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Testing for the stochastic dominance efficiency of a given portfolio

给定投资组合的随机占优有效性检验

We propose a new statistical test of the stochastic dominance efficiency of a given portfolio over a class of portfolios. We establish its null and alternative asymptotic properties, and define a method for consistently estimating critical values. We present some numerical evidence that our tests work well in moderate‐sized samples.

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Nonparametric estimation of a periodic sequence in the presence of a smooth trend

存在平滑趋势时周期序列的非参数估计

We investigate a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the…

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GLOBAL BAHADUR REPRESENTATION FOR NONPARAMETRIC CENSORED REGRESSION QUANTILES AND ITS APPLICATIONS

非参数删失回归分位数的全局 Bahadur 表示及其应用

This paper is concerned with the nonparametric estimation of regression quantiles of a response variable that is randomly censored. Using results on the strong uniform convergence rate of U-processes, we derive a global Bahadur representation for a class of locally weighted polynomial estimators, which is sufficiently accurate for many further theoretical analyses including inference. Implications of our results are demonstrated through the study of the asymptotic properties…

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ESTIMATION OF AND INFERENCE ABOUT THE EXPECTED SHORTFALL FOR TIME SERIES WITH INFINITE VARIANCE

无限方差时间序列的预期损失估计与推断

We study estimation and inference of the expected shortfall for time series with infinite variance. Both the smoothed and nonsmoothed estimators are investigated. The rate of convergence is determined by the tail thickness parameter, and the limiting distribution is in the stable class with parameters depending on the tail thickness parameter of the time series and on the dependence structure, which makes inference complicated. A subsampling procedure is proposed to carry…

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Nonparametric estimation and inference about the overlap of two distributions

两个分布重叠程度的非参数估计与推断

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a…

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LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE: UNIFORM CONSISTENCY WITH CONVERGENCE RATES

近历依赖下局部线性拟合的一致收敛及其速率

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory 23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear…

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Estimation of semiparametric locally stationary diffusion models

半参数局部平稳扩散模型的估计

This paper proposes a class of locally stationary diffusion processes. The model has a time varying but locally linear drift and a volatility coefficient that is allowed to vary over time and space. The model is semiparametric because we allow these functions to be unknown and the innovation process is parametrically specified, indeed completely known. We propose estimators of all the unknown quantities based on long span data. Our estimation method makes use of the property…

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Semiparametric estimation of Markov decision processes with continuous state space

连续状态空间马尔可夫决策过程的半参数估计

We propose a general two-step estimator for a popular Markov discrete choice model that includes a class of Markovian games with continuous observable state space. Our estimation procedure generalizes the computationally attractive methodology of Pesendorfer and Schmidt-Dengler (2008) that assumed finite observable states. This extension is non-trivial as the policy value functions are solutions to some type II integral equations. We show that the inverse problem is…

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A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom

用于非平衡数据的半参数面板模型:英国气候变化应用

This paper is concerned with developing a semiparametric panel model to explain the trend in UK temperatures and other weather outcomes over the last century. We work with the monthly averaged maximum and minimum temperatures observed at the twenty six Meteorological Office stations. The data is an unbalanced panel. We allow the trend to evolve in a nonparametric way so that we obtain a fuller picture of the evolution of common temperature in the medium timescale. Profile…

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Estimating features of a distribution from binomial data

从二元响应数据估计潜在分布特征

We propose estimators of features of the distribution of an unobserved random variable W. What is observed is a sample of Y,V,X where a binary Y equals one when W exceeds a threshold V determined by experimental design, and X are covariates. Potential applications include bioassay and destructive duration analysis. Our empirical application is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values W…

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ESTIMATION OF A SEMIPARAMETRIC IGARCH(1,1) MODEL

半参数 IGARCH(1,1) 模型的估计

We propose a semiparametric IGARCH model that allows for persistence in variance but also allows for more flexible functional form. We assume that the difference of the squared process is weakly stationary. We propose an estimation strategy based on the nonparametric instrumental variable method. We establish the rate of convergence of our estimator.

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Evaluating Value-at-Risk Models via Quantile Regression

通过分位数回归评估风险价值模型

This article is concerned with evaluating Value-at-Risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Manganelli (2004) are based on such variables. In this article we propose a new backtest that does not rely solely on binary variables. It is…

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Efficient estimation of a multivariate multiplicative volatility model

多元乘法波动率模型的有效估计

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various kernel-based estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a…

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UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL

局部多项式 M 回归估计的一致 Bahadur 表示及其加性模型应用

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {( Y i , X i )}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We…

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Identification and nonparametric estimation of a transformed additively separable model

变换加性可分模型的识别与非参数估计

Let r(x,z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses the identification and consistent estimation of the unknown functions H, M, G and F, where r(x,z)=H[M(x,z)], M(x,z)=G(x)+F(z), and H is strictly monotonic. An estimation algorithm is proposed for each of the model's unknown components when r(x,z) represents a conditional mean function. The resulting estimators use marginal integration to separate…

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An improved bootstrap test of stochastic dominance

改进的随机占优自助法检验

We propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling. The method admits prospects involving infinite as well as finite dimensional unknown parameters, so that the variables are allowed to be residuals from nonparametric and semiparametric models. The proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null…

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ESTIMATION FOR A NONSTATIONARY SEMI-STRONG GARCH(1,1) MODEL WITH HEAVY-TAILED ERRORS

重尾误差下非平稳半强 GARCH(1,1) 模型的估计

This paper studies the estimation of a semi-strong GARCH(1,1) model when it does not have a stationary solution, where semi-strong means that we do not require the errors to be independent over time. We establish necessary and sufficient conditions for a semi-strong GARCH(1,1) process to have a unique stationary solution. For the nonstationary semi-strong GARCH(1,1) model, we prove that a local minimizer of the least absolute deviations (LAD) criterion converges at the rate $\root \of n $…

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Consistent estimation of a general nonparametric regression function in time series

时间序列中一般非参数回归函数的一致估计

We propose an estimator of the conditional distribution of XtXt-1,Xt-2,..., and the corresponding regression function , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.

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Non-parametric regression with a latent time series

含潜在时间序列的非参数回归

In this paper we investigate a class of semi-parametric models for panel data sets where the cross-section and time dimensions are large. Our model contains a latent time series that is to be estimated and perhaps forecasted along with a non-parametric covariate effect. Our model is motivated by the need to be flexible with regard to the functional form of covariate effects but also the need to be practical with regard to forecasting of time series effects. We propose…

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Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error

内生及日内测量误差下二次变差的一致估计

We propose an econometric model that captures the effects of market microstructure on a latent price process. In particular, we allow for correlation between the measurement error and the return process and we allow the measurement error process to have a diurnal heteroskedasticity. We propose a modification of the TSRVÂ estimator of quadratic variation. We show that this estimator is consistent, with a rate of convergence that depends on the size of the measurement error,…

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Estimation of a semiparametric transformation model

半参数变换模型的估计

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the…

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Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

非参数匹配与位似可分函数的有效估计量

For vectors z and w and scalar v, let r(v, z, w) be a function that can be nonparametrically estimated consistently and asymptotically normally, such as a distribution, density, or conditional mean regression function. We provide consistent, asymptotically normal nonparametric estimators for the functions G and H, where r(v, z, w)=H[vG(z), w], and some related models. This framework encompasses homothetic and homothetically separable functions, and transformed partly…

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