A bivariate fractionally cointegrated relationship in the context of cyclical structures

This paper deals with the analysis of cointegration in a bivariate system. However, we depart from the classic concept of cointegration in two aspects. First, we permit fractional degrees of integration in both the parent series and in their linear combination. Second, instead of assuming that the pole or singularity in the spectrum takes places at the zero frequency, we consider the case where the singularity occurs at a frequency λ in the interval (0, π]. We use a procedure that follows the same lines as the two-step testing strategy of R.F. Engle, and C.W.J. Granger, [Cointegration and error correction model. Representation, estimation and testing, Econometrica 55 (1987), pp. 251–276]. Thus, we test first the order of integration in the individual series, which are specified in terms of the Gegenbauer polynomials. Then, if the two series share the same degree of integration at a given frequency, we test the null hypothesis of no cointegration against the alternative of fractional cyclical cointegration, by testing the order of integration on the estimated residuals from the cointegrating regression. Finite sample critical values are obtained, and the power properties of the test are examined. An empirical application is also carried out at the end of the article.     

A pseudo restricted MLE under multivariate order restrictions and its algorithm

Abstract

It is shown in this paper that a quasi order for the vectors in R^p is a cone induced if and only if the order is preservable under limits and under linear combinations with non-negative coefficients. For the mean vectors in MANOVA subject to the restriction of simple ordering, a pseudo restricted MLE is proposed. This estimator is a matrix projection onto a closed convex set inside the restricted domain. An algorithm for the pseudo restricted MLE is developed, that computes the matrix projections using only vector projections.     

Stability of the inverse correlation matrix. Partial ridge regression

In this paper we evaluate the stability of the inverse of a correlation matrix by studying the derivatives of each of its entries with respect to each entry of the correlation matrix. From them we deduce the derivatives of the squared length of the inverse matrix, the variance inflation factors (VIF), and the regression coefficients. To illustrate the procedure, we use a correlation matrix that has already been analyzed by Hoerl and Kennard (1970, Technometrics 12, 69–82), and, by looking at the derivatives of the squared length of the regression vector, we show that the addition of a constant to some of the diagonal entries of the matrix is sufficient for obtaining satisfying estimates of the regression coefficients. This ‘partial ridge regression’ is carried out on the previous matrix and modifies only the coefficients which are perturbed by the collinearity.     

Local linear regression with adaptive orthogonal fitting for the wind power application

Short-term forecasting of wind generation requires a model of the function for the conversion of meteorological variables (mainly wind speed) to power production. Such a power curve is nonlinear and bounded, in addition to being nonstationary. Local linear regression is an appealing nonparametric approach for power curve estimation, for which the model coefficients can be tracked with recursive Least Squares (LS) methods. This may lead to an inaccurate estimate of the true power curve, owing to the assumption that a noise component is present on the response variable axis only. Therefore, this assumption is relaxed here, by describing a local linear regression with orthogonal fit. Local linear coefficients are defined as those which minimize a weighted Total Least Squares (TLS) criterion. An adaptive estimation method is introduced in order to accommodate nonstationarity. This has the additional benefit of lowering the computational costs of updating local coefficients every time new observations become available. The estimation method is based on tracking the left-most eigenvector of the augmented covariance matrix. A robustification of the estimation method is also proposed. Simulations on semi-artificial datasets (for which the true power curve is available) underline the properties of the proposed regression and related estimation methods. An important result is the significantly higher ability of local polynomial regression with orthogonal fit to accurately approximate the target regression, even though it may hardly be visible when calculating error criteria against corrupted data.     

GIPSCAL revisited. A projected gradient approach

A model for analysis and visualization of asymmetric data—GIPSCAL—is reconsidered by means of the projected gradient approach. GIPSCAL problem is formulated as initial value problem for certain first order matrix ordinary differential equations. This results in a globally convergent algorithm for solving GIPSCAL. Additionally, first and second order optimality conditions for the solutions are established. A generalization of the GIPSCAL model for analyzing three-way arrays is also considered. Finally, results from simulation experiments are reported.     

