A self-normalizing approach to the specification test of mixed-frequency models

In econometrics and finance, variables are collected at different frequencies. One straightforward regression model is to aggregate the higher frequency variable to match the lower frequency with a fixed weight function. However, aggregation with fixed weight functions may overlook useful information in the higher frequency variable. On the other hand, keeping all higher frequencies may result in overly complicated models. In literature, mixed data sampling (MIDAS) regression models have been proposed to balance between the two. In this article, a new model specification test is proposed that can help decide between the simple aggregation and the MIDAS model.     

Hayter and Tsui's test with double sampling for the vector mean of multivariate normal population

Abstract

In this paper, we introduce a version of Hayter and Tsui's statistical test with double sampling for the vector mean of a population under multivariate normal assumption. A study showed that this new test was more or as efficient than the well-known Hotelling's T² with double sampling. Some nice features of Hayter and Tsui's test are its simplicity of implementation and its capability of identifying the errant variables when the null hypothesis is rejected. Taking that into consideration, a new control chart called HTDS is also introduced as a tool to monitor multivariate process vector mean when using double sampling.     

Some estimation procedures using a linear model in successive sampling

ABSTRACT

In successive sampling some recent works depict the use of super-population models where information on stable auxiliary variable over occasions has been utilized. Stability character of auxiliary variable may not sustain, if the duration between occasions is large. To cope with such situations, the present work is an attempt to develop some estimation procedures by utilizing the information on two independent auxiliary variables through a linear super-population model. Some estimators are proposed to estimate the current population mean in two occasions successive (rotation) sampling. Optimum replacement strategies are formulated and performances of the proposed estimators have been discussed. Results are interpreted through empirical studies.     

基于半参数混频误差修正模型的中国CPI预测研究

考虑宏观经济变量具有明显的非线性特征,将非线性误差修正项引入存在协整关系的非平稳混频数据抽样（MIDAS）模型中,构建半参数混频数据抽样误差修正（SEMI-ECM-MIDAS）模型。使用广义似然比（GLR）检验,拓展了混频数据下模型函数形式的一致性检验问题。模拟结果表明SEMI-ECM-MIDAS模型对存在非线性误差修正机制的数据具有显著的预测优势。最后使用该模型研究中国股票市场周度数据、广义货币发行量月度数据和国际原油市场月度数据对中国CPI的短期预测效果。基于AIC准则,对包含半参数模型在内的4种混频数据抽样模型和2种同频模型的连续预测效果进行了全面的比较。研究结果发现：GLR检验表明误差修正项具有明显的非线性特征且在回归中具有显著的反向修正机制,无论采用递归样本、滚动样本还是固定样本,本文提出的SEMI-ECM-MIDAS模型在进行连续预测时均具有最优的预测精度,且预测结果不受混频动态协整关系选择的影响。     

Hypothesis testing in smoothing spline models

Nonparametric regression models are often used to check or suggest a parametric model. Several methods have been proposed to test the hypothesis of a parametric regression function against an alternative smoothing spline model. Some tests such as the locally most powerful (LMP) test by Cox et al. (Cox, D., Koh, E., Wahba, G. and Yandell, B. (1988). Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models. Ann. Stat., 16, 113–119.), the generalized maximum likelihood (GML) ratio test and the generalized cross validation (GCV) test by Wahba (Wahba, G. (1990). Spline models for observational data. CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM.) were developed from the corresponding Bayesian models. Their frequentist properties have not been studied. We conduct simulations to evaluate and compare finite sample performances. Simulation results show that the performances of these tests depend on the shape of the true function. The LMP and GML tests are more powerful for low frequency functions while the GCV test is more powerful for high frequency functions. For all test statistics, distributions under the null hypothesis are complicated. Computationally intensive Monte Carlo methods can be used to calculate null distributions. We also propose approximations to these null distributions and evaluate their performances by simulations.     

Partly linear models on Riemannian manifolds

In partly linear models, the dependence of the response y on (x ^T, t) is modeled through the relationship y=x ^T β+g(t)+?, where ? is independent of (x ^T, t). We are interested in developing an estimation procedure that allows us to combine the flexibility of the partly linear models, studied by several authors, but including some variables that belong to a non-Euclidean space. The motivating application of this paper deals with the explanation of the atmospheric SO₂ pollution incidents using these models when some of the predictive variables belong in a cylinder. In this paper, the estimators of β and g are constructed when the explanatory variables t take values on a Riemannian manifold and the asymptotic properties of the proposed estimators are obtained under suitable conditions. We illustrate the use of this estimation approach using an environmental data set and we explore the performance of the estimators through a simulation study.     

