1,385 research outputs found

    Kernel conditional quantile estimation via reduction revisited

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    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

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    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

    The relation between the level and uncertainty of inflation

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    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

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    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

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    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%)

    Variance heterogeneity in experimental design

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    Statistical Methods
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