The limiting power of point optimal autocorrelation tests

This paper considers the point optimal tests for AR(1) errors in the linear regression model. It is shown that these tests have the same limiting power characteristics as the Durbin-Watson test. . The limiting power is zero or one when the regression has no intercept, but lies strictly between these values when an intercept is included.     

The limiting power of the durbin-watson test

We compute the limiting povwer of the Durbin-Watson test in a general linear regression model Our treatment includes previous results due to W. Kramer and H, Zeisel as well as new results. In particular, we provide new insight under which conditions the limiting power is zero or one. Stochastic-simulations correspond to our investigations.     

Score tests for heterogeneity and overdispersion in zero‐inflated Poisson and binomial regression models

Hall (2000) has described zero‐inflated Poisson and binomial regression models that include random effects to account for excess zeros and additional sources of heterogeneity in the data. The authors of the present paper propose a general score test for the null hypothesis that variance components associated with these random effects are zero. For a zero‐inflated Poisson model with random intercept, the new test reduces to an alternative to the overdispersion test of Ridout, Demério & Hinde (2001). The authors also examine their general test in the special case of the zero‐inflated binomial model with random intercept and propose an overdispersion test in that context which is based on a beta‐binomial alternative.     

面板数据单位根似然比检验研究

本文采用似然比类检验统计量进行面板单位根检验（简称为LR检验）研究,在局部备择假设成立的条件下,推导了其在无确定项、仅含截距项以及存在线性时间趋势项三种模型下所对应的渐近分布与局部渐近势函数。Monte Carlo模拟结果显示,当面板数据中含确定项（截距项或时间趋势项）时,LR检验水平比LLC和IPS检验水平更接近于给定的显著性检验水平;此外,当面板数据中包含发散个体时,经水平修正后的LR检验势要远远高于经水平修正后的LLC与IPS检验势,其中,经水平修正后的LLC与IPS检验势接近于零。     

On tests for normality of experimental error in ridge regression

Considered are tests for normality of the errors in ridge regression. If an intercept is included in the model, it is shown that test statistics based on the empirical distribution function of the ridge residuals have the same limiting distribution as in the one-sample test for normality with estimated mean and variance. The result holds with weak assumptions on the behavior of the independent variables; asymptotic normality of the ridge estimator is not required.     

Likelihood ratio type unit root tests for ar(1)models with nonconsecutive observations

For the nonconsecutively observed or missing data situation likelihood ratio type unit root tests in AR(1)models containing an intercept or both an intercept and a time trend are proposed and are shown to have the same limiting distributions as the likelihood ratio tests for the complete data case as tabulated by Dickey and Fuller(1981). Some simulation results on our tests in finite samples under A–B sampling schemes are also presented.     

Performance of asymmetric links and correction methods for imbalanced data in binary regression

In binary regression, imbalanced data result from the presence of values equal to zero (or one) in a proportion that is significantly greater than the corresponding real values of one (or zero). In this work, we evaluate two methods developed to deal with imbalanced data and compare them to the use of asymmetric links. The results based on simulation study show, that correction methods do not adequately correct bias in the estimation of regression coefficients and that the models with power links and reverse power considered produce better results for certain types of imbalanced data. Additionally, we present an application for imbalanced data, identifying the best model among the various ones proposed. The parameters are estimated using a Bayesian approach, considering the Hamiltonian Monte-Carlo method, utilizing the No-U-Turn Sampler algorithm and the comparisons of models were developed using different criteria for model comparison, predictive evaluation and quantile residuals.     

Sample size calculation for method validation using linear regression

In this article, we present a method for sample size calculation for studies involving both the intercept and slope parameters of a simple linear regression model. Some methods have been proposed in the literature to determine the adequate sample size. However, they are usually based on the line slope only. We propose a method based on the F statistic that involves both the intercept and the slope parameters of the model. The validation process is conducted by fitting a simple linear regression model and by testing a zero intercept and unity slope hypothesis. Compared to a traditional method and using Monte Carlo simulations, encouraging results attest for the clear superiority of the proposed method. The article ends with a real-life example showing the value of the new method in practice.     

Leverage and Regression through the Origin

The problem of deciding whether an intercept model or a no-intercept model is more appropriate for a given set of data is a problem with no simple solution. Often, the underlying physical situation will suggest an appropriate model; however, there still may be interest in assessing which model best fits the data or is the better predictor. In this article a different interpretation of regression through the origin is derived, that of a full fit to the original data set augmented by one further point. Examination of the leverage and influence of the augmented data point can provide help in comparing the models.     

