The FastHCS algorithm for robust PCA

Principal component analysis (PCA) is widely used to analyze high-dimensional data, but it is very sensitive to outliers. Robust PCA methods seek fits that are unaffected by the outliers and can therefore be trusted to reveal them. FastHCS (high-dimensional congruent subsets) is a robust PCA algorithm suitable for high-dimensional applications, including cases where the number of variables exceeds the number of observations. After detailing the FastHCS algorithm, we carry out an extensive simulation study and three real data applications, the results of which show that FastHCS is systematically more robust to outliers than state-of-the-art methods.     

Gompertz model with time-dependent covariate in the presence of interval-, right- and left-censored data

In this paper, the Gompertz model is extended to incorporate time-dependent covariates in the presence of interval-, right-, left-censored and uncensored data. Then, its performance at different sample sizes, study periods and attendance probabilities are studied. Following that, the model is compared to a fixed covariate model. Finally, two confidence interval estimation methods, Wald and likelihood ratio (LR), are explored and conclusions are drawn based on the results of the coverage probability study. The results indicate that bias, standard error and root mean square error values of the parameter estimates decrease with the increase in study period, attendance probability and sample size. Also, LR was found to work slightly better than the Wald for parameters of the model.     

Mean and cell-mean imputation resulting in the use of a semicontinuous distribution and a mixture of semicontinuous distributions

Zero-inflated models are commonly used for modeling count and continuous data with extra zeros. Inflations at one point or two points apart from zero for modeling continuous data have been discussed less than that of zero inflation. In this article, inflation at an arbitrary point α as a semicontinuous distribution is presented and the mean imputation for a continuous response is discussed as a cause of having semicontinuous data. Also, inflation at two points and generally at k arbitrary points and their relation to cell-mean imputation in the mixture of continuous distributions are studied. To analyze the imputed data, a mixture of semicontinuous distributions is used. The effects of covariates on the dependent variable in a mixture of k semicontinuous distributions with inflation at k points are also investigated. In order to find the parameter estimates, the method of expectation–maximization (EM) algorithm is used. In a real data of Iranian Households Income and Expenditure Survey (IHIES), it is shown how to obtain a proper estimate of the population variance when continuous missing at random responses are mean imputed.     

Inflation in Transition Economies: An Empirical Analysis

The present research works with yearly data on backward looking measures of inflation i.e. GDP deflator series for Bulgaria, Czech Republic, Estonia, Hungary, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, and Slovakia. Because of the data limitations in the transition economies annual series are converted to smooth quarterly series before they are employed for inflation prognosis using state space models. The results show statistically significant evidence of time-varying volatility in Bulgaria, Czech Republic, Estonia, Hungary, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, and Slovakia using critical values obtained from χ₃² distributions. The results also show that the non-normality hypothesis cannot be rejected in all the series using critical values due McCulloch (J Bus Econ Stat 15:74–81, 1997). The efficiently estimated inflation forecast range between 0.925 for Bulgaria to 99.106 for Latvia. The estimated value of the characteristic exponent α of 2.000 for Hungary, and for the other countries having α equal to 1.999 shows tendency toward normal behavior in exception of Bulgaria, where α equals 1.861.      

Estimation in Truncated GLG Model for Ordered Categorical Spatial Data Using the SAEM Algorithm

In this article, we utilize a scale mixture of Gaussian random field as a tool for modeling spatial ordered categorical data with non-Gaussian latent variables. In fact, we assume a categorical random field is created by truncating a Gaussian Log-Gaussian latent variable model to accommodate heavy tails. Since the traditional likelihood approach for the considered model involves high-dimensional integrations which are computationally intensive, the maximum likelihood estimates are obtained using a stochastic approximation expectation–maximization algorithm. For this purpose, Markov chain Monte Carlo methods are employed to draw from the posterior distribution of latent variables. A numerical example illustrates the methodology.     

A New Procedure to Monitor the Mean of a Quality Characteristic

The Shewhart, Bonferroni-adjustment, and analysis of means (ANOM) control charts are typically applied to monitor the mean of a quality characteristic. The Shewhart and Bonferroni procedure are utilized to recognize special causes in production process, where the control limits are constructed by assuming normal distribution for known parameters (mean and standard deviation), and approximately normal distribution regarding to unknown parameters. The ANOM method is an alternative to the analysis of variance method. It can be used to establish the mean control charts by applying equicorrelated multivariate non central t distribution. In this article, we establish new control charts, in phases I and II monitoring, based on normal and t distributions having as a cause a known (or unknown) parameter (standard deviation). Our proposed methods are at least as effective as the classical Shewhart methods and have some advantages.     

Stock Returns Predictability in Transition Economies

I investigate the possible existence of predictable components in Croatia, Hungary, Latvia, Russia, Slovakia, and Ukraine excess returns over the relevant risk-free rates using non-Gaussian state space or unobservable-component models with stable distributions and volatility persistence. The results show that most stock markets in these countries encompass volatility persistence. Moreover, these markets have a stable characteristic exponent α ranging from 1.607 for Hungary to 1.749 for Latvia showing heavy tails. However, for Russia the characteristic exponent α of 1.999 is close to the value pertaining to normal behavior. Our findings reveal that even after accounting for nonnormality and volatility persistence, a predictable signal in return exists in Croatia, Hungary, Latvia, Slovakia, and Ukraine at the 5 percent level of significance using critical values from Monte Carlo simulations. The efficient estimated excess returns range from 0.003 (0.036) percent per month (annum) for Ukraine to 0.094 (1.128) percent per month (annum) for Russia.     

The augmentation of existing data for improving the path of steepest ascent

Response surface methodology is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several independent variables and the objective is to optimize this response. When we are at a point on the response surface that is remote from the optimum, such as the current operating conditions, there is little curvature in the system and the first-order model will be appropriate. In these circumstances, a preliminary procedure as the steepest ascent usually is employed to move sequentially in the direction of maximum increase in the response. To improve the estimation of parameters of the steepest ascent path, we present, in an efficient way, the augmentation of existing data such that the independent variables are made more orthogonal to each other. Additionally, when we estimate the true path using this method, the bias and magnitude of the covariance matrix of the estimated path is decreased, significantly.