Vector Of Independent Variables Research Articles

Visualization of multidimensional areas of solutions to mathematical models of complex objects

The visualization of mathematical models of multidimensional objects implicitly defined as surfaces F (X) = 0 is performed using two- and three-dimensional projections obtained by rotating and shifting coordinates. In the new coordinates, the model has the form y = f(x) where one of the variables is dependent (this is the direction of design), and the rest make up the vector of independent variables. A new model is often more convenient than the original one, but not all design directions adequately reflect its properties since it is possible to transfer projections of several points of the original surface into one (gluing). For some directions (directions of ambiguity), the projection may consist of points with several preimages (corresponding to the ambiguity of the function f). In this case, the projection is divided into the area of ambiguity and the area of unambiguity. For other directions (directions of uniqueness), the entire projection is the domain of uniqueness. The paper investigates the evolution of design directions and areas of ambiguity and unambiguity in projections of complex objects. A criterion for choosing the direction of unambiguity is proposed in which all points of the model remain different, i.e., multiplicity visually disappears (“hidden multiplicity”). Examples of applying the criterion to models of objects of various geometries are given.

A comparative analysis on the nexus between corruption and firm performance for a selection of Western Balkan countries

Purpose This paper aims to focus on analyzing the level of corruption of small- and medium-sized enterprises and their economic performance impact in Western Balkan countries. This study uses survey data from Enterprise Surveys (ES) from 2019, a shared project of the European Bank for Reconstruction and Development, the European Investment Bank and the World Bank Group. The selected countries are Albania, Bosnia and Herzegovina, North Macedonia, Kosovo, Montenegro and Serbia. The questions included in the data set contribute to understanding what firms experience in the private sector. Collected data are based on firms’ experiences and enterprises’ perceptions of the environment in which they operate. Design/methodology/approach This paper measures enterprise performance in terms of sales, employees and fixed assets growth. The vector of independent variables comprises enterprise characteristics such as enterprise age, size, ownership structure, legal status, access to formal banking services, gender ownership and other composed variables. Moreover, to capture the level of perceived corruption by firms, we will focus on the following ES questions: “Is it common to have to pay some irregular additional payment or gifts to get things done with regard to customs, taxes, licenses, regulations, services,” and the “corruption payment” is defined in the form of a dummy equal to one if the enterprise replies “frequently,” “usually” or “always.” Findings Preliminary empirical research results shed light on the level and effects of corruption on enterprises’ performance. However, the magnitude and statistical significance are different among the countries included in the sample. Originality/value Instead of firm-level characteristics, research on corruption frequently focuses on effects dependent on national and institutional characteristics. To better identify the kinds of businesses that are most at risk of corruption, we have selected to focus on differences among firm characteristics in this research. Understanding factors at the firm level is preferred from a policy perspective because these findings assist policymakers to make recommendations.

Visualization of multidimensional areas of solutions to mathematical models of complex objects

Visualization of mathematical models of multidimensional objects implicitly defined as a surface F (X) = 0 is performed using two- and three-dimensional projections obtained by rotating and shifting coordinates. In the new coordinates, the model has the form y = f(x) where one of the variables is dependent (this is the direction of design), and the rest make up the vector of independent variables. A new model is often more convenient than the original one, but not all design directions adequately reflect its properties since it is possible to transfer projections of several points of the original surface into one (gluing). For some directions (directions of ambiguity), the projection may consist of points with several preimages (corresponds to the ambiguity of the function f). In this case, the projection is divided into the area of ambiguity and the area of unambiguity. For other directions (directions of uniqueness), the entire projection is the domain of uniqueness. The paper investigates the evolution of design directions and areas of ambiguity and unambiguity of projections of complex objects. A criterion for choosing the direction of unambiguity is proposed in which all points of the model remain different, i.e., multiplicity visually disappears (“hidden multiplicity”). Examples of applying the criterion for models of objects of various geometries are given.

