Asymptotic Properties Of LS Estimator In Nonlinear Functional EV Models

Nonlinear regression models occur frequently in the modeling of stochastic phenomena.The study for the convergence problem of the least squares(LS)estimator in a nonlinear regression model has been the subject of investigation.In practical statistical work one often encounters such non-standard situations when the explanatory variables of the re-gression models can only be observed with errors.In the present paper,we will deal with the following model(?) where {Xn},{Yn} are observed,{?n},{?n} are random error terms,{?n} are(nonrandom)nuisance parameters,g is a known function and ? is a unknown parameter to be estimated.We call this as errors-in-variables(EV)regression model.Base on this model,One is the case that {(?n,?n)},n?1} are k-wise independent sequences,which extends previous results from independence between {?n} and {?n} to k-wise independence of {(?n,?n),n?1}.When the sequence(?n)n?1 is independent from the sequence(?n)n?1,which(?n)n?1 is a sequence of ?-mixing random variables,and(?n)n?1 is a sequence of ?-mixing random variables or martingale difference,we obtain the consistency and deviation inequality under some weaker conditions.Furthermore,we consider the case that(?n)n?1 is an ?-mixing random sequences and(?n)n?1 is an any random sequence,then under some conditions,the consistency and deviation inequality for the estimator hold.In order to provide a description of the main content of this paper,the related knowl-edge will be described in detail.In the second chapter,we will introduce some relevant probability basics,such as two asymptotic properties of random variables sequence,the definition of martingale difference and so on.Then,some lemmas of probability theory are introduced to prove the main results of the modelsOur main results and their proof will be given in the third chapter.The aims of this chapter are to in nonlinear EV models,it studies weak consistency of LS estimator,deviation inequality and strong consistency.