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a b s t r a c tWe consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated.

W e consider a problem where a firm produces a variety of fresh products to supply two markets: an export market and a local market. A public transportation service is utilized to deliver the products to the export market, which is cheap, but its schedule is often disrupted severely. Each time this happens, the firm faces the following questions.(i) For a product that has been finished and is waiting for delivery to the export market, should it continue to wait, at an increasing risk of decay, and when should the waiting be terminated and the product be put to the local market? (ii) For a product that has not been finished, should its processing be postponed, so as to reduce the loss from decay after its completion? (iii) What is the best sequence to process the remaining products, according to the information available? We develop, in this study, a model to address these and other related questions. We find optimal policies that minimize the total expected loss in both the make-to-order and make-to-stock production systems, respectively. For each finished product, we reveal relationships among the desirable waiting time, the price at the local market, and the decaying cost. For unfinished products, we find the optimal start times and processing sequence. Numerical experiments are also conducted to evaluate the optimal policies.