Dissertations / Theses on the topic 'Sequential nonparametric kernel regression'
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Dharmasena, Tibbotuwa Deniye Kankanamge Lasitha Sandamali, and Sandamali dharmasena@rmit edu au. "Sequential Procedures for Nonparametric Kernel Regression." RMIT University. Mathematical and Geospatial Sciences, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20090119.134815.
Full textSignorini, David F. "Practical aspects of kernel smoothing for binary regression and density estimation." Thesis, n.p, 1998. http://oro.open.ac.uk/19923/.
Full textWang, Sejong. "Three nonparametric specification tests for parametric regression models : the kernel estimation approach." Connect to resource, 1994. http://rave.ohiolink.edu/etdc/view.cgi?acc%5Fnum=osu1261492759.
Full textEl, Ghouch Anouar. "Nonparametric statistical inference for dependent censored data." Université catholique de Louvain, 2007. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-09262007-123927/.
Full textKim, Byung-Jun. "Semiparametric and Nonparametric Methods for Complex Data." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99155.
Full textDoctor of Philosophy
A variety of complex data has broadened in many research fields such as epidemiology, genomics, and analytical chemistry with the development of science, technologies, and design scheme over the past few decades. For example, in epidemiology, the matched case-crossover study design is used to investigate the association between the clustered binary outcomes of disease and a measurement error in covariate within a certain period by stratifying subjects' conditions. In genomics, high-correlated and high-dimensional(HCHD) data are required to identify important genes and their interaction effect over diseases. In analytical chemistry, multiple time series data are generated to recognize the complex patterns among multiple classes. Due to the great diversity, we encounter three problems in analyzing the following three types of data: (1) matched case-crossover data, (2) HCHD data, and (3) Time-series data. We contribute to the development of statistical methods to deal with such complex data. First, under the matched study, we discuss an idea about hypothesis testing to effectively determine the association between observed factors and risk of interested disease. Because, in practice, we do not know the specific form of the association, it might be challenging to set a specific alternative hypothesis. By reflecting the reality, we consider the possibility that some observations are measured with errors. By considering these measurement errors, we develop a testing procedure under the matched case-crossover framework. This testing procedure has the flexibility to make inferences on various hypothesis settings. Second, we consider the data where the number of variables is very large compared to the sample size, and the variables are correlated to each other. In this case, our goal is to identify important variables for outcome among a large amount of the variables and build their network. For example, identifying few genes among whole genomics associated with diabetes can be used to develop biomarkers. By our proposed approach in the second project, we can identify differentially expressed and important genes and their network structure with consideration for the outcome. Lastly, we consider the scenario of changing patterns of interest over time with application to gas chromatography. We propose an efficient detection method to effectively distinguish the patterns of multi-level subjects in time-trend analysis. We suggest that our proposed method can give precious information on efficient search for the distinguishable patterns so as to reduce the burden of examining all observations in the data.
Maity, Arnab. "Efficient inference in general semiparametric regression models." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-3075.
Full textDoruska, Paul F. "Methods for Quantitatively Describing Tree Crown Profiles of Loblolly pine (Pinus taeda L.)." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30638.
Full textPh. D.
Chu, Chi-Yang. "Applied Nonparametric Density and Regression Estimation with Discrete Data| Plug-In Bandwidth Selection and Non-Geometric Kernel Functions." Thesis, The University of Alabama, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10262364.
Full textBandwidth selection plays an important role in kernel density estimation. Least-squares cross-validation and plug-in methods are commonly used as bandwidth selectors for the continuous data setting. The former is a data-driven approach and the latter requires a priori assumptions about the unknown distribution of the data. A benefit from the plug-in method is its relatively quick computation and hence it is often used for preliminary analysis. However, we find that much less is known about the plug-in method in the discrete data setting and this motivates us to propose a plug-in bandwidth selector. A related issue is undersmoothing in kernel density estimation. Least-squares cross-validation is a popular bandwidth selector, but in many applied situations, it tends to select a relatively small bandwidth, or undersmooths. The literature suggests several methods to solve this problem, but most of them are the modifications of extant error criterions for continuous variables. Here we discuss this problem in the discrete data setting and propose non-geometric discrete kernel functions as a possible solution. This issue also occurs in kernel regression estimation. Our proposed bandwidth selector and kernel functions perform well in simulated and real data.
