59,468 research outputs found
Estimating the intercept in an orthogonally blocked experiment when the block effects are random.
Abstract: For an orthogonally blocked experiment, Khuri (1992) has shown that the ordinary least squares estimator and the generalized least squares estimator of the factor effects in a response surface model with random block effects coincide. However, the equivalence does not hold for the estimation of the intercept when the block sizes are heterogeneous. When the block sizes are homogeneous, ordinary and generalized least squares provide an identical estimate for the intercept.Effects;
Improving weighted least squares inference
These days, it is common practice to base inference about the coefficients in a hetoskedastic linear model on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can also used to base valid inference on a weighted least squares estimator and using such an estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on asymptotic approximations with plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. Similarly, tests can have null rejection probabilities that are above the nominal level. It is shown that under unknown hereroskedasticy, a bootstrap approximation to the sampling distribution of the weighted least squares estimator is valid, which allows for inference with improved finite-sample properties. For testing linear constraints, permutations tests are proposed which are exact when the error distribution is symmetric and is asymptotically valid otherwise. Another concern that has discouraged the use of weighting is that the weighted least squares estimator may be less efficient than the ordinary least squares estimator when the model used to estimate the unknown form of the heteroskedasticity is misspecified. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals
Robust continuum regression.
Several applications of continuum regression (CR) to non-contaminated data have shown that a significant improvement in predictive power can be obtained compared to the three standard techniques which it encompasses (ordinary least squares (OLS), principal component regression (PCR) and partial least squares (PLS)). For contaminated data continuum regression may yield aberrant estimates due to its non-robustness with respect to outliers. Also for data originating from a distribution which significantly differs from the normal distribution, continuum regression may yield very inefficient estimates. In the current paper, robust continuum regression (RCR) is proposed. To construct the estimator, an algorithm based on projection pursuit (PP) is proposed. The robustness and good efficiency properties of RCR are shown by means of a simulation study. An application to an X-ray fluorescence analysis of hydrometallurgical samples illustrates the method's applicability in practice.Regression; Applications; Data; Ordinary least squares; Least-squares; Squares; Partial least squares; Yield; Outliers; Distribution; Estimator; Projection-pursuit; Robustness; Efficiency; Simulation; Studies;
Cancerphobia: Electromagnetic Fields and Their Impact on Residential Loan Values
This article provides a matrix representation of the adjustment grid estimator. From this representation, one can invoke the Gauss-Mrkov theorem to examine the efficiency of ordinary least squares (OLS) and the grid estimator that uses OLS estimates of the adjustments (the "plug-in" grid method). In addition, this matrix representation suggests a generalized least squares version of the grid method, labeled herin as the total grid estimator. Based on the empirical experiments, the total grid estimator outperformed the plug-in grid estimator, which in turn outperformed the OLS.
Inference on Time-Invariant Variables using Panel Data: A Pre-Test Estimator with an Application to the Returns to Schooling
This paper proposes a new pre-test estimator of panel data models including time invariant variables based upon the Mundlak-Krishnakumar estimator and an "unrestrictedā Hausman-Taylor estimator. The paper evaluates the biases of currently used restricted estimators, omitting the average-over-time of at least one endogenous time-varying explanatory variable. Repeated Between, Ordinary Least Squares, Two stage restricted Between and Oaxaca-Geisler estimator, Fixed Effect Vector Decomposition, Generalized least squares may lead to wrong conclusions regarding the statistical significance of the estimated parameter values of time-invariant variables.Time-Invariant Variables, Panel data, Time-Series Cross-Sections, Pre-Test Estimator, Mundlak Estimator, Fixed Effects Vector Decomposition
Robustness or Efficiency, A Test to Solve the Dilemma
When dealing with the presence of outliers in a dataset, the problem of choosing between the classical ordinary least squares and robust regression methods is sometimes addressed inadequately. In this article, we propose using a Hausman-type test to determine whether a robust S- estimator is more appropriate than an ordinary least squares one in a multiple linear regression framework, on the basis of the trade-off betewen robustness and efficiency. An economic example is provided to illustrate the usefulness of the test.Efficiency, Hausman Test, Linear Regression, Robustness, S- estimator
Robust continuum regression.
Several applications of continuum regression to non-contaminated data have shown that a significant improvement in predictive power can be obtained compared to the three standard techniques which it encompasses (Ordinary least Squares, Principal Component Regression and Partial Least Squares). For contaminated data continuum regression may yield aberrant estimates due to its non-robustness with respect to outliers. Also for data originating from a distribution which significantly differs from the normal distribution, continuum regression may yield very inefficient estimates. In the current paper, robust continuum regression (RCR) is proposed. To construct the estimator, an algorithm based on projection pursuit is proposed. The robustness and good efficiency properties of RCR are shown by means of a simulation study. An application to an X-ray fluorescence analysis of hydrometallurgical samples illustrates the method's applicability in practice.Advantages; Applications; Calibration; Continuum regression (CR); Data; Distribution; Efficiency; Estimator; Least-squares; M-estimators; Methods; Model; Optimal; Ordinary least squares; Outliers; Partial least squares; Precision; Prediction; Projection-pursuit; Regression; Research; Robust continuum regression (RCR); Robust multivariate calibration; Robust regression; Robustness; Simulation; Squares; Studies; Variables; Yield;
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