391 research outputs found
Estimating European Temperature Trends
This paper presents estimates for common trends in European temperature panels using new estimators. The analyzed data contains 4000 Eurasian weather stations. A sampling algorithm robust against inherent geographical biases is developed, and appropriate estimators are evaluated. The estimations based on this evaluation show that commonalities in temperature movements disappear with growing geographical scope. They also reveal that European mean temperature increased by 1.8°C over the past 130 years, but estimates differ by region. A particularly pronounced increase has taken place since the 1980s. Further, a 20-year cycle is discovered, and a low-frequency fractal structure of temperature trends is proposed
Smoothness Adaptive AverageDerivative Estimation
Many important models, such as index models widely used in limiteddependent variables, partial linear models and nonparametric demand studiesutilize estimation of average derivatives (sometimes weighted) of theconditional mean function. Asymptotic results in the literature focus onsituations where the ADE converges at parametric rates (as a result ofaveraging); this requires making stringent assumptions on smoothness of theunderlying density; in practice such assumptions may be violated. We extendthe existing theory by relaxing smoothness assumptions. We consider boththe possibility of lack of smoothness and lack of precise knowledge of degreeof smoothness and propose an estimation strategy that produces the bestpossible rate without a priori knowledge of degree of density smoothness. Thenew combined estimator is a linear combination of estimators correspondingto different bandwidth/kernel choices that minimizes the trace of the part ofthe estimated asymptotic mean squared error that depends on the bandwidth.Estimation of the components of the AMSE, of the optimal bandwidths,selection of the set of bandwidths and kernels are discussed. Monte Carloresults for density weighted ADE confirm good performance of the combinedestimator.Nonparametric estimation, density weighted average derivativeestimator, combined estimator.
Stratified Learning: a general-purpose statistical method for improved learning under Covariate Shift
Covariate shift arises when the labelled training (source) data is not
representative of the unlabelled (target) data due to systematic differences in
the covariate distributions. A supervised model trained on the source data
subject to covariate shift may suffer from poor generalization on the target
data. We propose a novel, statistically principled and theoretically justified
method to improve learning under covariate shift conditions, based on
propensity score stratification, a well-established methodology in causal
inference. We show that the effects of covariate shift can be reduced or
altogether eliminated by conditioning on propensity scores. In practice, this
is achieved by fitting learners on subgroups ("strata") constructed by
partitioning the data based on the estimated propensity scores, leading to
balanced covariates and much-improved target prediction. We demonstrate the
effectiveness of our general-purpose method on contemporary research questions
in observational cosmology, and on additional benchmark examples, matching or
outperforming state-of-the-art importance weighting methods, widely studied in
the covariate shift literature. We obtain the best reported AUC (0.958) on the
updated "Supernovae photometric classification challenge" and improve upon
existing conditional density estimation of galaxy redshift from Sloan Data Sky
Survey (SDSS) data
A method of moments estimator for semiparametric index models
We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators. The functionals used provide moment conditions for the parameters of interest, which are used in the second step within a method-of-moments framework to estimate the parameters of interest. The estimator is shown to be root N consistent and asymptotically normal. We extend the procedure to multiple equation models. Our identification conditions and estimation framework provide natural tests for the number of indices in the model. In addition we discuss tests of separability, additivity, and linearity of the influence of the indices.Semiparametric estimation, multiple index models, average derivative functionals, generalized methods of moments estimator, rank testing
On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference
Nonparametric methods play a central role in modern empirical work. While
they provide inference procedures that are more robust to parametric
misspecification bias, they may be quite sensitive to tuning parameter choices.