Edwards, Adam Michael. "Precision Aggregated Local Models." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/102125.
Full textDoctor of Philosophy
Occasionally, when describing the relationship between two variables, it may be helpful to use a so-called ``non-parametric" regression that is agnostic to the function that connects them. Gaussian Processes (GPs) are a popular method of non-parametric regression used for their relative flexibility and interpretability, but they have the unfortunate drawback of being computationally infeasible for large data sets. Past work into solving the scaling issues for GPs has focused on ``divide and conquer" style schemes that spread the data out across multiple smaller GP models. While these model make GP methods much more accessible to large data sets they do so either at the expense of local predictive accuracy of global surface continuity. Precision Aggregated Local Models (PALM) is a novel divide and conquer method for GP models that is scalable for large data while maintaining local accuracy and a smooth global model. I demonstrate that PALM can be built quickly, and performs well predictively compared to other state of the art methods. This document also provides a sequential algorithm for selecting the location of each local model, and variations on the basic PALM methodology.
Song, Song. "Confidence bands in quantile regression and generalized dynamic semiparametric factor models." Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2010. http://dx.doi.org/10.18452/16341.
Full textIn many applications it is necessary to know the stochastic fluctuation of the maximal deviations of the nonparametric quantile estimates, e.g. for various parametric models check. Uniform confidence bands are therefore constructed for nonparametric quantile estimates of regression functions. The first method is based on the strong approximations of the empirical process and extreme value theory. The strong uniform consistency rate is also established under general conditions. The second method is based on the bootstrap resampling method. It is proved that the bootstrap approximation provides a substantial improvement. The case of multidimensional and discrete regressor variables is dealt with using a partial linear model. A labor market analysis is provided to illustrate the method. High dimensional time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science, e.g. macroeconomics, meteorology, medicine and financial engineering. One of the common approach is to separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via dynamic factor analysis. We propose a two-step estimation procedure. At the first step, we detrend the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under the dependent scenario. At the second step, we obtain the detrended low dimensional stochastic process (stationary).
Benelmadani, Djihad. "Contribution à la régression non paramétrique avec un processus erreur d'autocovariance générale et application en pharmacocinétique." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAM034/document.
Full textIn this thesis, we consider the fixed design regression model with repeated measurements, where the errors form a process with general autocovariance function, i.e. a second order process (stationary or nonstationary), with a non-differentiable covariance function along the diagonal. We are interested, among other problems, in the nonparametric estimation of the regression function of this model.We first consider the well-known kernel regression estimator proposed by Gasser and Müller. We study its asymptotic performance when the number of experimental units and the number of observations tend to infinity. For a regular sequence of designs, we improve the higher rates of convergence of the variance and the bias. We also prove the asymptotic normality of this estimator in the case of correlated errors.Second, we propose a new kernel estimator of the regression function based on a projection property. This estimator is constructed through the autocovariance function of the errors, and a specific function belonging to the Reproducing Kernel Hilbert Space (RKHS) associated to the autocovariance function. We study its asymptotic performance using the RKHS properties. These properties allow to obtain the optimal convergence rate of the variance. We also prove its asymptotic normality. We show that this new estimator has a smaller asymptotic variance then the one of Gasser and Müller. A simulation study is conducted to confirm this theoretical result.Third, we propose a new kernel estimator for the regression function. This estimator is constructed through the trapezoidal numerical approximation of the kernel regression estimator based on continuous observations. We study its asymptotic performance, and we prove its asymptotic normality. Moreover, this estimator allow to obtain the asymptotic optimal sampling design for the estimation of the regression function. We run a simulation study to test the performance of the proposed estimator in a finite sample set, where we see its good performance, in terms of Integrated Mean Squared Error (IMSE). In addition, we show the reduction of the IMSE using the optimal sampling design instead of the uniform design in a finite sample set.Finally, we consider an application of the regression function estimation in pharmacokinetics problems. We propose to use the nonparametric kernel methods, for the concentration-time curve estimation, instead of the classical parametric ones. We prove its good performance via simulation study and real data analysis. We also investigate the problem of estimating the Area Under the concentration Curve (AUC), where we introduce a new kernel estimator, obtained by the integration of the regression function estimator. We prove, using a simulation study, that the proposed estimators outperform the classical one in terms of Mean Squared Error. The crucial problem of finding the optimal sampling design for the AUC estimation is investigated using the Generalized Simulating Annealing algorithm
Sow, Mohamedou. "Développement de modèles non paramétriques et robustes : application à l’analyse du comportement de bivalves et à l’analyse de liaison génétique." Thesis, Bordeaux 1, 2011. http://www.theses.fr/2011BOR14257/document.