How Digital Are Albanian Esnterprises: A Microeconomic Analyses

This paper focuses on the analyses of the digitalization of enterprises and its performance impact in Albania. Using data from 2019 Enterprise Surveys (ES) we try to give answer questions related to digitalization that characterize Albanian enterprises. The survey was a shared project of the European Bank for Reconstruction and Development (EBRD), the European Investment Bank (EIB), and the World Bank Group (WBG). The data are collected in Albania between January and May 2019. The objective of the survey is to better understand firms` experience in the private sector. Collected data are based on firms’ experiences and perceptions of the environment in which they operate. The paper uses these specific questions to study Internet adoption. ES questionnaires focus on the following questions: (1) Does the firm have a high-speed Internet connection on its premises? (2) Does the establishment have its website? The dependent variable is the performance of the firms measured in terms of sales growth and labor productivity, while the vector of independent variables is composed of enterprise characteristics such as firm size, ownership structure, legal status, region, etc. Moreover, dummy variables are used to capture access to formal banking services and gender ownership.

CurveP Method for Rendering High-Throughput Screening Dose-Response Data into Digital Fingerprints.

The nature of high-throughput screening (HTS) puts certain limits on optimal test conditions for each particular sample; therefore, on top of usual data normalization, additional parsing is often needed to account for incomplete read outs or various artifacts that arise from signal interferences.CurveP is a heuristic, user-tunable curve-cleaning algorithm that attempts to find a minimum set of corrections, which would give a monotonic dose-response curve. After applying the corrections, the algorithm proceeds to calculate a set of numeric features, which can be used as a fingerprint characterizing the sample, or as a vector of independent variables (e.g., molecular descriptors in case of chemical substances testing). The resulting output can be a part of HTS data analysis or can be used as input for a broad spectrum of computational applications, such as quantitative structure-activity relationship (QSAR ) modeling, computational toxicology, bioinformatics, and cheminformatics.

Volatility coupling

This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting. Specifically, we propose uniform confidence bands for spot volatility, beta, idiosyncratic variance processes, and their nonlinear transforms. The theory is also applied to address an open question concerning the inference of monotone nonsmooth integrated volatility functionals such as the occupation time and its quantiles.

Knowledge-based Comparable Predicted Values in Regression Analysis

Regression analysis has a major role in predicting values of a dependent variable by using values of independent variables. The estimate of predicted values is obtained as projected values in a linear subspace spanned by vectors of independent variables. However, if the data set has been observed simultaneously from multiple different data sources, then we must create different linear subspaces to estimate the different predicted values corresponding to the different data sources. Then, we cannot compare the different predicted values, since the linear subspaces are different. In order to solve this problem, we propose a method to obtain comparable predicted values obtained from different data sources by utilizing a fuzzy clustering result and an orthogonal projector which projects two different vectors corresponded with the two different dependent variables to the same intersection of the two different linear subspaces. From this, since the different predicted values from different data sources can be obtained in the common space, we can compare the different predicted values.

Robust estimation in the additive hazards model

ABSTRACTIn the additive hazards model the hazard function of a survival variable T is modeled additively as , where λ0(t) is a common non parametric baseline hazard function and is a vector of independent variables. For this model, the pioneering work of Lin and Ying (1994) develops a closed-form estimator for the regression parameter from a new estimating equation. That equation has a similar structure to the corresponding partial likelihood score function for the multiplicative model (Cox 1972) in that it exploits a martingale structure and it allows estimation of separate from the baseline hazard function. Their estimator is asymptotically normal and highly efficient. However, a potential drawback is that it is very sensitive to outliers. In this paper we propose a family of robust alternatives for estimation of the parameter in the additive hazards model which is robust to outliers and still highly efficient and asymptotically normal. We prove Fisher-consistency, obtain the influence function, and illustrate the estimation with simulated and real data. The latter corresponds to the time-honored Welsh Nickels Refiners dataset first introduced by Doll et al. (1970) and subsequently analyzed by Breslow and Day (1987) and Lin and Ying (1994), among others.

CurveP Method for Rendering High-Throughput Screening Dose-Response Data into Digital Fingerprints.