Testing for an excessive number of zeros in time series of bounded counts

For the modeling of bounded counts, the binomial distribution is a common choice. In applications, however, one often observes an excessive number of zeros and extra-binomial variation, which cannot be explained by a binomial distribution. We propose statistics to evaluate the number of zeros and the dispersion with respect to a binomial model, which is based on the sample binomial index of dispersion and the sample binomial zero index. We apply this index to autocorrelated counts generated by a binomial autoregressive process of order one, which also includes the special case of independent and identically (i. i. d.) bounded counts. The limiting null distributions of the proposed test statistics are derived. A Monte-Carlo study evaluates their size and power under various alternatives. Finally, we present two real-data applications as well as the derivation of effective sample sizes to illustrate the proposed methodology.     

样本选择模型截距项的半参数估计及应用———户籍工资差异分解研究

样本选择模型是解决样本选择问题的主要工具,广泛应用于工资差异分解、平均处理效应测算等实证研究。截距项的估计是样本选择模型半参数估计中相对独立且重要的一部分,现有的以无穷处识别为代表的半参数估计方法存在窗宽参数难以选取的问题。为此,本文把无穷处识别等价转化为边界处识别,并基于新的识别关系给出样本选择模型截距项的核估计方法。这种新方法的好处在于将样本选择模型截距项的估计纳入核估计框架中,从而可以采用经验法则解决现有方法的窗宽选取难题。数值模拟结果表明,本文所提出的估计方法在不同设定下均有良好的有限样本表现。把这种新的半参数估计方法应用于户籍工资差异分解后发现,我国劳动力市场目前不存在明显的户籍差别待遇。     

The analytic construction of D-optimal designs for the two-variable binary logistic regression model without interaction

Candidate locally D-optimal designs for the binary two-variable logistic model with no interaction, which comprise 3 and 4 support points lying in the first quadrant of the two-dimensional Euclidean space, were introduced by Haines et al. (D-optimal designs for logistic regression in two variables. In: Lopez-Fidalgo J, Rodrigez-Diaz JM, Torsney B, editors. MODA8 – advances in model-oriented designs and analysis. Heidelberg: Physica-Verlag; 2007. p. 91–98). The authors proved algebraically the global D-optimality of the 3-point design for the special case in which the intercept parameter is equal to?1.5434. However for other selected values of the intercept parameter, the global D-optimality of the proposed 3- and 4-point designs was only demonstrated numerically. In this paper, we provide analytical proofs of the D-optimality of these 3- and 4-point designs for all negative and zero intercept parameters of the binary two-variable logistic model with no interaction. The results are extended to the construction of D-optimal designs on a rectangular design space and illustrated by means of two examples of which one is a real example taken from the literature.     

Generalized symmetrical partial linear model

In this work, we propose a new model called generalized symmetrical partial linear model, based on the theory of generalized linear models and symmetrical distributions. In our model the response variable follows a symmetrical distribution such a normal, Student-t, power exponential, among others. Following the context of generalized linear models we consider replacing the traditional linear predictors by the more general predictors in whose case one covariate is related with the response variable in a non-parametric fashion, that we do not specified the parametric function. As an example, we could imagine a regression model in which the intercept term is believed to vary in time or geographical location. The backfitting algorithm is used for estimating the parameters of the proposed model. We perform a simulation study for assessing the behavior of the penalized maximum likelihood estimators. We use the quantile residuals for checking the assumption of the model. Finally, we analyzed real data set related with pH rivers in Ireland.     

Robust difference-based outlier detection

Abstract

In this paper, we propose an outlier-detection approach that uses the properties of an intercept estimator in a difference-based regression model (DBRM) that we first introduce. This DBRM uses multiple linear regression, and invented it to detect outliers in a multiple linear regression. Our outlier-detection approach uses only the intercept; it does not require estimates for the other parameters in the DBRM. In this paper, we first employed a difference-based intercept estimator to study the outlier-detection problem in a multiple regression model. We compared our approach with several existing methods in a simulation study and the results suggest that our approach outperformed the others. We also demonstrated the advantage of our approach using a real data application. Our approach can extend to nonparametric regression models for outliers detection.     

