Conditional least squares estimation in nonstationary nonlinear stochastic regression models
非平稳非线性随机回归模型的条件最小二乘估计
Let {Zn} be a real nonstationary stochastic process such that $E(Z_{n}|{\mathcal{F}}_{n-1})\stackrel{\mathrm{a.s.}}<\infty$ and $E(Z_{n}^{2}|{\mathcal{F}}_{n-1})\stackrel{\mathrm{a.s.}}<\infty$, where $\{{\mathcal{F}}_{n}\}$ is an increasing sequence of σ-algebras. Assuming that $E(Z_{n}|{\mathcal{F}}_{n-1})=g_{n}(\theta_{0},\nu_{0})=g_{n}^{(1)}(\theta_{0})+g_{n}^{(2)}(\theta _{0},\nu_{0})$, θ0∈ℝp, p<∞, ν0∈ℝq and q≤∞, we study the asymptotic properties of $\widehat{\theta}_{n}:=\arg\min_{\theta}\sum_{k=1}^{n}(Z_{k}-g_{k}({\theta,\widehat{\nu}}))^{2}\lambda _{k}^{-1}$…