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Bernstein 多项式密度估计的收敛速度AI 解读

Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach.For a density on the unit interval, mixtures of beta densities form a flexible model. The class of Bernstein densities is a much smaller subclass of the beta mixtures defined by Bernstein polynomials, which can approximate any continuous density. A Bernstein polynomial prior is obtained by putting a prior distribution on the class of Bernstein densities. The…

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…

非参数回归问题中的参数化与推断AI 解读

Summary We consider local likelihood or local estimating equations, in which a multivariate function Θ(·) is estimated but a derived function λ(·) of Θ(·) is of interest. In many applications, when most naturally formulated the derived function is a non-linear function of Θ(·). In trying to understand whether the derived non-linear function is constant or linear, a problem arises with this approach: when the function is actually constant or linear, the expectation of the…

利用局部似然追踪断裂线与边界AI 解读

Summary We suggest locally parametric methods for estimating curves, such as boundaries of density supports or fault lines in response surfaces, in a variety of spatial problems. The methods are based on spatial approximations to the local likelihood that the curve passes through a given point in the plane, as a function of that point. The local likelihood might be a regular likelihood computed locally, with kernel weights (e.g. in the case of support boundary estimation) or…

利用广义估计方程进行聚类数据的半参数回归AI 解读

We consider estimation in a semiparametric generalized linear model for clustered data using estimating equations. Our results apply to the case where the number of observations per cluster is finite, whereas the number of clusters is large. The mean of the outcome variable μ is of the form g(μ) = XTβ + θ(T), where g(·) is a link function, X and T are covariates, β is an unknown parameter vector, and θ(t) is an unknown smooth function. Kernel estimating equations proposed…

基于软阈值的高维广义线性模型推断AI 解读

Summary We further develop and analyse penalized likelihood estimators for generalized linear models with a large number of coefficients. The methodology proposed leads to an adaptive selection of model terms without substantial variance inflation. Our proposal extends the soft thresholding strategy of Donoho and Johnstone and the lasso of Tibshirani to generalized linear models and multiple predictor variables. In addition, we develop an estimator for the covariance matrix…

离散值时间序列的平滑估计AI 解读

Summary We deal with smoothed estimators for conditional probability functions of discrete-valued time series {Yt} under two different settings. When the conditional distribution of Yt given its lagged values falls in a parametric family and depends on exogenous random variables, a smoothed maximum (partial) likelihood estimator for the unknown parameter is proposed. While there is no prior information on the distribution, various nonparametric estimation methods have been…

平移曲线的非参数最大似然估计AI 解读

Summary The analysis of a sample of curves can be done by self-modelling regression methods. Within this framework we follow the ideas of nonparametric maximum likelihood estimation known from event history analysis and the counting process set-up. We derive an infinite dimensional score equation and from there we suggest an algorithm to estimate the shape function for a simple shape invariant model. The nonparametric maximum likelihood estimator that we find turns out to be…

动态面板样本选择模型的估计AI 解读

This paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule, when the latent equations contain strictly exogenous variables, lags of the dependent variables, and unobserved individual effects. We derive a set of conditional moment restrictions which are then exploited to construct two-step GMM-type estimators for the parameters of the main equation. In the first step, the unknown parameters of the…

施加单调性约束的非参数核回归AI 解读

We suggest a method for monotonizing general kernel-type estimators, for example local linear estimators and Nadaraya .Watson estimators. Attributes of our approach include the fact that it produces smooth estimates, indeed with the same smoothness as the unconstrained estimate. The method is applicable to a particularly wide range of estimator types, it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has…

单指标模型中指标系数的直接估计AI 解读

Single-index modeling is widely applied in,for example,econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models. By such modeling the statistical analysis usually focuses on estimating the index coefficients. The average derivative estimator (ADE) of the index vector is based on the fact that the average gradient of a single index function $f(x^{\top}\beta)$ is proportional to the index vector…

