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兼顾数值误差与测量误差的非线性常微分方程系数筛估计AI 解读

This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge-Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical…

非参数可加模型中的变量选择AI 解读

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component…

Bootstrap 的不一致性：Grenander 估计量AI 解读

In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate n1/3. The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function f on [0, ∞), is a prototypical example. We focus on this example and explore different approaches to constructing bootstrap confidence intervals for f(t0), where t0 ∈ (0, ∞) is an…

非平稳时间序列分位数曲线的非参数推断AI 解读

The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type I error rates. A wild bootstrap procedure is implemented to alleviate the problem of slow…

双曲平面上的莫比乌斯反卷积及阻抗密度估计AI 解读

In this paper we consider a novel statistical inverse problem on the Poincaré, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of 2 × 2 real matrices of determinant one via Möbius transformations. Our approach is based on a deconvolution technique which relies on the Helgason–Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a…

半参数相对风险Cox模型的惩罚变量选择AI 解读

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts. Two penalties are applied sequentially. The first penalty, governing the smoothness of the multivariate nonlinear covariate…

指数族中的非参数回归AI 解读

Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In this paper we consider nonparametric regression in exponential families with the main focus on the natural exponential families with a quadratic variance function, which include, for example, Poisson regression, binomial regression and gamma…

多变量分数协整系统的半参数推断AI 解读

A semiparametric multivariate fractionally cointegrated system is considered, integration orders possibly being unknown and I(0) unobservable inputs having nonparametric spectral density. Two estimates of the vector of cointegrating parameters [nu] are considered. One involves inverse spectral weighting and the other is unweighted but uses a spectral estimate at frequency zero. Both corresponding Wald statistics for testing linear restrictions on [nu] are shown to have a…

非可分模型中的结构性测量误差AI 解读

This paper considers measurement error from a new perspective. In surveys, response errors are often caused by the fact that respondents recall past events and quantities imperfectly. We explore the consequences of limited recall for the identification of marginal effects. Our identification approach is entirely nonparametric, using Matzkin-type nonseparable models that nest a large class of potential structural models. We show that measurement error due to limited recall…

不完全信息同时行动博弈的半参数估计AI 解读

This paper studies the problem of estimating the normal-form payoff parameters of a simultaneous, discrete game where the realization of such payoffs is not common knowledge. The paper contributes to the existing literature in two ways. First, by making a comparison with the complete information case it formally describes a set of conditions under which allowing for private information in payoffs facilitates the identification of various features of the game. Second,…

高斯时间序列的贝叶斯非参数信号提取AI 解读

We consider the problem of unobserved components in time series from a Bayesian non-parametric perspective. The identification conditions are treated as unknown and analyzed in a probabilistic framework. In particular, informative prior distributions force the spectral decomposition to be in an identifiable region. Then, the likelihood function adapts the prior decompositions to the data. A full Bayesian analysis of unobserved components will be presented for financial high…

结合函数及导数数据的非参数最小二乘估计AI 解读

Cost function estimation often involves data on a function and a family of its derivatives. Such data can substantially improve convergence rates of nonparametric estimators. We propose series-type estimators which incorporate the various derivative data into a single nonparametric least-squares procedure. Convergence rates are obtained and it is shown that for low-dimensional cases, much of the beneficial impact is realized even if only data on ordinary first-order partials…

潜在竞标人数未知时的一价拍卖估计：误分类方法AI 解读

In this paper, we consider nonparametric identification and estimation of first-price auction models when N*, the number of potential bidders, is unknown to the researcher, but observed by bidders. Exploiting results from the recent econometric literature on models with misclassification error, we develop a nonparametric procedure for recovering the distribution of bids conditional on the unknown N*. Monte Carlo results illustrate that the procedure works well in practice.…

贝叶斯半参数随机波动率建模AI 解读

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of…

动态条件分位数模型的有效估计AI 解读

In this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data. We construct an M-estimator which achieves the semiparametric efficiency bound recently derived by Komunjer and Vuong (forthcoming). Our efficient M-estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density. The estimator…

一类 Lévy 过程的非参数估计AI 解读

We consider estimation for a class of Lévy processes, modelled as a sum of a drift, a symmetric stable process and a compound Poisson process. We propose a nonparametric approach to estimating unknown parameters of our model, including the drift, the scale and index parameters in the stable law, the mean of the Poisson process and the underlying jump size distribution. We show that regression and nonparametric deconvolution methods, based on the empirical characteristic…

谱密度估计的渐近理论AI 解读

We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

通过非参数回归与特征函数检验多因子连续时间马尔可夫模型AI 解读

We develop a nonparametric regression-based goodness-of-fit test for multifactor continuous-time Markov models using the conditional characteristic function, which often has a convenient closed form or can be approximated accurately for many popular continuous-time Markov models in economics and finance. An omnibus test fully utilizes the information in the joint conditional distribution of the underlying processes and hence has power against a vast class of continuous-time…

关于特征价格函数的非参数估计AI 解读

Abstract Recently, using mixed data on Canadian housing, Parmeter, Henderson, and Kumbhakar ( Journal of Applied Econometrics 2007; 22 : 695–699) found that a nonparametric approach for estimating a hedonic house price function is superior to formerly suggested parametric and semiparametric specifications. We carefully reanalyze these specifications for this dataset by applying a recent nonparametric specification test and simulation‐based prediction comparisons. For the…

部分线性空间自回归模型的剖面准最大似然估计AI 解读

We propose profile quasi-maximum likelihood estimation of spatial autoregressive models that are partially linear. The rate of convergence of the spatial parameter estimator depends on some general features of the spatial weight matrix of the model. The estimators of other finite-dimensional parameters in the model have the regular -rate of convergence and the estimator of the nonparametric component is consistent but with different restrictions on the choice of bandwidth…

半参数空间自回归模型的有效估计AI 解读

Efficient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing non-stochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the case of distribution of unknown, nonparametric, form, where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest. These estimates are as efficient as the ones based on a correct form, in particular…

半参数协整回归：年龄分布对消费与储蓄的影响AI 解读

We consider a semiparametric cointegrating regression model, for which the disequilibrium error is further explained nonparametrically by a functional of distributions changing over time. The paper develops the statistical theories of the model. We propose an efficient econometric estimator and obtain its asymptotic distribution. A specification test for the model is also investigated. The model and methodology are applied to analyze how an aging population in the US…

非参数传递函数模型AI 解读

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between 'input' and 'output' time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more…

数据依赖平滑参数下的非参数与半参数估计及检验AI 解读

We consider nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters. Most of the existing works on asymptotic distributions of a nonparametric/semiparametric estimator or a test statistic are based on some deterministic smoothing parameters, while in practice it is important to use data-driven methods to select the smoothing parameters. In this paper we give a simple sufficient condition that can be used to establish…