nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the ‘amount of nonlinearity’), rendering the linear test more powerful than the nonlinear one. Should however the error variance be small, the nonlinear test has better power against local alternatives. We illustrate this in an asymptotic framework of what we call persistent nonlinearity. The theoretical findings of this article explain previous results in the literature obtained by simulation. Furthermore, our own simulation results suggest that the user‐specified adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) has a much higher impact on the power of unit root tests than accounting for nonlinearity, at least under local (linear or nonlinear) alternatives.

Using Difference‐Based Methods for Inference in Regression with Fractionally Integrated Processes

Abstract. This paper suggests a difference‐based method for inference in the regression model involving fractionally integrated processes. Under suitable regularity conditions, our method can effectively deal with the inference problems associated with the regression model consisting of nonstationary, stationary and intermediate memory regressors, simultaneously. Although the difference‐based method provides a very flexible modelling framework for empirical studies, the implementation of this method is extremely easy, because it completely avoids the difficult problems of choosing a kernel function, a bandwidth parameter, or an autoregressive lag length for the long‐run variance estimation. The asymptotic local power of our method is investigated with a sequence of local data‐generating processes (DGP) in what Davidson and MacKinnon [Canadian Journal of Economics. (1985) Vol. 18, pp. 38–57] call ‘regression direction’. The simulation results indicate that the size control of our method is excellent even when the sample size is only 100, and the pattern of power performance is highly consistent with the theoretical finding from the asymptotic local power analysis conducted in this paper.

Generalized Spectral Tests for Serial Dependence

Summary Two tests for serial dependence are proposed using a generalized spectral theory in combination with the empirical distribution function. The tests are generalizations of the Cramér-von Mises and Kolmogorov-Smirnov tests based on the standardized spectral distribution function. They do not involve the choice of a lag order, and they are consistent against all types of pairwise serial dependence, including those with zero autocorrelation. They also require no moment condition and are distribution free under serial independence. A simulation study compares the finite sample performances of the new tests and some closely related tests. The asymptotic distribution theory works well in finite samples. The generalized Cramér-von Mises test has good power against a variety of dependent alternatives and dominates the generalized Kolmogorov-Smirnov test. A local power analysis explains some important stylized facts on the power of the tests based on the empirical distribution function.

Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach

This paper proposes some tests for parameter constancy in linear regressions. The tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free. The local power analysis reveals that the proposed tests have nontrivial local power against a wide range of alternatives. In particular, the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances. The model allows for both dynamic and trending regressors. The residuals may be obtained based on any root-n consistent estimator (under the null) of regression parameters. As an intermediate result, some weak convergence for (stochastically) weighted sequential empirical processes is established.