The problem of multicollinearity and outliers in the dataset can strongly distort ordinary least squares estimates and lead to unreliable results. We propose a new Robust Liu-type M-estimator to cope with this combined problem of multicollinearity and outliers in the y-direction. Our new estimator has advantages over two parameter Liu-type estimator, Ridge-type M-estimator and Mestimator. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.
Several alternative methods for derivation of the restricted ridge regression estimator (RRRE) are provided. Theoretical comparison and relationship of RRRE with related methods for regression with the multicollinearity problem are described. We also find inter-connections among RRRE, ordinary ridge regression estimator (ORRE), restricted least squares estimator (RLSE), modified ridge regression estimator (MRRE) and restricted modified generalized ridge estimator (RMGRE). Finally, numerical comparison, in addition to theoretical derivation, is also conducted with a Monte Carlo simulation and a real data example.
The finite distributed lag models include highly correlated variables as well as lagged and unlagged values of the same variables. Some problems are faced for this model when applying the ordinary least squares (OLS) method or econometric models such as Almon and Koyck models. The primary aim of this study is to compare performances of alternative estimators to the OLS estimator defined by combining the Almon estimator with some estimators using Almon (1965) data. A simulation study with different model parameters is performed and the estimators are compared according to the root mean square error (RMSE) and prediction mean square error (PMSE).
The authors share their experience on a collision tumor of growth hormone (GH)-secreting adenoma and gangliocytoma in the pituitary gland, which was reported by few articles in the literature. Also, an intraoperative view of this tumor, operated via endoscopic endonasal transsphenoidal approach, is presented for the first time. A 39-year-old female patient was admitted with clinical manifestation of acromegaly present in a 2-year period. Laboratory investigations revealed high levels of GH and insulinlike growth factor 1. Sellar computed tomography scan and magnetic resonance imaging showed a sellar mass diagnosed as a pituitary adenoma. Based on clinical, biochemical, and radiologic evaluations, GH-secreting pituitary adenoma was diagnosed and operated by endoscopic endonasal transsphenoidal approach achieving total removal of the tumor. Histopathologic examination revealed a collision tumor of GH-secreting adenoma and gangliocytoma. Postoperative radiologic and biochemical investigations showed no residual tumor and total remission. The endoscopic endonasal transsphenoidal approach promotes a close intraoperative view of sellar pathologies. We believe that a detailed histopathologic workup is necessary to diagnose collision tumors, because even a close intraoperative view does not facilitate to differentiate these tumors from a regular pituitary adenoma.
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