A martingale-based test for independence of time to failure and cause of failure for competing risks models

In this article, we introduce a class of tests, using a martingale approach, for testing independence of failure time and cause of failure for competing risks data. Asymptotic distribution of the proposed test statistic is derived. The procedure is illustrated with a real-life data. A simulation study is carried out to assess the level and power of the test.     

Generalized Kerridge’s inaccuracy measure for conditionally specified models

Recently, conditional Renyi’s divergence of order α and Kerridge’s inaccuracy measures are studied by Navarro et al. (2014 Navarro, J., Sunoj, S.M., Linu, M.N. (2014). Characterizations of bivariate models using some dynamic conditional information divergence measures. Commun. Stat. Theory Methods 43:1939–1948.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). In the present article, a generalized dynamic conditional Kerridge’s inaccuracy measure is introduced, which can be represented as the sum of conditional Renyi’s divergence and Renyi’s entropy. Some useful bounds are obtained using the concept of likelihood ratio order. The results are extended to weighted distributions. Sufficient conditions are obtained for the monotonicity of the proposed measure. Characterizations for bivariate exponential conditional distribution are presented based on the proposed measure.     

A small but practically useful modification to the Hodrick–Prescott filtering: A note

The Hodrick–Prescott (HP) filtering is widely applied to decompose macroeconomic time series, such as real Gross Domestic Product, into cyclical and trend components. This paper presents a small but practically useful modification to this approach. The reason why this modified filtering is of practical use is that it provides not only identical trend estimates as the HP filtering but also extrapolations of the trend. We provide a proof based on a ridge regression representation of the modified HP filtering. This is mainly because it enhances our understanding of the approach.     

The exponentiated reduced Kies distribution: Properties and applications

Here we consider an exponentiated version of the reduced Kies distribution and discuss some of its properties. The parameters of the distribution are estimated by the method of maximum likelihood and illustrated with the help of certain real-life data sets. Asymptotic behavior of the maximum likelihood estimators of the parameters of the distribution is also studied by using certain simulated data sets.     

Role of stylized features in constructing better estimators

This article discusses the role played by stylized features of financial time series in constructing better estimators for the model parameters. We study in detail one such estimator for the transition probabilities of a simple regime switching model. The estimator is based on the squared autocovariances of the time series, which has been discussed in several empirical studies of economic and financial time series. The effectiveness of this estimator in improving the estimation accuracy is investigated, using both finite sample and asymptotic computations. We also report simulation results to confirm our findings and to extend our conclusions over a bigger region of the parameter space.     

Trend estimation of multivariate time series with controlled smoothness

This paper extends the univariate time series smoothing approach provided by penalized least squares to a multivariate setting, thus allowing for joint estimation of several time series trends. The theoretical results are valid for the general multivariate case, but particular emphasis is placed on the bivariate situation from an applied point of view. The proposal is based on a vector signal-plus-noise representation of the observed data that requires the first two sample moments and specifying only one smoothing constant. A measure of the amount of smoothness of an estimated trend is introduced so that an analyst can set in advance a desired percentage of smoothness to be achieved by the trend estimate. The required smoothing constant is determined by the chosen percentage of smoothness. Closed form expressions for the smoothed estimated vector and its variance-covariance matrix are derived from a straightforward application of generalized least squares, thus providing best linear unbiased estimates for the trends. A detailed algorithm applicable for estimating bivariate time series trends is also presented and justified. The theoretical results are supported by a simulation study and two real applications. One corresponds to Mexican and US macroeconomic data within the context of business cycle analysis, and the other one to environmental data pertaining to a monitored site in Scotland.     

Application of an imputation method for variance estimation under pseudo-likelihood when missing data are NMAR

When data are outcome-dependent non response, pseudo-likelihood yields consistent regression coefficients without specifying the missing data mechanism. However, it is onerous to derive parameter estimators including their standard errors from the regression coefficients under pseudo-likelihood (PL). The present study applies an imputation method to compute the asymptotic standard errors of parameter estimators. The proposed method is simpler than Delta method and it showed similar effect size of the standard errors to bootstrapping in simulation and application studies.     

Complete moment convergence of widely orthant dependent random variables

It is known that the dependence structure of widely orthant dependent (WOD) random variables is weaker than those of negatively associated (NA) random variables, negatively superadditive dependent (NSD) random variables, negatively orthant dependent (NOD) random variables, and extended negatively dependent (END) random variables. In this article, the results of complete moment convergence and complete convergence are presented for WOD sequence under the same moment conditions as independent sequence in classical result (Chow 1988 Chow, Y. (1988). On the rate of moment convergence of sample sums and extremes. Bull. Inst. Math. Acad. Sin. 16(3):177–201. [Google Scholar]).     

The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss

For the variance parameter of the hierarchical normal and inverse gamma model, we analytically calculate the Bayes rule (estimator) with respect to a prior distribution IG (alpha, beta) under Stein's loss function. This estimator minimizes the posterior expected Stein's loss (PESL). We also analytically calculate the Bayes rule and the PESL under the squared error loss. Finally, the numerical simulations exemplify that the PESLs depend only on alpha and the number of observations. The Bayes rules and PESLs under Stein's loss are unanimously smaller than those under the squared error loss.