The nature of high-throughput screening (HTS) puts certain limits on optimal test conditions for each particular sample, therefore, on top of usual data normalization, additional parsing is often needed to account for incomplete read outs or various artifacts that arise from signal interferences.CurveP is a heuristic, user-tunable, curve-cleaning algorithm that attempts to find a minimum set of corrections, which would give a monotonic dose-response curve. After applying the corrections, the algorithm proceeds to calculate a set of numeric features, which can be used as a fingerprint characterizing the sample, or as a vector of independent variables (e.g., molecular descriptors in case of chemical substances testing). The resulting output can be a part of HTS data analysis or can be used as input for a broad spectrum of computational applications, such as Quantitative Structure-Activity Relationship (QSAR) modeling, computational toxicology, bio- and cheminformatics.

Robust Differentiable Functionals for the Additive Hazards Model

In this article, we present a new family of estimators for the regression parameter β in the Additive Hazards Model which represents a gain in robustness not only against outliers but also against unspecific contamination schemes. They are consistent and asymptotically normal and furthermore, and they have a nonzero breakdown point. In Survival Analysis, the Additive Hazards Model proposes a hazard function of the form , where is a common nonparametric baseline hazard function and z is a vector of independent variables. For this model, the seminal work of Lin and Ying (1994) develops an estimator for the regression parameter β which is asymptotically normal and highly efficient. However, a potential drawback of that classical estimator is that it is very sensitive to outliers. In an attempt to gain robustness, álvarez and Ferrarrio (2013) introduced a family of estimators for β which were still highly efficient and asymptotically normal, but they also had bounded influence functions. Those estimators, which are developed using classical Counting Processes methodology, still retain the drawback of having a zero breakdown point.

Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μ i , where μ i decreases in i. Arrivals have associated vectors (X 1, …, X n ) of binary variables, with X i = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting I j be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I 1, …, I r ) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(X i = 1) increases in i.

Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μi, where μi decreases in i. Arrivals have associated vectors (X1, …, Xn) of binary variables, with Xi = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting Ij be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I1, …, Ir) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(Xi = 1) increases in i.

Uniformly continuous dependence of a solution to a controlled functional operator equation on a shift of control

We establish sufficient conditions for the uniform (with respect to the set of admissible controls) continuous dependence of a solution to a controlled functional operator equation on a shift of control along a vector of independent variables. The shift of control may mean, in particular, some time delay (or outstripping) of the control. We illustrate the use of general results by an example of a mixed boundary-value problem associated with a wave equation.

Extracting Cross Sections from Rate Coefficients: Application to Molecular Gas Dissociation

E = collision energy, J e = unit vector F = least mean-square measure of distance between two rate coefficients, cm s 2 k T = rate coefficient, cm s 1 KB = Boltzmann constant, JK 1 mr = reduced mass, kg NT = number of temperature points considered in minimization process P = vector of independent variables parametrizing a given functional form for a cross section T = temperature, K = cross section, A

Investigating the Performance of Alternate Regression Weights by Studying All Possible Criteria in Regression Models with a Fixed Set of Predictors

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n×1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a full-rank predictor correlation matrix, Rxx, of order n, and for regression models with constant R2 (coefficient of determination), the OLS weight vectors for all possible criteria terminate on the surface of an n-dimensional ellipsoid. The population performance of alternate regression weights—such as equal weights, correlation weights, or rounded weights—can be modeled as a function of the Cartesian coordinates of the ellipsoid. These geometrical notions can be easily extended to assess the sampling performance of alternate regression weights in models with either fixed or random predictors and for models with any value of R2. To illustrate these ideas, we describe algorithms and R (R Development Core Team, 2009) code for: (1) generating points that are uniformly distributed on the surface of an n-dimensional ellipsoid, (2) populating the set of regression (weight) vectors that define an elliptical arc in ℝn, and (3) populating the set of regression vectors that have constant cosine with a target vector in ℝn. Each algorithm is illustrated with real data. The examples demonstrate the usefulness of studying all possible criteria when evaluating alternate regression weights in regression models with a fixed set of predictors.