The modified permutation entropy-based independence test of time series

Abstract

In time series, it is essential to check the independence of data by means of a proper method or an appropriate statistical test before any further analysis. Therefore, among different independence tests, a powerful and productive test has been introduced by Matilla-García and Marín via m-dimensional vectorial process, in which the value of the process at time t includes m-histories of the primary process. However, this method causes a dependency for the vectors even when the independence assumption of random variables is considered. Considering this dependency, a modified test is obtained in this article through presenting a new asymptotic distribution based on weighted chi-square random variables. Also, some other alterations to the test have been made via bootstrap method and by controlling the overlap. Compared with the primary test, it is obtained that not only the modified test is more accurate but also, it possesses higher power.     

Confidence Intervals for the Median of a Finite Population Based on the Sign Test

This article presents methods for constructing confidence intervals for the median of a finite population under simple random sampling without replacement, stratified random sampling, and cluster sampling. The confidence intervals, as well as point estimates and test statistics, are derived from sign estimating functions which are based on the well-known sign test. Therefore, a unified approach for inference about the median of a finite population is given.     

Testing Heterogeneity for Frailty Distribution in Shared Frailty Model

Abstract

The frailties, representing extra variations due to unobserved measurements, are often assumed to be iid in shared frailty models. In medical applications, however, a speculation can arise that a data set might violate the iid assumption. In this paper we investigate this conjecture through an analysis of the kidney infection data in McGilchrist and Aisbett (McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466). As a test procedure, we consider the cusum of squares test which is frequently used for monitoring a variance change in statistical models. Our result strongly sustains the heterogeneity of the frailty distribution.     

The pitfall of instrumental variables in big data: What the rule of thumb can't give you

ABSTRACT

Background: Instrumental variables (IVs) have become much easier to find in the “Big data era” which has increased the number of applications of the Two-Stage Least Squares model (TSLS). With the increased availability of IVs, the possibility that these IVs are weak has increased. Prior work has suggested a ‘rule of thumb’ that IVs with a first stage F statistic at least ten will avoid a relative bias in point estimates greater than 10%. We investigated whether or not this threshold was also an efficient guarantee of low false rejection rates of the null hypothesis test in TSLS applications with many IVs.

Objective: To test how the ‘rule of thumb’ for weak instruments performs in predicting low false rejection rates in the TSLS model when the number of IVs is large.

Method: We used a Monte Carlo approach to create 28 original data sets for different models with the number of IVs varying from 3 to 30. For each model, we generated 2000 observations for each iteration and conducted 50,000 iterations to reach convergence in rejection rates. The point estimate was set to 0, and probabilities of rejecting this hypothesis were recorded for each model as a measurement of false rejection rate. The relationship between the endogenous variable and IVs was carefully adjusted to let the F statistics for the first stage model equal ten, thus simulating the ‘rule of thumb.’

Results: We found that the false rejection rates (type I errors) increased when the number of IVs in the TSLS model increased while holding the F statistics for the first stage model equal to 10. The false rejection rate exceeds 10% when TLSL has 24 IVs and exceed 15% when TLSL has 30 IVs.

Conclusion: When more instrumental variables were applied in the model, the ‘rule of thumb’ was no longer an efficient guarantee for good performance in hypothesis testing. A more restricted margin for F statistics is recommended to replace the ‘rule of thumb,’ especially when the number of instrumental variables is large.     

A New Goodness-of-Fit Test Based on the Laplace Statistic for a Large Class of NHPP Models

ABSTRACT

Nonhomogeneous Poisson processes (NHPP) provide many models for hardware and software reliability analysis. In order to get an appropriate NHPP model, goodness-of-Fit (GOF for short) tests have to be carried out. For the power-law processes, lots of GOF tests have been developed. For other NHPP models, only the Conditional Probability Integral Transformation (CPIT) test has been proposed. However, the CPIT test is less powerful and cannot be applied to some NHPP models. This article proposes a general GOF test based on the Laplace statistic for a large class of NHPP models with intensity functions of the form αλ(t, β). The simulation results show that this test is more powerful than CPIT test.     

Bayesian inference for zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables

Abstract

In the fields of internet financial transactions and reliability engineering, there could be more zero and one observations simultaneously. In this paper, considering that it is beyond the range where the conventional model can fit, zero-and-one-inflated geometric distribution regression model is proposed. Ingeniously introducing Pólya-Gamma latent variables in the Bayesian inference, posterior sampling with high-dimensional parameters is converted to latent variables sampling and posterior sampling with lower-dimensional parameters, respectively. Circumventing the need for Metropolis-Hastings sampling, the sample with higher sampling efficiency is obtained. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, a doctoral dissertation data set is analyzed to illustrate the practicability of the proposed method, research shows that zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables can achieve better fitting results.     