Full textThe development of robust and nonparametric approaches for the analysis and statistical treatment of high-dimensional data sets exhibiting high variability, as seen in the environmental and genetic fields, is instrumental. Here, we model complex biological data with application to the analysis of bivalves’ behavior and to linkage analysis. The application of mathematics to the analysis of mollusk bivalves’behavior gave us the possibility to quantify and translate mathematically the animals’behavior in situ, in close or far field. We proposed a nonparametric regression model and compared three nonparametric estimators (recursive or not) of the regressionfunction to optimize the best estimator. We then characterized the biological rhythms, formalized the states of opening, proposed methods able to discriminate the behaviors, used shot-noise analysis to characterize various opening/closing transitory states and developed an original approach for measuring online growth.In genetics, we proposed a more general framework of robust statistics for linkage analysis. We developed estimators robust to distribution assumptions and the presence of outlier observations. We also used a statistical approach where the dependence between random variables is specified through copula theory. Our main results showed the practical interest of these estimators on real data for QTL and eQTL analysis
Amiri, Aboubacar. "Estimateurs fonctionnels récursifs et leurs applications à la prévision." Phd thesis, Université d'Avignon, 2010. http://tel.archives-ouvertes.fr/tel-00565221.
Full textTernynck, Camille. "Contributions à la modélisation de données spatiales et fonctionnelles : applications." Thesis, Lille 3, 2014. http://www.theses.fr/2014LIL30062/document.
Full textIn this dissertation, we are interested in nonparametric modeling of spatial and/or functional data, more specifically based on kernel method. Generally, the samples we have considered for establishing asymptotic properties of the proposed estimators are constituted of dependent variables. The specificity of the studied methods lies in the fact that the estimators take into account the structure of the dependence of the considered data.In a first part, we study real variables spatially dependent. We propose a new kernel approach to estimating spatial probability density of the mode and regression functions. The distinctive feature of this approach is that it allows taking into account both the proximity between observations and that between sites. We study the asymptotic behaviors of the proposed estimates as well as their applications to simulated and real data. In a second part, we are interested in modeling data valued in a space of infinite dimension or so-called "functional data". As a first step, we adapt the nonparametric regression model, introduced in the first part, to spatially functional dependent data framework. We get convergence results as well as numerical results. Then, later, we study time series regression model in which explanatory variables are functional and the innovation process is autoregressive. We propose a procedure which allows us to take into account information contained in the error process. After showing asymptotic behavior of the proposed kernel estimate, we study its performance on simulated and real data.The third part is devoted to applications. First of all, we present unsupervised classificationresults of simulated and real spatial data (multivariate). The considered classification method is based on the estimation of spatial mode, obtained from the spatial density function introduced in the first part of this thesis. Then, we apply this classification method based on the mode as well as other unsupervised classification methods of the literature on hydrological data of functional nature. Lastly, this classification of hydrological data has led us to apply change point detection tools on these functional data
Tencaliec, Patricia. "Developments in statistics applied to hydrometeorology : imputation of streamflow data and semiparametric precipitation modeling." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAM006/document.
