The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Peter Hall - One of the best experts on this subject based on the ideXlab platform.
-
approximating Conditional Distribution functions using dimension reduction
Annals of Statistics, 2005Co-Authors: Peter Hall, Qiwei YaoAbstract:Motivated by applications to prediction and forecasting, we sug- gest methods for approximating the Conditional Distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the Distribution of Y |X, but that of Y |� T X, where the unit vectoris selected so that the approximation is opti- mal under a least-squares criterion. We show thatmay be estimated root-n consistently. Furthermore, estimation of the Conditional distri- bution function of Y , givenT X, has the same first-order asymptotic properties that it would enjoy ifwere known. The proposed method is illustrated using both simulated and real-data examples, showing its effectiveness for both independent datasets and data from time series. Numerical work corroborates the theoretical result thatcan be estimated particularly accurately.
-
approximating Conditional Distribution functions using dimension reduction
LSE Research Online Documents on Economics, 2005Co-Authors: Peter Hall, Qiwei YaoAbstract:Motivated by applications to prediction and forecasting, we suggest methods for approximating the Conditional Distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the Distribution of Y|X, but that of Y|\theta^TX, where the unit vector \theta is selected so that the approximation is optimal under a least-squares criterion. We show that \theta may be estimated root-n consistently. Furthermore, estimation of the Conditional Distribution function of Y, given \theta^TX, has the same first-order asymptotic properties that it would enjoy if \theta were known. The proposed method is illustrated using both simulated and real-data examples, showing its effectiveness for both independent datasets and data from time series. Numerical work corroborates the theoretical result that \theta can be estimated particularly accurately.
-
order preserving nonparametric regression with applications to Conditional Distribution and quantile function estimation
Journal of the American Statistical Association, 2003Co-Authors: Peter Hall, Hansgeorg MullerAbstract:In some regression problems we observe a “response” Yti to level t of a “treatment” applied to an individual with level Xi of a given characteristic, where it has been established that response is monotone increasing in the level of the treatment. A related problem arises when estimating Conditional Distributions, where the raw data are typically independent and identically distributed pairs (Xi, Zi), and Yti denotes the proportion of Zi's that do not exceed t. We expect the regression means gt(x) = E(Yti|Xi = x) to enjoy the same order relation as the responses, that is, gt ≤ gs whenever s ≤ t. This requirement is necessary to obtain bona fide Conditional Distribution functions, for example. If we estimate gt by passing a linear smoother through each dataset χt = {(Xi, Yti) : 1 ≤ i ≤ n}, then the order-preserving property is guaranteed if and only if the smoother has nonnegative weights. However, in such cases the estimators generally have high levels of boundary bias. On the other hand, the order-preser...
-
methods for estimating a Conditional Distribution function
LSE Research Online Documents on Economics, 1999Co-Authors: Peter Hall, Rodney C Wolff, Qiwei YaoAbstract:Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for Conditional Distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces Distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the Nadaraya-Watson estimator. It preserves the bias and variance properties of a class of second-order estimators introduced by Yu and Jones but has the added advantage of always being a Distribution itself. Our methods also have application outside the time series setting; for example, to quantile estimation for independent data. This problem motivated the work of Yu and Jones.
Andrew Harvey - One of the best experts on this subject based on the ideXlab platform.
-
time series models with an egb2 Conditional Distribution
Journal of Time Series Analysis, 2014Co-Authors: Michele Caivano, Andrew HarveyAbstract:A time-series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation-driven model, based on an exponential generalized beta Distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the Conditional Distribution. This specification produces a model that is not only easy to implement but which also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic Distribution of the maximum-likelihood (ML) estimator. Score-driven models of this kind can also be based on Conditional t Distributions, but whereas these models carry out what, in the robustness literature, is called a soft form of trimming, the EGB2 Distribution leads to a soft form of Winsorizing. An exponential general autoregressive Conditional heteroscedastic (EGARCH) model based on the EGB2 Distribution is also developed. This model complements the score-driven EGARCH model with a Conditional t Distribution. Finally, dynamic location and scale models are combined and applied to data on the UK rate of inflation.
-
time series models with an egb2 Conditional Distribution
Research Papers in Economics, 2013Co-Authors: Michele Caivano, Andrew HarveyAbstract:A time series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on an exponential generalized beta Distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the Conditional Distribution. This specification produces a model that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straight-forward theory for the asymptotic Distribution of the maximum likelihood estimator. The model is fitted to US macroeconomic time series and compared with Gaussian and Student-t models. A theory is then developed for an EGARCH model based on the EGB2 Distribution and the model is fitted to exchange rate data. Finally dynamic location and scale models are combined and applied to data on the UK rate of inflation.
Qiwei Yao - One of the best experts on this subject based on the ideXlab platform.