Recurrence relations of coefficients of the generalized hypergeometric function in multivariate analysis

James(1960) defined the zonal polynomials and used it to represent the joint distributions of latent roots of VVisfiart matrix. The zonal polviionnals played an important role to define the generalized hypergeometric function of symmetric matrix argument Since then, many density functions and moments based on Wishart matrix have been expressed in terms of the generalized hy¬pergeometric Function. The purpose of this paper is to get the recurrence relations for the coefficients of it. In Section 1 we derive a partial differen¬tial equations having the generalized hypergeometric function as the unique solution. Then we ubtain the recurrence relations until order 7 in Section 2.     

Simple Estimators for Invertible Index Models

This article considers estimation of the unknown linear index coefficients of a model in which a number of nonparametrically identified reduced form parameters are assumed to be smooth and invertible function of one or more linear indices. The results extend the previous literature by allowing the number of reduced form parameters to exceed the number of indices (i.e., the indices are “overdetermined” by the reduced form parameters. The estimator of the unknown index coefficients (up to scale) is the eigenvector of a matrix (defined in terms of a first-step nonparametric estimator of the reduced form parameters) corresponding to its smallest (in magnitude) eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal, and under additional restrictions an efficient choice of a “weight matrix” is derived in the overdetermined case.     

Yule–Walker type estimators in periodic bilinear models: strong consistency and asymptotic normality

This paper studies the covariance structure and the asymptotic properties of Yule–Walker (YW) type estimators for a bilinear time series model with periodically time-varying coefficients. We give necessary and sufficient conditions ensuring the existence of moments up to eighth order. Expressions of second and third order joint moments, as well as the limiting covariance matrix of the sample moments are given. Strong consistency and asymptotic normality of the YW estimator as well as hypotheses testing via Wald’s procedure are derived. We use a residual bootstrap version to construct bootstrap estimators of the YW estimates. Some simulation results will demonstrate the large sample behavior of the bootstrap procedure.     

Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

Generalised regression estimation via the bootstrap

A generalised regression estimation procedure is proposed that can lead to much improved estimation of population characteristics, such as quantiles, variances and coefficients of variation. The method involves conditioning on the discrepancy between an estimate of an auxiliary parameter and its known population value. The key distributional assumption is joint asymptotic normality of the estimates of the target and auxiliary parameters. This assumption implies that the relationship between the estimated target and the estimated auxiliary parameters is approximately linear with coefficients determined by their asymptotic covariance matrix. The main contribution of this paper is the use of the bootstrap to estimate these coefficients, which avoids the need for parametric distributional assumptions. First‐order correct conditional confidence intervals based on asymptotic normality can be improved upon using quantiles of a conditional double bootstrap approximation to the distribution of the studentised target parameter estimate.     

Characterization of information matrices for balanced two-level fractional factorial designs of odd resolution derived from two-symbol simple arrays

We consider a balanced fractional 2^m factorial design of resolution 2?+1 which permits estimation of all factorial effects up through ?-factor interactions under the situation in which all (?+1)-factor and higher order interactions are to be negligible for an integer satisfying [m/2]<lE;?m, where [x] denotes the greatest integer not exceeding x. This paper investigates algebraic structure of the information matrix of such a design derived from a simple array through that of an atomic array. We obtain an explicit expression for the irreducible matrix representation based on the above design and its algebraic properties. The results in this paper will be useful to characterize the designs under consideration.     

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.     

Some conditions on the design of a regression model

We study some conditions on the design of a regression model which provide √n-consistent least squares estimators of the regression coefficients, where n is the sample size. Under these conditions the Fisher information matrix is of order at least n.     

Erratum to “Progressively Type-II right censored order statistics from discrete distributions” [J. Statist. Plann. Inference 138 (2008) 845–856]

In this note, we correct the proof of Representation 1 of Balakrishnan and Dembińska [2008. Progressively Type-II right censored order statistics from discrete distributions. J. Statist. Plann. Inference 138, 845–856] which relates the joint distribution of progressively Type-II right censored order statistics corresponding to an arbitrary population to progressively Type-II right censored order statistics from the standard uniform distribution.     

