scholarly journals EFFICIENT REGRESSIONS VIA OPTIMALLY COMBINING QUANTILE INFORMATION

2014 ◽  
Vol 30 (6) ◽  
pp. 1272-1314 ◽  
Author(s):  
Zhibiao Zhao ◽  
Zhijie Xiao
Keyword(s):  
Upper Bound ◽  
Regression Models ◽  
Statistical Estimation ◽  
Asymptotic Variance ◽  
Fixed Number ◽  
Efficient Estimation ◽  
Superior Performance ◽  
Quantile Regressions ◽  
Monte Carlo Experiments ◽  
Combining Information

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance between the efficiency of the proposed estimator and the Fisher information. As the number of quantiles increases, this upper bound decreases and the asymptotic variance of the proposed estimator approaches the Cramér–Rao lower bound under appropriate conditions. In the case of nonregular statistical estimation, the proposed estimator leads to super-efficient estimation. We illustrate the proposed method for several widely used regression models. Both asymptotic theory and Monte Carlo experiments show the superior performance over existing methods.

scholarly journals A novel causality-centrality-based method for the analysis of the impacts of air pollutants on PM2.5 concentrations in China

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bocheng Wang
Keyword(s):  
Air Pollutants ◽  
Regression Models ◽  
Large Population ◽  
Vital Role ◽  
Superior Performance ◽  
Causal Direction ◽  
Northern Cities ◽  
Main Components ◽  
Surrounding Areas ◽  
Centrality Analysis

AbstractIn this paper, we analyzed the spatial and temporal causality and graph-based centrality relationship between air pollutants and PM2.5 concentrations in China from 2013 to 2017. NO2, SO2, CO and O3 were considered the main components of pollution that affected the health of people; thus, various joint regression models were built to reveal the causal direction from these individual pollutants to PM2.5 concentrations. In this causal centrality analysis, Beijing was the most important area in the Jing-Jin-Ji region because of its developed economy and large population. Pollutants in Beijing and peripheral cities were studied. The results showed that NO2 pollutants play a vital role in the PM2.5 concentrations in Beijing and its surrounding areas. An obvious causality direction and betweenness centrality were observed in the northern cities compared with others, demonstrating the fact that the more developed cities were most seriously polluted. Superior performance with causal centrality characteristics in the recognition of PM2.5 concentrations has been achieved.

scholarly journals Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 123
Author(s):  
María Jaenada ◽  
Leandro Pardo
Keyword(s):  
Generalized Linear Models ◽  
Influence Function ◽  
Regression Models ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Significant Loss ◽  
Superior Performance ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Type Test

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.

scholarly journals Interactions in Fixed Effects Regression Models

2020 ◽  
pp. 004912412091493
Author(s):  
Marco Giesselmann ◽  
Alexander W. Schmidt-Catran
Keyword(s):  
Monte Carlo ◽  
Time Constant ◽  
Fixed Effects ◽  
Regression Models ◽  
Time Varying ◽  
Unit Level ◽  
Monte Carlo Experiments ◽  
Product Term ◽  
Fixed Effects Regression ◽  
Effect Heterogeneity

An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. However, algebraic transformations reveal that this strategy does not yield a within-unit estimator. Instead, the standard FE interaction estimator reflects unit-level differences of the interacted variables. This property allows interactions of a time-constant variable and a time-varying variable in FE to be estimated but may yield unwanted results if both variables vary within units. In such cases, Monte Carlo experiments confirm that the standard FE estimator of x ⋅ z is biased if x is correlated with an unobserved unit-specific moderator of z (or vice versa). A within estimator of an interaction can be obtained by first demeaning each variable and then demeaning their product. This “double-demeaned” estimator is not subject to bias caused by unobserved effect heterogeneity. It is, however, less efficient than standard FE and only works with T > 2.

scholarly journals An Upper Bound on the k-Modem Illumination Problem

2015 ◽  
Vol 25 (04) ◽  
pp. 299-308
Author(s):  
Frank Duque ◽  
Carlos Hidalgo-Toscano
Keyword(s):  
Upper Bound ◽  
Line Segment ◽  
Time Algorithm ◽  
Fixed Number ◽  
Light Sources ◽  
Wireless Devices ◽  
Orthogonal Polygon ◽  
Illumination Problem ◽  
Number Formula ◽  
Interior Points

