1,721,025 research outputs found
Nonparametric Permutation-Based Control Charts for Ordinal Data
No full textIn the literature of statistical process control (SPC), design and implementation of traditional Shewart-based control charts requires the assumption that the process response distribution follows a parametric form (e.g., normal). However, since in practice, ordinal observations may not follow the pre-specified parametric distribution these charts may not be reliable. In this connection, this work aims at providing a contribution to the nonparametric SPC literature, proposing univariate and multivariate nonparametric permutation-based control charts for ordinal response variables which are not only interesting as methodological solution but they have a very practical value particularly within the context of monitoring some measure of user’s satisfaction, loyalty, etc. related to use of a given service. As confirmed by the simulation study and by the application to a real case study in the field of monitoring of customer satisfaction in services, we can state that the proposed NPC chart for ordered categorical response variables is certainly a good alternative with respect to the literature counterparts
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High-dimensional Estimation of Autocovariances and Inverse Autocovariances
Get PDFWe consider the problem of using an autoregressive (AR) approximation to estimate the spectral density function and the autocovariance matrixbased on stationary data .
The consistency of the autoregressive spectral density estimator
has been proven since the 1970s
under a linearity assumption. We extend these ideas to
the non-linear setting, and give an application to estimating the autocovariance matrix.
Under mild assumptions on the underlying dependence structure and the order of the fitted model, we are able to show that the autoregressive spectral estimate and the
associated AR-based autocovariance matrix estimator are consistent. We are also able to establish an explicit bound on the rate of convergence of the proposed estimators. Cleveland (1972) introduced the inverse autocovariance function (iacf) for weaklystationary time series.
He proposed two ways to estimate the inverse autocovariances: one way is to fit an autoregressive (AR) model to the data and use the fitted model's inverse autocovariance as the iacf estimator, and the other method is to employ a kernel-smoothed spectral density estimator to construct iacf estimator. Bhansali (1980) then proved consistency
of the iacf estimator at a fixed lag based on a linear time series condition.
In the paper at hand, we relax the linearity assumption and provide sufficient conditions for
the consistency of the iacf estimator.
We further consider the problem of estimating the vector consisting of the iacf
at lags up to , based on a sample of size . We propose several competing
estimators of the iacf vector, and study their
convergence. Lastly, we
consider the inverse autocovariance matrix, i.e., the by Toeplitz matrix with element given by the iacf at lag ; we propose an estimator and
investigate its consistency properties
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Prediction in Time Series Models and Model-free Inference with a Specialization in Financial Return Data
Get PDFThe main aim of this dissertation is to study the prediction of financial returns or squared financial returns. As is known, financial returns data have the distribution with fatter tails than the normal and often show significant correlation and the phenomenon of volatility clustering. To capture these features is the most challenging thing in modeling financial returns data. The most popular nonlinear time series models for financial returns data now are ARCH (Autoregressive Conditional Heteroscedasticity) and GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models. Early this century, a Model-free prediction approach was also derived to understand this complex type of data. One application of the model-free approach, NoVaS (Normalizing and Variance-Stabilizing) transformation has been proved to outperform ARCH and GARCH models under stationary financial data. In Chapter 1, we extend the realm of application of NoVaS to non-stationary data and compare the performance with GARCH in the one-step point prediction and prediction intervals of squared financial returns. In addition, we show the applicability of NoVaS transformation for estimating realized volatility. A new approach to the multi-step ahead prediction of squared financial returns is defined and analyzed in Chapter 2. Our work on linear time series model such as Autoregression are shown in the last two chapters. Chapter 3 describes in detail the situations that a simplified autoregressive models should be considered and the theoretical support was also given there for further study. In the last Chapter, we construct the prediction intervals of regression with model selections in the bootstrap world, which give better performance than the standard bootstrap methods. All the work here are mainly focusing on financial returns time series
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Towards a Theoretical Foundation of the Model-free Bootstrap for Regression and Time Series