Increasing the Power of the Test Through Pre-Test – A Robust Method

Robust test procedures are developed for testing the intercept of a simple regression model when the slope is (i) completely unspecified, (ii) specified to a fixed value, or (iii) suspected to be a fixed value. Defining (i) unrestricted (UT), (ii) restricted (RT), and (iii) pre-test test (PTT) functions for the intercept parameter under the three choices of the slope, tests are formulated using the M-estimation methodology. The asymptotic distributions of the test statistics and their asymptotic power functions are derived. The analytical and graphical comparisons of the tests reveal that the PTT achieves a reasonable dominance over the other tests.     

Testing base load with non-sample prior information on process load

Inference about population parameters could be improved using non- sample prior information (NSPI) from reliable sources along with the available data. This paper studies the problem of testing the intercept parameter of a simple regression model when NSPI is available on the value of the slope. The information on the slope may have the three different scenarios: (i) unknown (unspecified), (ii) known (certain or specified), and (iii) uncertain if the suspected value is unsure, for which we define the unrestricted test (UT), restricted test (RT) and pre-test test (PTT) for the intercept parameter. The test statistics, their sampling distributions, and power functions are derived. Comparison of the power functions and size of the tests are used to search and recommend a best test. The study reveals that the PTT has a reasonable dominance over the UT and RT both in terms of achieving highest power and lowest size.     

Goodness-of-fit testing under long memory

This paper discusses the problem of fitting a distribution function to the marginal distribution of a long memory moving average process. Because of the uniform reduction principle, unlike in the i.i.d. set up, classical tests based on empirical process are relatively easy to implement. More importantly, we discuss fitting the marginal distribution of the error process in location, scale, location–scale and linear regression models. An interesting observation is that in the location model, location–scale model, or more generally in the linear regression models with non-zero intercept parameter, the null weak limit of the first order difference between the residual empirical process and the null model is degenerate at zero, and hence it cannot be used to fit an error distribution in these models for the large samples. This finding is in sharp contrast to a recent claim of Chan and Ling (2008) that the null weak limit of such a process is a continuous Gaussian process. This note also proposes some tests based on the second order difference for the location case. Another finding is that residual empirical process tests in the scale problem are robust against not knowing the scale parameter.     

A Note on an Approximation of the Mobile Communications Expenditures Distribution Function Using a Mixture Model

Approximating the distribution of mobile communications expenditures (MCE) is complicated by zero observations in the sample. To deal with the zero observations by allowing a point mass at zero, a mixture model of MCE distributions is proposed and applied. The MCE distribution is specified as a mixture of two distributions, one with a point mass at zero and the other with full support on the positive half of the real line. The model is empirically verified for individual MCE survey data collected in Seoul, Korea. The mixture model can easily capture the common bimodality feature of the MCE distribution. In addition, when covariates were added to the model, it was found that the probability that an individual has non-expenditure significantly varies with some variables. Finally, the goodness-of-fit test suggests that the data are well represented by the mixture model.     

On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests

Elliott and Müller (2006) considered the problem of testing for general types of parameter variations, including infrequent breaks. They developed a framework that yields optimal tests, in the sense that they nearly attain some local Gaussian power envelop. The main ingredient in their setup is that the variance of the process generating the changes in the parameters must go to zero at a fast rate. They recommended the so-called qL?L test, a partial sums type test based on the residuals obtained from the restricted model. We show that for breaks that are very small, its power is indeed higher than other tests, including the popular sup-Wald (SW) test. However, the differences are very minor. When the magnitude of change is moderate to large, the power of the test is very low in the context of a regression with lagged dependent variables or when a correction is applied to account for serial correlation in the errors. In many cases, the power goes to zero as the magnitude of change increases. The power of the SW test does not show this non-monotonicity and its power is far superior to the qL?L test when the break is not very small. We claim that the optimality of the qL?L test does not come from the properties of the test statistics but the criterion adopted, which is not useful to analyze structural change tests. Instead, we use fixed-break size asymptotic approximations to assess the relative efficiency or power of the two tests. When doing so, it is shown that the SW test indeed dominates the qL?L test and, in many cases, the latter has zero relative asymptotic efficiency.     

Power properties of the modified CUSUM tests

The CUSUM test has played an important role in theory and applications related to structural change, but its drawback is that it loses power when the break is orthogonal to the mean of the regressors. In this study, we consider two modified CUSUM tests that have been proposed, implicitly or explicitly, in the literature to detect such structural changes and investigate the limiting power properties of these tests under a fixed alternative. We demonstrate that the modified tests are superior to the classic tests in terms of both asymptotic theory and in finite samples when detecting an orthogonal structural shift.