A variation on the classical polygon illumination problem was introduced in [Aichholzer et al. EuroCG’09]. In this variant light sources are replaced by wireless devices called [Formula: see text]-modems, which can penetrate a fixed number [Formula: see text], of “walls”. A point in the interior of a polygon is “illuminated” by a [Formula: see text]-modem if the line segment joining them intersects at most [Formula: see text] edges of the polygon. It is easy to construct polygons of [Formula: see text] vertices where the number of [Formula: see text]-modems required to illuminate all interior points is [Formula: see text]. However, no non-trivial upper bound is known. In this paper we prove that the number of kmodems required to illuminate any polygon of [Formula: see text] vertices is [Formula: see text]. For the cases of illuminating an orthogonal polygon or a set of disjoint orthogonal segments, we give a tighter bound of [Formula: see text]. Moreover, we present an [Formula: see text] time algorithm to achieve this bound.

scholarly journals Edge Mostar Indices of Cacti Graph With Fixed Cycles

2021 ◽  
Vol 9 ◽  
Author(s):  
Farhana Yasmeen ◽  
Shehnaz Akhter ◽  
Kashif Ali ◽  
Syed Tahir Raza Rizvi
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Thermodynamic Characteristics ◽  
Chemical Compounds ◽  
Fixed Number ◽  
Common Vertex ◽  
Topological Invariants ◽  
Cactus Graph ◽  
Number Of Cycles

Topological invariants are the significant invariants that are used to study the physicochemical and thermodynamic characteristics of chemical compounds. Recently, a new bond additive invariant named the Mostar invariant has been introduced. For any connected graph ℋ, the edge Mostar invariant is described as Moe(ℋ)=∑gx∈E(ℋ)|mℋ(g)−mℋ(x)|, where mℋ(g)(or mℋ(x)) is the number of edges of ℋ lying closer to vertex g (or x) than to vertex x (or g). A graph having at most one common vertex between any two cycles is called a cactus graph. In this study, we compute the greatest edge Mostar invariant for cacti graphs with a fixed number of cycles and n vertices. Moreover, we calculate the sharp upper bound of the edge Mostar invariant for cacti graphs in ℭ(n,s), where s is the number of cycles.

scholarly journals Selection of the Number of Participants in Intensive Longitudinal Studies: A User-friendly Shiny App and Tutorial to Perform Power Analysis in Multilevel Regression Models that Account for Temporal Dependencies

2020 ◽  
Author(s):  
Ginette Lafit ◽  
Janne Adolf ◽  
Egon Dejonckheere ◽  
Inez Myin-Germeys ◽  
Wolfgang Viechtbauer ◽  
...  
Keyword(s):  
Longitudinal Studies ◽  
Psychological Functioning ◽  
Regression Models ◽  
Longitudinal Research ◽  
Fixed Number ◽  
Correlated Errors ◽  
Multilevel Regression ◽  
Shiny App ◽  
User Friendly ◽  
Temporal Dependencies

In recent years the popularity of procedures to collect intensive longitudinal data, such as the Experience Sampling Method, has immensely increased. The data collected using such designs allow researchers to study the dynamics of psychological functioning, and how these dynamics differ across individuals. To this end, the data are often modeled with multilevel regression models. An important question that arises when designing intensive longitudinal studies is how to determine the number of participants needed to test specific hypotheses regarding the parameters of these models with sufficient power. Power calculations for intensive longitudinal studies are challenging, because of the hierarchical data structure in which repeated observations are nested within the individuals and because of the serial dependence that is typically present in this data. We, therefore, present a user-friendly application and step-by-step tutorial to perform simulation-based power analyses for a set of models that are popular in intensive longitudinal research. Since many studies use the same sampling protocol (i.e., a fixed number of at least approximately equidistant observations) within individuals, we assume this protocol fixed and focus on the number of participants. All included models explicitly account for the temporal dependencies in the data by assuming serially correlated errors or including autoregressive effects.

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