ADAPTIVE PROCEDURES FOR ESTIMATION OF LINEAR REGRESSION MODELS WITH KNOWN AND UNKNOWN HETEROSCEDASTIC ERRORS

This dissertation is concerned with the concocting of new adaptive procedures of estimation of linear regression models. We take into account the case of known and unknown heteroscedastic errors, a case that frequently exists in practical regression problems. Since all type of econometric data can be classified into three main categories; Cross-sectional Data, Time Series Data, and Pooled or Panel Data so we break up our study with respect to linear regression models with heteroscedasticity, based on these three data types. For general linear regression models based on cross-sectional data, keeping in view already existent adaptive estimators; the restrictive implications of kernel estimator presented by Carroll (1982) following Watson (1964), problem of selection of nearest number in Nearest- Neighbour (NN) estimator proposed by Robinson (1987), and observations of Fuller and Rao (1978) about using estimated weighted least squares (EWLS) as used by Pasha and Ord (1994) in their adaptive formulation, we formulate a new adaptive estimator. Our adaptive estimator is based on heteroscedasticity consistent covariance estimator (HCCME) as discussed by White (1980) and White and Mackinnon (1985) at very nominal assumptions. We follow Wu's (1986) idea to estimate the unknown error variances. After proving the adaptation of our estimator in the sense of Bickel (1982), we provide finite sample properties by means of a. Monte Carlo study as used by Carroll (1982). For time series data, we focus on linear regression model with autoregressive conditional heteroscedastic (ARCH) errors founded by Engle (1982) and generalized ARCH (GARCH) presented by Bollerslev (1986). In available literature, the adaptive estimation has been limitized to the variance estimation (e.g., see Linton, 1993; Meddahi and Renault, 1998, and Drost et al, 1997) that involves, naturally, in nonlinear regression model estimation. But we fix our interest in adaptive estimation of mean parameters of regression models following (G)ARCH errors. We proposed a straight forward and computationally cheaper approach to formulate adaptive estimation procedures for mean parameters. Our approach is based on two-stage estimation. In the first stage, following Linton (1993) and Meddahi and Renault (1998), we find initial consistent estimates of the mean and variance parameters and estimate the (G)ARCH model while in the second stage we use the estimated variances to transform the model for usual correction of heteroscedasticity. For empirical results, we use the Monte Carlo scheme as used by Demos and Sentana (1998) in their work. For linear regression models based on panel data, we take into account unit-specific heteroscedasticity and propose a new adaptive estimator as a competitor to that proposed by Roy (1999) following Baltagi and Griffin (1988), Li and Stengos (1994). Our estimator is again tailored by keeping the same lines that we adapt for general linear regression models. We also justify our new adaptations not only by taking gain in efficiency but also by adequate performances in testing of hypothesis in terms of size and power of test. A number of illustrative examples are also included in the thesis.