Full textPrecipitation and streamflow are the two most important meteorological and hydrological variables when analyzing river watersheds. They provide fundamental insights for water resources management, design, or planning, such as urban water supplies, hydropower, forecast of flood or droughts events, or irrigation systems for agriculture.In this PhD thesis we approach two different problems. The first one originates from the study of observed streamflow data. In order to properly characterize the overall behavior of a watershed, long datasets spanning tens of years are needed. However, the quality of the measurement dataset decreases the further we go back in time, and blocks of data of different lengths are missing from the dataset. These missing intervals represent a loss of information and can cause erroneous summary data interpretation or unreliable scientific analysis.The method that we propose for approaching the problem of streamflow imputation is based on dynamic regression models (DRMs), more specifically, a multiple linear regression with ARIMA residual modeling. Unlike previous studies that address either the inclusion of multiple explanatory variables or the modeling of the residuals from a simple linear regression, the use of DRMs allows to take into account both aspects. We apply this method for reconstructing the data of eight stations situated in the Durance watershed in the south-east of France, each containing daily streamflow measurements over a period of 107 years. By applying the proposed method, we manage to reconstruct the data without making use of additional variables, like other models require. We compare the results of our model with the ones obtained from a complex approach based on analogs coupled to a hydrological model and a nearest-neighbor approach, respectively. In the majority of cases, DRMs show an increased performance when reconstructing missing values blocks of various lengths, in some of the cases ranging up to 20 years.The second problem that we approach in this PhD thesis addresses the statistical modeling of precipitation amounts. The research area regarding this topic is currently very active as the distribution of precipitation is a heavy-tailed one, and at the moment, there is no general method for modeling the entire range of data with high performance. Recently, in order to propose a method that models the full-range precipitation amounts, a new class of distribution called extended generalized Pareto distribution (EGPD) was introduced, specifically with focus on the EGPD models based on parametric families. These models provide an improved performance when compared to previously proposed distributions, however, they lack flexibility in modeling the bulk of the distribution. We want to improve, through, this aspect by proposing in the second part of the thesis, two new models relying on semiparametric methods.The first method that we develop is the transformed kernel estimator based on the EGPD transformation. That is, we propose an estimator obtained by, first, transforming the data with the EGPD cdf, and then, estimating the density of the transformed data by applying a nonparametric kernel density estimator. We compare the results of the proposed method with the ones obtained by applying EGPD on several simulated scenarios, as well as on two precipitation datasets from south-east of France. The results show that the proposed method behaves better than parametric EGPD, the MIAE of the density being in all the cases almost twice as small.A second approach consists of a new model from the general EGPD class, i.e., we consider a semiparametric EGPD based on Bernstein polynomials, more specifically, we use a sparse mixture of beta densities. Once again, we compare our results with the ones obtained by EGPD on both simulated and real datasets. As before, the MIAE of the density is considerably reduced, this effect being even more obvious as the sample size increases
Azaïs, Romain. "Estimation non paramétrique pour les processus markoviens déterministes par morceaux." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00844395.
Full textKowolowski, Alexander. "Vývoj moderních akustických parametrů kvantifikujících hypokinetickou dysartrii." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2019. http://www.nusl.cz/ntk/nusl-401990.
Full textAloui, Nadia. "Localisation sonore par retournement temporel." Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENT079/document.
Full textThe objective of this PhD is to propose a location solution that should be simple and robust to multipath that characterizes the indoor environments. First, a location system that exploits the time domain of channel parameters has been proposed. The system adopts the time of arrival of the path of maximum amplitude as a signature and estimates the target position through nonparametric kernel regression. The system was evaluated in experiments for two main configurations: a privacy-oriented configuration with code-division multiple-access operation and a centralized configuration with time-division multiple-access operation. A comparison between our privacy-oriented system and another acoustic location system based on code-division multiple-access operation and lateration method confirms the results found in radiofrequency-based localization. However, our experiments are the first to demonstrate the detrimental effect that reverberation has on acoustic localization approaches. Second, a location system based on time reversal technique and able to localize simultaneously sources with different location precisions has been tested through simulations for different values of the number of sources. The system has then been validated by experiments. Finally, we have been interested in reducing the audibility of the localization signal through psycho-acoustics. A filter, set from the absolute threshold of hearing, is then applied to the signal. Our results showed an improvement in precision, when compared to the location system without psychoacoustic model, thanks to the use of matched filter at the receiver. Moreover, we have noticed a significant reduction in the audibility of the filtered signal compared to that of the original signal
Somé, Sobom Matthieu. "Estimations non paramétriques par noyaux associés multivariés et applications." Thesis, Besançon, 2015. http://www.theses.fr/2015BESA2030/document.