Model averaging for multivariate multiple regression models

The theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.     

Nonlinearity testing and modeling for threshold moving average models

In this paper, we suggest a simple test and an easily applicable modeling procedure for threshold moving average (TMA) models. Firstly, based on the fitted residuals by maximum likelihood estimate (MLE) for MA models, we construct a simple statistic, which is obtained by linear arrange regression and follows F-distribution approximately, to test for threshold nonlinearity and specify the threshold variables. And then, we use some scatterplots to identify the number and locations of the potential thresholds. Finally, with the statistic and Akaike information criterion, we propose the procedure to build TMA models. Both the power of test statistic and the convenience of modeling procedure can work very well demonstrated by simulation experiments and the application to a real example.     

A NONPARAMETRIC TEST FOR THE EQUALITY OF DEPENDENT CORRELATION COEFFICIENTS UNDER NORMALITY

ABSTRACT

A nonparametric testing method for the equality of two correlation coefficients in trivariate normal distribution, namely, one of the variables are common, is discussed. Using a permutation test, we obtain asymptotically exact solutions. The performance of this test is compared with the likelihood ratio test and a method of using the limiting distribution of correlation coefficients.     

Homogeneity test based on ranked set samples

Abstract

The homogeneity hypothesis is investigated in a location family of distributions. A moment-based test is introduced based on data collected from a ranked set sampling scheme. The asymptotic distribution of the proposed test statistic is determined and the performance of the test is studied via simulation. Furthermore, for small sample sizes, the bootstrap procedure is used to distinguish the homogeneity of data. An illustrative example is also presented to explain the proposed procedures in this paper.     

OPTIMAL DESIGN OF PLANS FOR ACCEPTANCE SAMPLING BY VARIABLES WITH INVERSE GAUSSIAN DISTRIBUTION

ABSTRACT

A vast majority of the literature on the design of sampling plans by variables assumes that the distribution of the quality characteristic variable is normal, and that only its mean varies while its variance is known and remains constant. But, for many processes, the quality variable is nonnormal, and also either one or both of the mean and the variance of the variable can vary randomly. In this paper, an optimal economic approach is developed for design of plans for acceptance sampling by variables having Inverse Gaussian (IG) distributions. The advantage of developing an IG distribution based model is that it can be used for diverse quality variables ranging from highly skewed to almost symmetrical. We assume that the process has two independent assignable causes, one of which shifts the mean of the quality characteristic variable of a product and the other shifts the variance. Since a product quality variable may be affected by any one or both of the assignable causes, three different likely cases of shift (mean shift only, variance shift only, and both mean and variance shift) have been considered in the modeling process. For all of these likely scenarios, mathematical models giving the cost of using a variable acceptance sampling plan are developed. The cost models are optimized in selecting the optimal sampling plan parameters, such as the sample size, and the upper and lower acceptance limits. A large set of numerical example problems is solved for all the cases. Some of these numerical examples are also used in depicting the consequences of: 1) using the assumption that the quality variable is normally distributed when the true distribution is IG, and 2) using sampling plans from the existing standards instead of the optimal plans derived by the methodology developed in this paper. Sensitivities of some of the model input parameters are also studied using the analysis of variance technique. The information obtained on the parameter sensitivities can be used by the model users on prudently allocating resources for estimation of input parameters.     

Bootstrap procedures for variance breaks test in time series with a changing trend

In this article, we consider the problem of testing for variance breaks in time series in the presence of a changing trend. In performing the test, we employ the cumulative sum of squares (CUSSQ) test introduced by Inclán and Tiao (1994, J.?Amer.?Statist.?Assoc., 89, 913 ? 923). It is shown that CUSSQ test is not robust in the case of broken trend and its asymptotic distribution does not convergence to the sup of a standard Brownian bridge. As a remedy, a bootstrap approximation method is designed to alleviate the size distortions of test statistic while preserving its high power. Via a bootstrap functional central limit theorem, the consistency of these bootstrap procedures is established under general assumptions. Simulation results are provided for illustration and an empirical example of application to a set of high frequency real data is given.     

Some tests for the allometric extension model in regression

The allometric extension model is a multivariate regression model recently proposed by Tarpey and Ivey (2006 Tarpey, T., Ivey, C.T. (2006). Allometric extension for multivariate regression. J. Data Sci. 4:479–495. [Google Scholar]). This model holds when the matrix of covariances between the variables in the response vector y and the variables in the vector of regressors x has a particular structure. In this paper, we consider tests of hypotheses for this structure when (y′, x′)′ has a multivariate normal distribution. In particular, we investigate the likelihood ratio test and a Wald test.