英国宏观经济预测面板分析AI 解读

This paper looks at unobserved components models and examines the implied weighting patterns for signal extraction. There are four main themes. The first concerns the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is about the way in which ARIMA-based methods for trend extraction relate to those based on unobserved components. The third explores the impact of heteroscedasticity and…

摘要暂缺

通过混合实现自适应回归AI 解读

Adaptation over different procedures is of practical importance. Different procedures perform well under different conditions. In many practical situations, it is rather hard to assess which conditions are (approximately) satisfied so as to identify the best procedure for the data at hand. Thus automatic adaptation over various scenarios is desirable. A practically feasible method, named adaptive regression by mixing (ARM), is proposed to convexly combine general candidate…

时间聚合与协整系统中谱回归估计量的有限样本表现AI 解读

The finite sample performance of spectral regression estimators in temporally aggregated cointegrated systems is investigated via the use of simulation experiments. The simulations address issues such as “optimal” choice of bandwidth parameter and effects of smoothing kernel in constructing estimates of spectral densities that are used by the spectral regression estimators; the effects of stock and flow variables and mixtures of the two, including the relative finite sample…

时间序列非参数估计的马尔可夫局部重抽样方案AI 解读

In this paper we study the properties of a pth-order Markovian local resampling procedure in approximating the distribution of nonparametric (kernel) estimators of the conditional expectation m(x;φ). Under certain regularity conditions, asymptotic validity of the proposed resampling scheme is established for a class of stochastic processes that is broader than the class of stationary Markov processes. Some simulations illustrate the finite sample performance of the proposed…

谱密度估计与学生化样本均值的 Edgeworth 展开AI 解读

We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the sample mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our…

截断动态与扩散方程估计AI 解读

We study inference on continuous-time processes from discrete data with a given time interval between consecutive observations, and propose a modification of the sieve estimation method based on the infinitesimal generator. Our approach consists on truncating the initial process to improve the estimation of the eigenfunctions at the boundaries of the set of admissible values. For diffusion processes, nonparametric estimation of the drift and volatility are derived. A prior…

利用小波方法检验未知形式的序列相关AI 解读

A wavelet-based consistent test for serial correlation of unknown form is proposed. As a spatially adaptive estimation method, wavelets can effectively detect local features such as peaks and spikes in a spectral density, which can arise as a result of strong autocorrelation or seasonal or business cycle periodicities in economic and financial time series. The proposed test statistic is constructed by comparing a wavelet-based spectral density estimator and the null spectral…

空间自适应回归样条与精确结点选择方案AI 解读

Spline procedures have proven effective in estimating smooth functions. However, spline procedures based on stepwise addition and/or deletion have some drawbacks. They suffer from the knot compounding problem, making their performance suboptimal. Furthermore, due to computational complexity, spline procedures may not achieve their full potential. In this article, we propose a novel knot selection algorithm for regression spline estimation in nonparametric regression. The…

非参数曲线估计的置信区间AI 解读

Numerous nonparametric regression methods exist that yield consistent estimators of function curves. Often, one is also interested in constructing confidence intervals for the unknown function. When a function estimate is based on a single global smoothing parameter the resulting confidence intervals may hold their desired confidence level 1 – α on average but because bias in nonparametric estimation is not uniform, they do not hold the desired level uniformly at all design…

多元伯努利观测的平滑样条方差分析及眼科应用AI 解读

We combine a smoothing spline analysis of variance (SS-ANOVA) model and a log-linear model to build a partly flexible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The log odds ratio is used to measure the association between outcome variables. A numerical scheme based on the block one-step successive over relaxation SOR–Newton-Ralphson algorithm is proposed to obtain an approximate solution for the…

异质风险率回归模型：理论与应用AI 解读

Summary A class of non-proportional hazards regression models is considered to have hazard specifications consisting of a power form of cross-effects on the base-line hazard function. The primary goal of these models is to deal with settings in which heterogeneous distribution shapes of survival times may be present in populations characterized by some observable covariates. Although effects of such heterogeneity can be explicitly seen through crossing cumulative hazards…

多元线性样条的贝叶斯回归AI 解读

Summary We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both…