The Extended Birnbaum–Saunders Distribution Based on the Scale Shape Mixture of Skew Normal Distributions

In this article, a large class of univriate Birnbaum–Saunders distributions based on the scale shape mixture of skew normal distributions is introduced which generates suitable subclasses for modeling asymmetric data in a variety of settings. The moments and maximum likelihood estimation procedures are disscused via an ECM-algorithm. The observed information matrix to approximate the asymptotic covariance matrix of the parameter estimates is then derived in some subclasses. A simulation study is also performed to evaluate the finite sample properties of ML estimators and finally, a real data set is analyzed for illustrative purposes.

Covariances in Pólya urn schemes

By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are “structural,” our purpose here is “computational.” We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.

Estimating the Covariance Matrix of the Maximum Likelihood Estimator Under Linear Cluster-Weighted Models

In recent years, the research into cluster-weighted models has been intense. However, estimating the covariance matrix of the maximum likelihood estimator under a cluster-weighted model is still an open issue. Here, an approach is developed in which information-based estimators of such a covariance matrix are obtained from the incomplete data log-likelihood of the multivariate Gaussian linear cluster-weighted model. To this end, analytical expressions for the score vector and Hessian matrix are provided. Three estimators of the asymptotic covariance matrix of the maximum likelihood estimator, based on the score vector and Hessian matrix, are introduced. The performances of these estimators are numerically evaluated using simulated datasets in comparison with a bootstrap-based estimator; their usefulness is illustrated through a study aiming at evaluating the link between tourism flows and attendance at museums and monuments in two Italian regions.

INSTRUMENTAL VARIABLE ESTIMATION OF STRUCTURAL VAR MODELS ROBUST TO POSSIBLE NONSTATIONARITY

This paper considers the estimation of dynamic causal effects using a proxy structural vector-autoregressive model with possibly nonstationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither knowledge of the presistence properties of the variables nor pretests for nonstationarity. The proposed consistent covariance matrix estimator is robust and is easy to implement in practice. When all regressors are indeed stationary, the method becomes the same as the standard procedure.

Finite time analysis of vector autoregressive models under linear restrictions

This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region ρ(A) ≤ 1 + c/n, where ρ(A) is the spectral radius of the transition matrix A in the Var(1) representation, n is the time horizon and c > 0 is a universal constant. The linear restriction framework encompasses various existing models such as banded/network vector autoregressive models. We show that the restrictions reduce the error bounds via not only the reduced dimensionality but also a scale factor resembling the asymptotic covariance matrix of the estimator in the fixed-dimensional set-up: as long as the model is correctly specified, this scale factor is decreasing in the number of restrictions. It is revealed that the phase transition from slow to fast error rate regimes is determined by the smallest singular value of A, a measure of the least excitable mode of the system. The minimax lower bounds are derived across different regimes. The developed non-asymptotic theory not only bridges the theoretical gap between stable and unstable regimes but precisely characterizes the effect of restrictions and its interplay with model parameters. Simulations support our theoretical results.

Bivariate Power-Skew-Elliptical Distribution

In this article, we introduce a power-skew-elliptical (PSE) distribution in the bivariate setting. The new bivariate model arises in the context of conditionally specified distributions. The proposed bivariate model is an absolutely continuous distribution whose marginals are univariate PSE distributions. The special case of the bivariate power-skew-normal (BPSN) distribution is studied in details. General properties of the BPSN distribution are derived and the estimation of the unknown parameters by maximum pseudo-likelihood is discussed. Further, a sandwich type matrix, which is a consistent estimator for the asymptotic covariance matrix of the maximum likelihood (ML) estimator is determined. Two applications for real data of the proposed bivariate distribution is provided for illustrative purposes.

Determinants of credit demand of farmers in Lam Dong, Vietnam

Purpose The purpose of this paper is twofold: to explain access to formal and informal credit in agriculture of Vietnam; and to compare the effectiveness between regular econometrics and machine learning techniques. Design/methodology/approach The multinomial logit (MNL) regression model and the random forest (RF) technique are employed for comparison purposes. To avoid heteroskedasticity, the robust covariance matrix is computed to estimate the sandwich estimator which in turn provides an asymptotic covariance matrix for biased estimators. Additionally, multicollinearity is tested among independent variables with variance inflation factors less than 3. Adequacy approach and sensitivity analysis are used to determine relevant levels of predictors. For models comparison, statistical evaluation metrics including Cohen’s κ, mean absolute error, root mean squared error and relative absolute error are employed. Findings The discrepancy between sensitivity analysis and adequacy approach revealed that MNL is more compatible for explaining determinants of credit participation. Due to insignificant differences in the evaluation metrics between models, the winner of choice is undetermined. Among other determinants, collateral, farmsize, income, procedure, literacy and all risk variables stand out to be critical factors when deciding borrowing schemes. While financially literate farmers tend to acquire loans from both sources, borrowing decisions against different risk sources depend on risk type and famers’ own desire to borrow. Originality/value Results of the MNL model are more consistent with literatures, which reinforce the role of collateral in the local credit scheme. Besides, financial literacy and farmers’ perception on different risk sources also influence how farmers’ borrowing strategies vary among sources.

Asymptotic Comparison of Parameters Estimates of Two-parameter Weibull Distribution

The Weibull distribution is frequently applied in various fields, ranging from economy, business, biology, to engineering. This paper aims at estimating the parameters of two-parameter Weibull distribution are determined. For this purpose, the method of quantiles (three different choices of quantiles) and Weibull probability plot method is utilized. The asymptotic covariance matrix of the parameter estimates is derived for both methods. For optimal random choices of quantiles, the variance, covariance and generalized variance is computed. The main contribution of this study is the introduction of the best choice of percentiles for the method of quantiles and the joint asymptotic efficiency comparison of applied methods.