Abstract: Based on the quasi-likelihood estimates obtained by the
local linear method,~the generalized likelihood ratio tests for the
models were established.~Under the null hypothesis the test
statistic followed asymptotically the $\chi^{2}$-distribution with
the scale constants and the degree of freedom being independent of
the nuisance parameters and the nuisance functions,~which was called
the Wilks phenomenon.~A simulated example was presented to
illustrate the proposed methods.

Key words: quasi-likelihood estimates, generalized likelihood ratio tests, Wilks phenomenon , local linear method, quasi-likelihood estimates, generalized likelihood ratio tests, Wilks phenomenon