This paper studies how the sample rotation method is applied to the case where item nonresponse occurs in surveys. The two cases where the response to the first occasion is complete or incomplete are considered. Using ratio imputation method, the estimators of the current population mean are proposed, which are valid under uniform response regardless of the model and under the ratio model regardless of the response mechanism. Under uniform response, the variances of the proposed estimators are derived. Interestingly, although their expressions are similar, the estimator for the case of incomplete response on the first occasion can have smaller variance than the one for the case of complete response on the first occasion under uniform response. The linearized jackknife variance estimators are also given. These variance estimators prove to be approximately design-unbiased under uniform response. It should be noted that similar property on variance estimators has not been discussed in literature.
Consider the standard non-linear regression model yi = g(xi, θo) +εi, i = 1,..., n where g(x.θ) is a continuous function on a bounded closed region X × О-, θ00 is the unknown parameter vector in О- C R^p, {x1, x2 …… xn} is a deterministic design of experiment and {ε1, ε2 …… εn} is a sequence of independent random variables. Tiffs paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time. we point out that Theorem 2 of Wang (1995) (J. of Multivariate Analysis, vol. 54, pp. 227 238,Corrigenda. vol. 55, p. 350) is not correct.