Get PDFThe model-free bootstrap (MFB), first introduced in Politis [2013] followed by the monograph of Politis [2015], and further investigated in a series of papers (cf. Pan and Politis [2016b], Chen and Politis [2019], Das and Politis [2020], etc), is a recent advent in the bootstrap literature. The principle of MFB is to (invertibly) transform the original data to a space of i.i.d. variables, wherein the standard i.i.d. bootstrap is performed for the variables, and then the inverse transform is used to obtain bootstrap samples in the original data space. Because of the wide selection of applicable transforms, the MFB framework can be easily extended for complex data scenarios – such as regression and time series. The term "model-free" relates to the fact that thetransformations are estimated without model assumptions, i.e., nonparametrically.The main purpose of this dissertation is to build a theoretical foundation for the MFB under different setups. Specifically, in Chapter 1, we analyze the MFB under model-free regres- sion setup, and compare it with other methods of interest focusing on conditional coverage of prediction intervals. The concept of pertinent prediction intervals is extended to this setup, and we propose the notion of conjecture testing for predictive inference. In Chapter 2, we establish bootstrap validity of various statistics for a general class of univariate time series under very basic dependence assumptions, using the recently developed m ́approximation technique. In Chapter 3, the MFB algorithm of chapter 2 is further extended to handle multivariate time series, wherein we specifically focus on the generation of prediction regions. We also link the MFB under multivariate context with the well-known copula models. Finally in Chapter 4, we propose a new MFB algorithm for quantile autoregressive processes based on the MFB framework for general Markov process by Pan and Politis [2016b], using an augmented quantile regression estimator
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Regression with complex data: regularization, prediction and bootstrap
Get PDFAnalyzing a linear model is a fundamental topic in statistical inference and has been well-studied. However, the complex nature of modern data brings new challenges to statisticians, i.e., the existing theories and methods may fail to provide consistent results. Focusing on a high dimensional linear model with i.i.d. errors or heteroskedastic and dependent errors, this dissertation introduces a new ridge regression method called `the debiased and thresholded ridge regression'; then adopts this method to fit the linear model. After that, it introduces new bootstrap algorithms and applies them to generate consistent simultaneous confidence intervals/performs hypothesis testing for linear combinations of parameters in the linear model. In addition, this paper applies bootstrap algorithm to construct the simultaneous prediction intervals for future observations. Numerical algorithms show that the new ridge regression method has a good performance compared to other complex methods like Lasso or the threshold Lasso.This thesis also studies the properties of a residual-based bootstrap prediction interval. It derives the asymptotic distribution of the difference between {the conditional coverage probability of a nominal prediction interval} and {the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap}. This result shows that the residual-based bootstrap prediction interval has about 50% possibility of yielding conditional under-coverage. Moreover, it introduces a new bootstrap prediction interval that has the desired asymptotic conditional coverage probability and the possibility of conditional under-coverage
An open Problem on Strongly Consistent Learning of the Best Prediction for Gaussian Processes
No full textSemiparametric Bayesian Small Area Estimation Based on Dirichlet Process Priors
No full textSmall area estimation concerns the problem of releasing estimates for domains that are not planned by design in statistical surveys. For such domains the observed sample size may often be too small to allow for accurate estimation of aggregates of interest. To borrow strength from related domains, the vast majority of small area models relies on mixed effects regression models. Whereas inference on the fixed effects is shown to be robust to deviations from normality, estimation of the random effects is crucial for predicting small area quantities. The potential impact of distributional assumptions on the random effects is shown to be important; missing covariates can lead to multimodal distributions for the random effects; the latter may also be skewed. Any parametric assumption, applying to nonobservable quantities, is difficult to check. This contribution examines a Bayesian semiparametric version of the Fay-Herriot model in which the default normality assumption for the random effects is replaced by a nonparametric specification, based on the Dirichlet process. Viability of the approach and the effect of introducing a flexible specification of the random effects are investigated through an application to simulated data
A cost based reweighted scheme of principal support vector machine
No full textIn this work, a reweighted scheme is used to improve the performance of the algorithm. We present basic theoretical results and demonstrate the effectiveness of the reweighted algorithm through simulations and real data application
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