Robust multivariate estimation based on statistical depth filters

In the classical contamination models, such as the gross-error (Huber and Tukey contamination model or case-wise contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when the number of considered variables is moderately small. Alqallaf et al. (Ann Stat 37(1):311–331, 2009) show the limits of this approach for a larger number of variables and introduced the independent contamination model (cell-wise contamination) where now the cells are the units to be identified as outliers or not. One approach to deal, at the same time, with both type of contamination is filter out the contaminated cells from the data set and then apply a robust procedure able to handle case-wise outliers and missing values. Here, we develop a general framework to build filters in any dimension based on statistical data depth functions. We show that previous approaches, e.g., Agostinelli et al. (TEST 24(3):441–461, 2015b) and Leung et al. (Comput Stat Data Anal 111:59–76, 2017), are special cases. We illustrate our method by using the half-space depth.

Innovative entrepreneurship and quality of life. The case of Ecuador

PurposeThis article is based on the assumption that entrepreneurship improves quality of life (HDI). Its main objective is to establish causal relationships between entrepreneurship variables such as credits, innovation (R&D), business growth, foreign direct investment and the Global Competitiveness Index and how these have influenced a country's development.Design/methodology/approachTo analyse and validate this assumption, relevant information has been extracted about Ecuador (the subject of the study) for the 1998–2017 period. The information has received the respective econometric treatment, through a multivariate estimation by the autoregressive vector (ARV) method that made it possible to establish impulse-response functions.ResultsThe results indicate that there is a significant and positive statistical impact between the variables related to entrepreneurship and quality of life (HDI), with the exception of “Innovation”, which is not representative in the model, demonstrating that the investment made at country level in R&D is not sufficient to have an impact on the HDI. It was also determined that promoting entrepreneurship would be useful as this would alter the trend of the variables, making them conducive to increasing the HDI.Originality/valueThis article is one of the few to address this issue. It includes the self-regressive vector model as a key methodology used to evaluate and establish public policies. RVM has provided positive results in the field of economics and can be adopted in the area of entrepreneurship.

Lp-Adaptive Estimation Under Partially Linear Constraint in Regression Model

We study the problem of multivariate estimation in the nonparametric regression model with random design. We assume that the regression function to be estimated possesses partially linear structure, where parametric and nonparametric components are both unknown. Based on Goldenshulger and Lepski methodology, we propose estimation procedure that adapts to the smoothness of the nonparametric component, by selecting from a family of specific kernel estimators. We establish a global oracle inequality (under the Lp-norm, 1≤p＜1) and examine its performance over the anisotropic H¨older space.

Credit Where Credit Is Due

A belief-as-benefit effect (BABE)—the positive association between well-being and religiosity/spirituality—is recurrently reported. Past BABE research has however been critiqued for predominantly utilizing unrepresentative samples, questionable psychometric measures and bivariate designs. Employing a multivariate design, I explore the incremental validity of the BABE in two community samples. Hierarchical models—initially including socio-demographic factors and religiosity/spirituality and subsequently adding trait agreeableness and conscientiousness—are used. Simple correlations confirm the BABE (with an unexceptional effect size). However the unique association observed using multivariate estimation is substantially weaker and occasionally indicates an adverse association. That cross-sectional analyses cannot establish cause is fully acknowledged. Yet, establishing cause is not the current aim; multivariate models are simply used to substantiate the cross-sectional BABE.

Multivariate estimation of production duration of steel wire batches on the basis of situational-regulatory models. Message 2

Accurate accounting and rating of duration of production cycles is necessary for rational planning and forecasting of production time. Production duration of products batches is the basis for operational schedules design. Without duration of cycles, it is impossible to establish calendar dates for start-up of semi-finished products to a particular stage of processing, as well as to determine timing of production and timing of the products batch for individual production sites. The considered task of multivariate estimation of standard duration of manufacturing of a specific batch of steel wire is to determine optimal duration of operations required for this batch production for each situation. To solve it, it is necessary: to build models of production processes performed in each branch of steelwire complex; to determine composition, duration and conditions for performing technological, natural, labor, control and transport operations; to specify the type and amount of equipment used in each department; tolist types of material flow units (riots, skeins, coils); to establish nature and type of movement of semi-finished products (products) in operations of each process; to specify ways of moving products from each previous peration for each subsequent (piece, batch, batch), as well as the number of packages and lots being moved; to take into account the type of applied production lines (continuous, semi-continuous, discrete). All of the above is reflected in presented multi-loop algorithm, approbation of which is performed by simulation method using field data of operating enterprise.

Added-variable plots with confidence intervals

An added-variable plot is an effective way to show the correlation between an independent variable and a dependent variable conditional on other independent variables. For multivariate estimation, a simple scatterplot showing x versus y is not adequate to show the partial correlation of x with y, because it ignores the impact of the other covariates. Added-variable plots are especially effective for showing the correlation of a dummy x variable with y because the dummy variable conditional on other covariates becomes a continuous variable, making the relationship easier to visualize. Added-variable plots are also useful for spotting influential outliers in the data that affect the estimated regression parameters. Stata provides added-variable plots after ordinary least-squares regressions with the avplot command. I present a new command, avciplot, that adds a confidence interval and other options to the avplot command.