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适应未知误差分布的非参数回归估计量AI 解读

We propose a new kernel estimator for nonparametric regression with unknown error distribution. We show that the proposed estimator is adaptive in the sense that it is asymptotically equivalent to the infeasible local likelihood estimator (Staniswalis, 1989, Journal of the American Statistical Association 84, 276–283; Fan, Farmen, and Gijbels, 1998, Journal of the Royal Statistical Society, Series B 60, 591–608; and Fan and Chen, 1999, Journal of the Royal Statistical…

近历元依赖条件下的局部线性拟合AI 解读

Local linear fitting of nonlinear processes under strong (i.e., α-) mixing conditions has been investigated extensively. However, it is often a difficult step to establish the strong mixing of a nonlinear process composed of several parts such as the popular combination of autoregressive moving average (ARMA) and generalized autoregressive conditionally heteroskedastic (GARCH) models. In this paper we develop an asymptotic theory of local linear fitting for near epoch…

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GARCH(1,1) 模型的闭式估计量AI 解读

We propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum likelihood estimator (QMLE) that it can be easily implemented and does not require the use of any numerical optimization procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T(κ−1)/κ-consistency for some κ ∈ (1,2) when the fourth moment exists and…

非平衡时间序列数据的非参数推断AI 解读

This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data are unbalanced or incomplete. In this case, one can work with only the common sample, to which a standard HAC/bootstrap theory applies, but at the expense of throwing away data and perhaps losing efficiency. An alternative is to use some sort of imputation method, but this requires additional modeling assumptions, which we would rather avoid. We show how…

广义可加波动模型的 LIVE 方法AI 解读

We investigate a new separable nonparametric model for time series, which includes many autoregressive conditional heteroskedastic (ARCH) models and autoregressive (AR) models already discussed in the literature. We also propose a new estimation procedure called LIVE, or local instrumental variable estimation, that is based on a localization of the classical instrumental variable method. Our method has considerable computational advantages over the competing marginal…

Consistent standard errors for target variance approach to GARCH estimation.

响应随机缺失时的半参数回归分析AI 解读

We develop inference tools in a semiparametric partially linear regression model with missing response data. A class of estimators is defined that includes as special cases a semiparametric regression imputation estimator, a marginal average estimator, and a (marginal) propensity score weighted estimator. We show that any of our class of estimators is asymptotically normal. The three special estimators have the same asymptotic variance. They achieve the semiparametric…

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Consistent standard errors for target variance approach to GARCH estimation.

目标函数不光滑时半参数模型的估计AI 解读

We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated. Our results extend existing theories such as those of Pakes and Pollard (1989), Andrews (1994a), and Newey (1994). We also show that…

风险溢价的形状AI 解读

We examine the relationship between the risk premium on the Center for Research on Security Prices (CRSP) value-weighted index total return and its conditional variance. We propose a new semiparametric model in which the conditional variance process is parametric and the conditional mean is an arbitrary function of the conditional variance. For monthly CRSP value-weighted excess returns, the relationship between the two moments that we uncover is nonlinear and nonmonotonic.

椭圆对称下资本资产定价模型的有效检验：半参数方法AI 解读

Abstract We develop new tests of the capital asset pricing model that take account of and are valid under the assumption that the distribution generating returns is elliptically symmetric; this assumption is necessary and sufficient for the validity of the CAPM. Our test is based on semiparametric efficient estimation procedures for a seemingly unrelated regression model where the multivariate error density is elliptically symmetric, but otherwise unrestricted. The…

聚合数据下的非参数估计AI 解读

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical…

非参数删失与截断回归AI 解读

The nonparametric censored regression model, with a fixed, known censoring point (normalized to zero), is y = max[0,m(x) + e], where both the regression function m(x) and the distribution of the error e are unknown. This paper provides estimators of m(x) and its derivatives. The convergence rate is the same as for an uncensored nonparametric regression and its derivatives. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients…

半参数工具变量估计量与检验统计量的 Edgeworth 近似AI 解读

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable considered in Newey (1990) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and [a version of] nearest neighbour estimates as special cases. Our expansions are valid to order n^(-2ϵ) for some 0 < ϵ < ½, where ϵ…

通过部分 Lq 范数估计加性非参数模型：分数阶的代价AI 解读

We propose a new method for estimating additive nonparametric regression models based on taking the L q median of a sample of kernel estimators. We establish the consistency and asymptotic normality of our procedures. The rate of convergence depends on the value of q . For q > 3/2 one has the usual one-dimensional rate, but if q ≤ 3/2 the rate can be slower.

核平滑方法下的收益率曲线估计AI 解读

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approach is nonparametric and does not assume a particular functional form for the discount function although we do show how to impose various restrictions in the estimation. Our method is based on kernel smoothing and is defined as the minimum of some localized population moment condition. The solution to the sample problem is not…

自适应回归估计量的二阶近似AI 解读

We derive asymptotic expansions for semiparametric adaptive regression estimators. In particular, we derive the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form. We then show how the choice of smoothing parameters influences the estimator through higher order terms. A method of bandwidth selection is defined by minimizing the second-order mean squared error. We examine both…

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随机时间序列李雅普诺夫指数非参数估计的渐近分布AI 解读

This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root-T consistency and asymptotic normality, while in the second case, which is more relevant for chaotic processes, we are only able to establish asymptotic normality at a slower rate of convergence. We provide consistent confidence intervals for both cases. We apply our…

具有灵活协变量效应的半参数生存模型AI 解读

A semiparametric hazard model with parametrized time but general covariate dependency is formulated and analyzed inside the framework of counting process theory. A profile likelihood principle is introduced for estimation of the parameters: the resulting estimator is $n^{1/2}$-consistent, asymptotically normal and achieves the semiparametric efficiency bound. An estimation procedure for the nonparametric part is also given and its asymptotic properties are derived. We…

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