-
approximating Conditional Distribution functions using dimension reduction
Annals of Statistics, 2005Co-Authors: Peter Hall, Qiwei YaoAbstract:Motivated by applications to prediction and forecasting, we sug- gest methods for approximating the Conditional Distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the Distribution of Y |X, but that of Y |� T X, where the unit vectoris selected so that the approximation is opti- mal under a least-squares criterion. We show thatmay be estimated root-n consistently. Furthermore, estimation of the Conditional distri- bution function of Y , givenT X, has the same first-order asymptotic properties that it would enjoy ifwere known. The proposed method is illustrated using both simulated and real-data examples, showing its effectiveness for both independent datasets and data from time series. Numerical work corroborates the theoretical result thatcan be estimated particularly accurately.
-
approximating Conditional Distribution functions using dimension reduction
LSE Research Online Documents on Economics, 2005Co-Authors: Peter Hall, Qiwei YaoAbstract:Motivated by applications to prediction and forecasting, we suggest methods for approximating the Conditional Distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the Distribution of Y|X, but that of Y|\theta^TX, where the unit vector \theta is selected so that the approximation is optimal under a least-squares criterion. We show that \theta may be estimated root-n consistently. Furthermore, estimation of the Conditional Distribution function of Y, given \theta^TX, has the same first-order asymptotic properties that it would enjoy if \theta were known. The proposed method is illustrated using both simulated and real-data examples, showing its effectiveness for both independent datasets and data from time series. Numerical work corroborates the theoretical result that \theta can be estimated particularly accurately.
-
methods for estimating a Conditional Distribution function
LSE Research Online Documents on Economics, 1999Co-Authors: Peter Hall, Rodney C Wolff, Qiwei YaoAbstract:Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for Conditional Distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces Distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the Nadaraya-Watson estimator. It preserves the bias and variance properties of a class of second-order estimators introduced by Yu and Jones but has the added advantage of always being a Distribution itself. Our methods also have application outside the time series setting; for example, to quantile estimation for independent data. This problem motivated the work of Yu and Jones.
Stephen Gray - One of the best experts on this subject based on the ideXlab platform.
-
modeling the Conditional Distribution of interest rates as a regime switching process
Journal of Financial Economics, 1996Co-Authors: Stephen GrayAbstract:This paper develops a generalized regime-switching (GRS) model of the short-term interest rate. The model allows the short rate to exhibit both mean reversion and Conditional heteroskedasticity and nests the popular generalized autoregressive Conditional heteroskedasticity (GARCH) and square root process specifications. Thus, the Conditional variance process accommodates volatility clustering and dependence on the level of the interest rate. Switching between regimes is governed by a first-order Markov process with state-dependent transition probabilities. The GRS model is compared with various existing models of the short rate in terms of the statistical fit of short-term interest rate data and in terms of out-of-sample forecasting performance.
-
modeling the Conditional Distribution of interest rates as a regime switching process
Journal of Financial Economics, 1996Co-Authors: Stephen GrayAbstract:Abstract This paper develops a generalized regime-switching (GRS) model of the short-term interest rate. The model allows the short rate to exhibit both mean reversion and Conditional heteroskedasticity and nests the popular generalized autoregressive Conditional heteroskedasticity (GARCH) and square root process specifications. The Conditional variance process accommodates volatility clustering and dependence on the level of the interest rate. A first-order Markov process with state-dependent transition probabilities governs the switching between regimes. The GRS model is compared with various existing models of the short rate in terms of (1) the statistical fit of short-term interest rate data and (2) out-of-sample forecasting performance.
Noel Veraverbeke - One of the best experts on this subject based on the ideXlab platform.
-
smooth copula based estimation of the Conditional density function with a single covariate
Journal of Multivariate Analysis, 2017Co-Authors: Paul Janssen, Noel Veraverbeke, Jan W H SwanepoelAbstract:Some recent papers deal with smooth nonparametric estimators for copula functions and copula derivatives. These papers contain results on copula-based Bernstein estimators for Conditional Distribution functions and related functionals such as regression and quantile functions. The focus in the present paper is on new copula-based smooth Bernstein estimators for the Conditional density. Our approach avoids going through separate density estimation of numerator and denominator. Our estimator is defined as a smoother of the copula-based Bernstein estimator of the Conditional Distribution function. We establish asymptotic properties of bias and variance and discuss the asymptotic mean squared error in terms of the smoothing parameters. We also obtain the asymptotic normality of the new estimator. In a simulation study we show the good performance of the new estimator in comparison with other estimators proposed in the literature.
-
preadjusted non parametric estimation of a Conditional Distribution function
Journal of The Royal Statistical Society Series B-statistical Methodology, 2014Co-Authors: Noel Veraverbeke, Irène Gijbels, Marek OmelkaAbstract:type="main" xml:id="rssb12041-abs-0001"> The paper deals with non-parametric estimation of a Conditional Distribution function. We suggest a method of preadjusting the original observations non-parametrically through location and scale, to reduce the bias of the estimator. We derive the asymptotic properties of the estimator proposed. A simulation study investigating the finite sample performances of the estimators discussed is provided and reveals the gain that can be achieved. It is also shown how the idea of the preadjusting opens the path to improved estimators in other settings such as Conditional quantile and density estimation, and Conditional survival function estimation in the case of censored data.