Subset Of Regressors Research Articles

Fast Bayesian inference for large occupancy datasets.

In recent years, the study of species' occurrence has benefited from the increased availability of large-scale citizen-science data. While abundance data from standardized monitoring schemes are biased toward well-studied taxa and locations, opportunistic data are available for many taxonomic groups, from a large number of locations and across long timescales. Hence, these data provide opportunities to measure species' changes in occurrence, particularly through the use of occupancy models, which account for imperfect detection. These opportunistic datasets can be substantially large, numbering hundreds of thousands of sites, and hence present a challenge from a computational perspective, especially within a Bayesian framework. In this paper, we develop a unifying framework for Bayesian inference in occupancy models that account for both spatial and temporal autocorrelation. We make use of the Pólya-Gamma scheme, which allows for fast inference, and incorporate spatio-temporal random effects using Gaussian processes (GPs), for which we consider two efficient approximations: subset of regressors and nearest neighbor GPs. We apply our model to data on two UK butterfly species, one common and widespread and one rare, using records from the Butterflies for the New Millennium database, producing occupancy indices spanning 45 years. Our framework can be applied to a wide range of taxa, providing measures of variation in species' occurrence, which are used to assess biodiversitychange.

High-dimensional inference robust to outliers with -norm penalization

This article studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their proportion goes to 0. We propose a two-step procedure for inference on the coefficients of a fixed subset of regressors. The first step is a based on several square-root lasso -norm penalized estimators, while the second step is the ordinary least squares estimator applied to a well-chosen regression. We establish asymptotic normality of the two-step estimator. The proposed procedure is efficient in the sense that it attains the semiparametric efficiency bound when applied to the model without outliers under homoscedasticity. This approach is also computationally advantageous, it amounts to solving a finite number of convex optimization programs.

Convergence in Regional Poverty Rates in Bangladesh

Bangladesh has made remarkable progress in reduction of poverty headcounts, poverty gap, and squared poverty gap since 2000. While scores of studies rigorously looked into drivers of poverty reduction from the perspective of sources, both the cross country and single country literature on poverty convergence is scant. Even most of these convergence estimates are biased arising out of omitted variable due to ignorance of unobserved individual heterogeneity and endogeneity of at least a subset of regressors. This paper exploits a unique set of data to provide credible evidence of convergence in poverty across the districts of Bangladesh during 2000-2016 using the Arellano-Bond system dynamic panel estimator and panel generalized method of moments estimator. We find that poverty convergence is present during this period both through direct estimation and decomposition with relevant indirect estimates. Our results are robust to the alternative frequency of data (cross-section vis-à-vis panel) and the consequent estimation techniques, sources of data (direct estimates from the Household Income and Expenditure Surveys vis-à-vis small area estimates) and the alternative transformation of the dependent variables. Both growth-accounted poverty convergence effect and strong growth effect dominate the adverse effect of initial poverty on growth effectiveness to ensure strong overall poverty convergence found across the districts.

Gaussian process regression coupled with MPT-AES for quantitative determination of multiple elements in ginseng

A comprehensive understanding of spectral information is the most reliable approach to identify ginseng characteristics and quality. More data is produced due to the use of a high resolution spectrometer, which in turn requires high-efficiency computational capability. To well address such problems, chemometrics plays a significant part and shows satisfactory results. In this paper, a Gaussian process regression (GPR) is proposed to couple microwave plasma torch-atomic emission spectrometry (MPT-AES) for quantitative determination of multiple elements in ginseng. GPR as a probabilistic method is capable of dealing with massive data and illustrating the outputs with probabilistic meanings. With high-dimension input variables involved, the principal component analysis (PCA) is proposed to reduce computational amount and improve variable representativeness. The results show that GPR is superior to the conventional approach compared with support vector regression (SVR) by evaluation indexes. All the work is performed based on real ginseng spectral data. Taking into account the computational amount caused by large datasets of scales, three approximation methods (subset of datasets (SD), subset of regressors (SR) and projected process (PP)) are applied to address this problem, which in a way shrink the training set with a certain similar result. It is concluded that the Gaussian process performs well in spectral analysis and has the potential for further practical applications.

Addressing missing covariates for the regression analysis of competing risks: Prognostic modelling for triaging patients diagnosed with prostate cancer

Competing risks arise in medical research when subjects are exposed to various types or causes of death. Data from large cohort studies usually exhibit subsets of regressors that are missing for some study subjects. Furthermore, such studies often give rise to censored data. In this article, a carefully formulated likelihood-based technique for the regression analysis of right-censored competing risks data when two of the covariates are discrete and partially missing is developed. The approach envisaged here comprises two models: one describes the covariate effects on both long-term incidence and conditional latencies for each cause of death, whilst the other deals with the observation process by which the covariates are missing. The former is formulated with a well-established mixture model and the latter is characterised by copula-based bivariate probability functions for both the missing covariates and the missing data mechanism. The resulting formulation lends itself to the empirical assessment of non-ignorability by performing sensitivity analyses using models with and without a non-ignorable component. The methods are illustrated on a 20-year follow-up involving a prostate cancer cohort from the National Cancer Institutes Surveillance, Epidemiology, and End Results program.

Determinant Efficiencies in Ill‐Conditioned Models

The canonical correlations between subsets of OLS estimators are identified with design linkage parameters between their regressors. Known collinearity indices are extended to encompass angles between each regressor vector and remaining vectors. One such angle quantifies the collinearity of regressors with the intercept, of concern in the corruption of all estimates due to ill‐conditioning. Matrix identities factorize a determinant in terms of principal subdeterminants and the canonical Vector Alienation Coefficients between subset estimators—by duality, the Alienation Coefficients between subsets of regressors. These identities figure in the study of D and Ds as determinant efficiencies for estimators and their subsets, specifically, Ds‐efficiencies for the constant, linear, pure quadratic, and interactive coefficients in eight known small second‐order designs. Studies on D‐ and Ds‐efficiencies confirm that designs are seldom efficient for both. Determinant identities demonstrate the propensity for Ds‐inefficient subsets to be masked through near collinearities in overall D‐efficient designs.

