Two types of spatial regression models, a spatial lag model (SLM) and a spatial error model (SEM), were applied to fit the height–diameter relationship of trees. SEM had better model fitting and performance than both SLM and ordinary least squares. Moran’s I coefficients showed that SEM effectively reduced the spatial autocorrelation in the model residuals. Both real data and Monte Carlo simula...

Factor models are widely used in summarizing large datasets with few underlying latent factors and in building time series forecasting models for economic variables. In these models, the reduction of the predictors and the modeling and forecasting of the response y are carried out in two separate and independent phases. We introduce a potentially more attractive alternative, Sufficient Dimensio...

We propose and derive the asymptotic distribution of a tapered narrow-band least squares estimator (NBLSE) of the cointegration parameter in the framework of fractional cointegration. This tapered estimator is invariant to deterministic polynomial trends. In particular, we allow for arbitrary linear time trends that often occur in practice. Our simulations show that, in the case of no determini...

Alternative Estimation Procedures to OLS We have seen that OLS does a nice job in model estimation when the CLRM assumptions are met. We have also seen that violations of the CLRM lead to inefficiency and estimators that are not BLUE. We have also seen that the model y=Xβ+ε can be transformed to produce estimators that are BLUE. We now consider additional estimation techniques to least squares....

Ordinary Least Squares (OLS) is omnipresent in regression modeling. Occasionally Least Absolute Deviations (LAD) or other methods are used as an alternative when there are outliers. Although some data adaptive estimators have been proposed they are typically difficult to implement. In this note, we propose an easy to compute adaptive estimator which is simply a linear combination of OLS and LAD...

The scaled total least-squares (STLS) method unifies the ordinary least-squares (OLS), the total leastsquares (TLS), and the data least-squares (DLS) methods. In this paper we perform a backward perturbation analysis of the STLS problem. This also unifies the backward perturbation analyses of the OLS, TLS and DLS problems. We derive an expression for an extended minimal backward error of the ST...