1,385 research outputs found
Kernel conditional quantile estimation via reduction revisited
Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches.
Using auxiliary residuals to detect conditional heteroscedasticity in inflation
In this paper we consider a model with stochastic trend, seasonal and transitory components with the disturbances of the trend and transitory disturbances specified as QGARCH models. We propose to use the differences between the autocorrelations of squares and the squared autocorrelations of the auxiliary residuals to identify which component is heteroscedastic. The finite sample performance of these differences is analysed by means of Monte Carlo experiments. We show that conditional heteroscedasticity truly present in the data can be rejected when looking at the correlations of observations or of standardized residuals while the autocorrelations of auxiliary residuals allow us to detect adequately whether there is heteroscedasticity and which is the heteroscedastic component. We also analyse the finite sample behaviour of a QML estimator of the parameters of the model. Finally, we use auxiliary residuals to detect conditional heteroscedasticity in monthly series of inflation of eight OECD countries. We conclude that, for most of these series, the conditional heteroscedasticity affects the transitory component while the long-run and seasonal components are homoscedastic. Furthermore, in the countries where there is a significant relationship between the volatility and the level of inflation, this relation is positive, supporting the Friedman hypothesis
Recommended from our members
Bayesian recursive parameter estimation for hydrologic models
The uncertainty in a given hydrologic prediction is the compound effect of the parameter, data, and structural uncertainties associated with the underlying model. In general, therefore, the confidence in a hydrologic prediction can be improved by reducing the uncertainty associated with the parameter estimates. However, the classical approach to doing this via model calibration typically requires that considerable amounts of data be collected and assimilated before the model can be used. This limitation becomes immediately apparent when hydrologic predictions must be generated for a previously ungauged watershed that has only recently been instrumented. This paper presents the framework for a Bayesian recursive estimation approach to hydrologic prediction that can be used for simultaneous parameter estimation and prediction in an operational setting. The prediction is described in terms of the probabilities associated with different output values. The uncertainty associated with the parameter estimates is updated (reduced) recursively, resulting in smaller prediction uncertainties as measurement data are successively assimilated. The effectiveness and efficiency of the method are illustrated in the context of two models: a simple unit hydrograph model and the more complex Sacramento soil moisture accounting model, using data from the Leaf River basin in Mississippi
The relation between the level and uncertainty of inflation
This paper focus on the problems faced in the empirical investigation of the relation between the level and volatility of inflation. Monthly inflation series seem to be affected by both the presence of outliers and conditional heteroscedasticity. First, the paper illustrates the implications that the presence of outliers and conditional heteroscedasticity have on the usual residual diagnostics. Then, estimates of the level and volatility of inflation are obtained for each of the countries of the G-7 group. Empirical evidence for the majority of the inflation series for these countries indicates both the presence of outliers and conditional heteroscedasticity, and that estimates of the latter are sensitive to the presence of outliers. Finally, the temporal dependence found in the conditional variance is enduring.Conditional Heteroscedasticity, Diagnostic, Inflation, Outlier, Stochastic Volatility.
Overviews of Optimization Techniques for Geometric Estimation
We summarize techniques for optimal geometric estimation from noisy observations for computer
vision applications. We first discuss the interpretation of optimality and point out that geometric
estimation is different from the standard statistical estimation. We also describe our noise
modeling and a theoretical accuracy limit called the KCR lower bound. Then, we formulate estimation
techniques based on minimization of a given cost function: least squares (LS), maximum
likelihood (ML), which includes reprojection error minimization as a special case, and Sampson
error minimization. We describe bundle adjustment and the FNS scheme for numerically solving
them and the hyperaccurate correction that improves the accuracy of ML. Next, we formulate
estimation techniques not based on minimization of any cost function: iterative reweight, renormalization,
and hyper-renormalization. Finally, we show numerical examples to demonstrate that
hyper-renormalization has higher accuracy than ML, which has widely been regarded as the most
accurate method of all. We conclude that hyper-renormalization is robust to noise and currently is
the best method
Regression Models for Estimating Aboveground Biomass and Stand Volume Using Landsat-Based Indices in Post-Mining Area
This paper describes the use of remotely sensed data to measure vegetation variables such as basal area, biomass and stand volume. The objective of this research was developed regression models to estimate basal area (BA), aboveground biomass (AGB), and stand volume (SV) using Landsat-based vegetation indices. The examined vegetation indices were SAVI, MSAVI, EVI, NBR, NBR2 and NDMI. Regression models were developed based on least-squared method using several forms of equation, i.e., linear, exponential, power, logarithm and polynomial. Among those models, it was recognized that the best fit of model was obtained from the exponential model, log (y) = ax + b for estimating BA, AGB & SV. The MSAVI had been identified as the most accurate independent variable to estimates basal area with R² of 0.70 and average verification values of 16.39% (4%-32.66%); while the EVI become the best independent variable for estimating aboveground biomass (AGB) with R2 of 0.72 and average of verification values of 18,10% (9%-28.01%); and the NDMI was recognized to be the best independent variable to estimate stand volume with R2 of 0.69 and average of verification values of 24.37% (-15%-38.11%)
- …