We study the effects of bias correction on confidence interval coverage in the
context of kernel density and local polynomial regression estimation, and prove
that bias correction can be preferred to undersmoothing for minimizing coverage
error and increasing robustness to tuning parameter choice. This is achieved
using a novel, yet simple, Studentization, which leads to a new way of
constructing kernel-based bias-corrected confidence intervals. In addition, for
practical cases, we derive coverage error optimal bandwidths and discuss
easy-to-implement bandwidth selectors. For interior points, we show that the
MSE-optimal bandwidth for the original point estimator (before bias correction)
delivers the fastest coverage error decay rate after bias correction when
second-order (equivalent) kernels are employed, but is otherwise suboptimal
because it is too "large". Finally, for odd-degree local polynomial regression,
we show that, as with point estimation, coverage error adapts to boundary
points automatically when appropriate Studentization is used; however, the
MSE-optimal bandwidth for the original point estimator is suboptimal. All the
results are established using valid Edgeworth expansions and illustrated with
simulated data. Our findings have important consequences for empirical work as
they indicate that bias-corrected confidence intervals, coupled with
appropriate standard errors, have smaller coverage error and are less sensitive
to tuning parameter choices in practically relevant cases where additional
smoothness is available
A Comparison of Two Linear Nonparametric Regression Techniques
This thesis presented a useful tool in regression. Nonparametric linear regression techniques were described in the general context of regression. A comparison of two of these techniques, kernel regression and iterative regression, showed various aspects of nonparametric linear regressors
QUANTILE REGRESSION FOR CLIMATE DATA
Quantile regression is a developing statistical tool which is used to explain the relationship between response and predictor variables. This thesis describes two examples of climatology using quantile regression.Our main goal is to estimate derivatives of a conditional mean and/or conditional quantile function. We introduce a method to handle autocorrelation in the framework of quantile regression and used it with the temperature data. Also we explain some properties of the tornado data which is non-normally distributed. Even though quantile regression provides a more comprehensive view, when talking about residuals with the normality and the constant variance assumption, we would prefer least square regression for our temperature analysis. When dealing with the non-normality and non constant variance assumption, quantile regression is a better candidate for the estimation of the derivative
Advances in forecast evaluation
This paper surveys recent developments in the evaluation of point forecasts. Taking West’s (2006) survey as a starting point, we briefly cover the state of the literature as of the time of West’s writing. We then focus on recent developments, including advancements in the evaluation of forecasts at the population level (based on true, unknown model coefficients), the evaluation of forecasts in the finite sample (based on estimated model coefficients), and the evaluation of conditional versus unconditional forecasts. We present original results in a few subject areas: the optimization of power in determining the split of a sample into in-sample and out-of-sample portions; whether the accuracy of inference in evaluation of multistep forecasts can be improved with the judicious choice of HAC estimator (it can); and the extension of West’s (1996) theory results for population-level, unconditional forecast evaluation to the case of conditional forecast evaluation.Forecasting ; Time-series analysis
Advances in forecast evaluation
This paper surveys recent developments in the evaluation of point forecasts. Taking West's (2006) survey as a starting point, we briefly cover the state of the literature as of the time of West's writing. We then focus on recent developments, including advancements in the evaluation of forecasts at the population level (based on true, unknown model coefficients), the evaluation of forecasts in the finite sample (based on estimated model coefficients), and the evaluation of conditional versus unconditional forecasts. We present original results in a few subject areas: the optimization of power in determining the split of a sample into in-sample and out-of-sample portions; whether the accuracy of inference in evaluation of multi-step forecasts can be improved with judicious choice of HAC estimator (it can); and the extension of West's (1996) theory results for population-level, unconditional forecast evaluation to the case of conditional forecast evaluation.Forecasting
Local linear density estimation for filtered survival data, with bias correction
A class of local linear kernel density estimators based on weighted least-squares kernel estimation is considered within the framework of Aalen's multiplicative intensity model. This model includes the filtered data model that, in turn, allows for truncation and/or censoring in addition to accommodating unusual patterns of exposure as well as occurrence. It is shown that the local linear estimators corresponding to all different weightings have the same pointwise asymptotic properties. However, the weighting previously used in the literature in the i.i.d. case is seen to be far from optimal when it comes to exposure robustness, and a simple alternative weighting is to be preferred. Indeed, this weighting has, effectively, to be well chosen in a 'pilot' estimator of the survival function as well as in the main estimator itself. We also investigate multiplicative and additive bias-correction methods within our framework. The multiplicative bias-correction method proves to be the best in a simulation study comparing the performance of the considered estimators. An example concerning old-age mortality demonstrates the importance of the improvements provided
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