Greedy regression ensemble selection: Theory and an application to water quality prediction

This paper studies the greedy ensemble selection family of algorithms for ensembles of regression models. These algorithms search for the globally best subset of regressors by making local greedy decisions for changing the current subset. We abstract the key points of the greedy ensemble selection algorithms and present a general framework, which is applied to an application domain with important social and commercial value: water quality prediction.

Multiple Augmentation with Partial Missing Regressors

In large cohort studies, it is common that a subset of the regressors may be missing for some study subjects by design or happenstance. In this article, we apply the multiple data augmentation techniques to semiparametric models for epidemiologic data when a subset of the regressors are missing for some subjects, under the assumption that the data are missing at random in the sense of Rubin (2004) and that the missingness probabilities depend jointly on the observable subset of regressors, on a set of observable extraneous variables and on the outcome. Computational algorithms for the Poor Man's and the Asymptotic Normal data augmentations are investigated. Simulation studies show that the data augmentation approach generates satisfactory estimates and is computationally affordable. Under certain simulation scenarios, the proposed approach can achieve asymptotic efficiency similar to the maximum likelihood approach. We apply the proposed technique to the Multi-Ethic Study of Atherosclerosis (MESA) data and the South Wales Nickel Worker Study data.

NONLINEAR STRUCTURE IDENTIFICATION WITH LINEAR LEAST SQUARES AND ANOVA

The objective of this paper is to find the structure of a nonlinear system from measurement data, as a prior step to model estimation. Applying ANOVA directly on a dataset is compared to applying ANOVA on residuals from a linear model. The distributions of the involved test variables are computed and used to show that ANOVA is effective in finding which regressors give linear effects and what regressors produce nonlinear effects. The ability to find nonlinear substructures depending on only subsets of regressors is an ANOVA feature which is shown not to be affected by subtracting a linear model.

Bayesian Modeling and Forecasting of Intraday Electricity Load

The advent of wholesale electricity markets has brought renewed focus on intraday electricity load forecasting. This article proposes a multi-equation regression model with a diagonal first-order stationary vector autoregresson (VAR) for modeling and forecasting intraday electricity load. The correlation structure of the disturbances to the VAR and the appropriate subset of regressors are explored using Bayesian model selection methodology. The full spectrum of finite-sample inference is obtained using a Bayesian Markov chain Monte Carlo sampling scheme. This includes the predictive distribution of load and the distribution of the time and level of daily peak load, something that is difficult to obtain with other methods of inference. The method is applied to several multiequation models of half-hourly total system load in New South Wales, Australia. A detailed model based on 3 years of data reveals trend, seasonal, bivariate temperature/humidity, and serial correlation components that all vary intraday, justifying the assumption of a multiequation approach. Short-term forecasts from simple models highlight the gains that can be made if accurate temperature predictions are exploited. Bayesian predictive means for half-hourly load compare favorably with point forecasts obtained using iterated generalized least squares estimation of the same models.

Consistent selection of the actual model in regression analysis

Summary In regression analysis, a best subset of regressors is usually selected by minimizing Mallows's C statistic or some other equivalent criterion, such as the Akaike lambda information criterion or cross-validation. It is known that the resulting procedure suffers from a lack of consistency that can lead to a model with too many variables. For this reason, corrections have been proposed that yield consistent procedures. The object of this paper is to show that these corrected criteria, although asymptotically consistent, are usually too conservative for finite sample sizes. The paper also proposes a new correction of Mallows's statistic that yields better results. A simulation study is conducted that shows that the proposed criterion performs well in a variety of situations.

Brickmaking and the Collinear Arts: A Cautionary Tale

In their model of induced unemployment and unemployment insurance benefits Grubel, Maki, and Sax (1975) break the collinearity between two subsets of regressors by replacing one subset with the residuals from the regression of that subset on the other. This note works out the statistical implications of this orthogonalization procedure in the general linear model. It is shown that a subset of estimators is always biased and inconsistent and that conventional inference is thereby invalidated. Furthermore, we demonstrate that orthogonalization can actually worsen collinearity if measured by its effect on estimated variances. The implications of these results for the model simplification procedure used recently in Baba, Hendry, and Starr (1992) are also discussed.

Search for the best decision rules with the help of a probabilistic estimate

The problem of how to find the best decision rule in the course of a search, based on sample set analysis, is considered. Specifically the problem of selecting the best subset of regressors is highlighted. In the considered formulation the problem is an important case of how to learn a dependence by examples.

Price and income elasticities of demand for hospital care free of quality bias

Our estimates based on a cross-section of time-series for the individual states over 1965–1977 indicate that the elasticity of bed-day demand with respect to net price is -0.20 in the long run and the same with respect to income is 0.40. The variation in the quality of care has been modeled in terms of unobserved error components, correlated with a sub-set of regressors.

Testing for Zero Intercept in Multivariate Normal Regression Using the Univariate Multiple-RegressionFTest

Abstract A likelihood ratio test is derived for comparing the performance potential of a subset of a population of financial assets to the performance potential of the entire population. The test is shown to be equivalent to a test for zero intercept in a multivariate normal regression model. Rao's F approximation to Wilks' Lamda is shown to be equivalent in this case to the conventional F test used to test the significance of a subset of regressors in a univariate multiple-regression model. The test is illustrated using a sample of returns from ten stocks from the New York Stock Exchange.