Estimation of dependences based on Bayesian correction of a committee of classification algorithms

Estimation of dependence of a scalar variable on the vector of independent variables based on a training sample is considered. No a priori conditions are imposed on the form of the function. An approach to the estimation of the functional dependence is proposed based on the solution of a finite number of special classification problems constructed on the basis of the training sample and on the subsequent prediction of the value of the function as a group decision. A statistical model and Bayes’ formula are used to combine the recognition results. A generic algorithm for constructing the regression is proposed for different approaches to the selection of the committee of classification algorithms and to the estimation of their probabilistic characteristics. Comparison results of the proposed approach with the results obtained using other models for the estimation of dependences are presented.

The Changing Neighborhood Contexts of the Immigrant Metropolis

To understand the impacts of large-scale immigration on neighborhood contexts, we employ locational-attainment models, in which two characteristics of a neighborhood, its average household income and the majority group's percentage among its residents, are taken as the dependent variables and a number of individual and household characteristics, such as race/ethnicity and household composition, form the vector of independent variables. Models are estimated separately for major racial/ethnic populations - whites, blacks, Asians, and Latinos - in five different metropolitan regions of immigrant concentration - Chicago, Los Angeles, Miami, New York, and San Francisco. In the cross section, thefindings largely uphold the well-known model of spatial assimilation, in that socioeconomic status, assimilation level, and suburban residence are all strongly linked to residence in neighborhoods displaying greater affluence and with a greater number of non-Hispanic whites. Yet when the results are considered longitudinally, by comparing them with previously estimated models for 1980, the consistency with spatial-assimilation theory is no longer so striking. The impact of immigration is evident in the changing racial/ethnic composition of the neighborhoods of all groups, but especially for those where Asians and Latinos reside.

The Changing Neighborhood Contexts of the Immigrant Metropolis

To understand the impacts of large-scale immigration on neighborhood contexts, we employ locational-attainment models, in which two characteristics of a neighborhood, its average household income and the majority group's percentage among its residents, are taken as the dependent variables and a number of individual and household characteristics, such as race/ethnicity and household composition, form the vector of independent variables. Models are estimated separately for major racial/ethnic populations — whites, blacks, Asians, and Latinos — in five different metropolitan regions of immigrant concentration — Chicago, Los Angeles, Miami, New York, and San Francisco. In the cross section, the findings largely uphold the well-known model of spatial assimilation, in that socioeconomic status, assimilation level, and suburban residence are all strongly linked to residence in neighborhoods displaying greater affluence and with a greater number of non-Hispanic whites. Yet when the results are considered longitudinally, by comparing them with previously estimated models for 1980, the consistency with spatial-assimilation theory is no longer so striking. The impact of immigration is evident in the changing racial/ethnic composition of the neighborhoods of all groups, but especially for those where Asians and Latinos reside.

Robust measures of association in the correlation model

In the correlation model, the classical coefficient of multiple determination R 2 is a measure of association between the dependent random variable Y and the random vector of independent variables x . Slight departures from normality, however, can have a pronounced effect on the measure. In the regression model robust estimates of the regression coefficients are less sensitive to outlying points than least squares estimates. These estimates are often obtained by minimizing an objective (dispersion) function. For such robust estimates, the proportion of explained dispersion is a natural analogue to the statistic R 2. Although this statistic is generally not robust, it leads to robust statistics which are consistent estimates of functionals in the correlation model. These functionals are robust measures of association between Y and x . They are efficiently robust and have bounded influence provided the robust estimator on which they are based has bounded influence.

Tenure choice and expected mobility: A synthesis

This study employs a joint logit probability model to estimate the effects of a vector of independent variables on the household's current tenure choice and expected mobility which are hypothesized to be simultaneously determined. In the empirical analysis it was found that the coefficient on the endogenous variables (tenure choice and expected mobility) is the most highly significant of all the coefficients estimated. In addition, in previous analyses the age of the household head has always exhibited a highly significant positive effect on the probability of ownership. However, in this analysis it is demonstrated that this age variable was acting as a proxy for the expected mobility and wealth of the household.