国内市场一体化对出口技术复杂度的影响及作用机制

本文从中国经济特有优势出发,系统梳理和归纳了国内市场一体化影响出口技术复杂度的理论机制,并利用中国2003-2016年30个省份（西藏除外）的面板数据,构建中介效应模型,对理论预期进行了实证检验。研究结果表明：国内市场一体化显著促进了出口技术复杂度的提升,并且随着时间的推移,这种促进作用逐渐增强。市场一体化对出口技术复杂度的影响存在行业及区域差异性。市场一体化对技术密集型行业出口技术复杂度的提升作用最为突出。内陆地区的市场一体化系数显著为正,而沿海地区市场一体化的正向影响效应不显著。市场一体化除了直接对出口技术复杂度发挥促进作用,还可以通过技术创新效应、需求驱动效应、制度改进效应等机制促进出口技术复杂度提升,其中技术创新的中介效应最为有效。本文的研究结论对中国推进国内统一大市场建设,实现贸易强国目标和经济转型发展具有借鉴意义。     

A MATRIX VARIATE GENERALIZATION OF THE POWER EXPONENTIAL FAMILY OF DISTRIBUTIONS

ABSTRACT

This paper proposes a matrix variate generalization of the power exponential distribution family, which can be useful in generalizing statistical procedures in multivariate analysis and in designing robust alternatives to them. An example is added to show an application of the generalization.     

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

In a previous paper the authors proposed a simple method to extend results about almost sure convergence for weighted sums of real random variables to the case of Banach-valued random elements. The method arises from the extension of Skorohod's Representation Theorem for weakly convergent sequences due to Blackwell and Dubins, applied to the general framework of weakly equivalent tight sequences of probability measures. This provides a scheme which permits us to handle separately a problem that behaves like the Glivenko-Cantelli Theorem and a question on uniform integrability which generally is reduced to the real valued version of the general problem to be solved.

In this paper we prove that Wasserstein's metrics can play the same role as Skorohod's Representation Theorem in the preceding scheme. We also show that our method can be applied to obtain results with respect to various summability methods (Abel, Euler, …) even in the case in which the ‘weights’ are linear operators.     

Estimation of two ordered normal means when a covariance matrix is known

Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada [Confidence interval estimation subject to order restrictions. Ann Statist. 1994;22(1):67–93] and Peddada et al. [Estimation of order-restricted means from correlated data. Biometrika. 2005;92:703–715]. The estimators are also compared under the Pitman nearness criterion and it is shown that the MLE is closer to ordered means than the other two estimators. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the MLE to dominate the other estimators in terms of mean squared error.     

Using Heteroscedasticity-Consistent Standard Errors for the Linear Regression Model with Correlated Regressors

The use of heteroscedasticity-consistent covariance matrix (HCCM) estimators is very common in practice to draw correct inference for the coefficients of a linear regression model with heteroscedastic errors. However, in addition to the problem of heteroscedasticity, linear regression models may also be plagued with some considerable degree of collinearity among the regressors when two or more regressors are considered. This situation causes many adverse effects on the least squares measures and alternatively, the ordinary ridge regression method is used as a common practice. But in the available literature, the problems of multicollinearity and heteroscedasticity have not been discussed as a combined issue especially, for the inference of the regression coefficients. The present article addresses the inference about the regression coefficients taking both the issues of multicollinearity and heteroscedasticity into account and suggests the use of HCCM estimators for the ridge regression. This article proposes t- and F-tests, based on these HCCM estimators, that perform adequately well in the numerical evaluation of the Monte Carlo simulations.     

Covariance Matrix Estimation via Network Structure

In this article, we employ a regression formulation to estimate the high-dimensional covariance matrix for a given network structure. Using prior information contained in the network relationships, we model the covariance as a polynomial function of the symmetric adjacency matrix. Accordingly, the problem of estimating a high-dimensional covariance matrix is converted to one of estimating low dimensional coefficients of the polynomial regression function, which we can accomplish using ordinary least squares or maximum likelihood. The resulting covariance matrix estimator based on the maximum likelihood approach is guaranteed to be positive definite even in finite samples. Under mild conditions, we obtain the theoretical properties of the resulting estimators. A Bayesian information criterion is also developed to select the order of the polynomial function. Simulation studies and empirical examples illustrate the usefulness of the proposed methods.