Full textThis work is about nonparametric approach using multivariate mixed associated kernels for densities, probability mass functions and regressions estimation having supports partially or totally discrete and continuous. Some key aspects of kernel estimation using multivariate continuous (classical) and (discrete and continuous) univariate associated kernels are recalled. Problem of supports are also revised as well as a resolution of boundary effects for univariate associated kernels. The multivariate associated kernel is then defined and a construction by multivariate mode-dispersion method is provided. This leads to an illustration on the bivariate beta kernel with Sarmanov's correlation structure in continuous case. Properties of these estimators are studied, such as the bias, variances and mean squared errors. An algorithm for reducing the bias is proposed and illustrated on this bivariate beta kernel. Simulations studies and applications are then performed with bivariate beta kernel. Three types of bandwidth matrices, namely, full, Scott and diagonal are used. Furthermore, appropriated multiple associated kernels are used in a practical discriminant analysis task. These are the binomial, categorical, discrete triangular, gamma and beta. Thereafter, associated kernels with or without correlation structure are used in multiple regression. In addition to the previous univariate associated kernels, bivariate beta kernels with or without correlation structure are taken into account. Simulations studies show the performance of the choice of associated kernels with full or diagonal bandwidth matrices. Then, (discrete and continuous) associated kernels are combined to define mixed univariate associated kernels. Using the tools of unification of discrete and continuous analysis, the properties of the mixed associated kernel estimators are shown. This is followed by an R package, created in univariate case, for densities, probability mass functions and regressions estimations. Several smoothing parameter selections are implemented via an easy-to-use interface. Throughout the paper, bandwidth matrix selections are generally obtained using cross-validation and sometimes Bayesian methods. Finally, some additionnal informations on normalizing constants of associated kernel estimators are presented for densities or probability mass functions
Ahmed, Mohamed Salem. "Contribution à la statistique spatiale et l'analyse de données fonctionnelles." Thesis, Lille 3, 2017. http://www.theses.fr/2017LIL30047/document.
Full textThis thesis is about statistical inference for spatial and/or functional data. Indeed, weare interested in estimation of unknown parameters of some models from random or nonrandom(stratified) samples composed of independent or spatially dependent variables.The specificity of the proposed methods lies in the fact that they take into considerationthe considered sample nature (stratified or spatial sample).We begin by studying data valued in a space of infinite dimension or so-called ”functionaldata”. First, we study a functional binary choice model explored in a case-controlor choice-based sample design context. The specificity of this study is that the proposedmethod takes into account the sampling scheme. We describe a conditional likelihoodfunction under the sampling distribution and a reduction of dimension strategy to definea feasible conditional maximum likelihood estimator of the model. Asymptotic propertiesof the proposed estimates as well as their application to simulated and real data are given.Secondly, we explore a functional linear autoregressive spatial model whose particularityis on the functional nature of the explanatory variable and the structure of the spatialdependence. The estimation procedure consists of reducing the infinite dimension of thefunctional variable and maximizing a quasi-likelihood function. We establish the consistencyand asymptotic normality of the estimator. The usefulness of the methodology isillustrated via simulations and an application to some real data.In the second part of the thesis, we address some estimation and prediction problemsof real random spatial variables. We start by generalizing the k-nearest neighbors method,namely k-NN, to predict a spatial process at non-observed locations using some covariates.The specificity of the proposed k-NN predictor lies in the fact that it is flexible and allowsa number of heterogeneity in the covariate. We establish the almost complete convergencewith rates of the spatial predictor whose performance is ensured by an application oversimulated and environmental data. In addition, we generalize the partially linear probitmodel of independent data to the spatial case. We use a linear process for disturbancesallowing various spatial dependencies and propose a semiparametric estimation approachbased on weighted likelihood and generalized method of moments methods. We establishthe consistency and asymptotic distribution of the proposed estimators and investigate thefinite sample performance of the estimators on simulated data. We end by an applicationof spatial binary choice models to identify UADT (Upper aerodigestive tract) cancer riskfactors in the north region of France which displays the highest rates of such cancerincidence and mortality of the country
Lu, Fan. "Regularized nonparametric logistic regression and kernel regularization." 2006. http://www.library.wisc.edu/databases/connect/dissertations.html.
Full textLien, Ya-Ting, and 連雅亭. "Nonparametric Kernel Regression Estimation inDeterminants of Religious Giving." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/04580167685015635070.
Full text國立臺灣大學
政治學研究所
104
The parametric estimation method used to make several assumptions on the population and data. In real case, however, researchers often have to ignore these violations. In non-parametric methods, researchers don’t have to make so many assumptions as they do in parametric estimation. In addition, using non-parametric methods, researchers can get a better fitted model for the data. The application of non-parametric methods in religious giving studies is quite rare, therefore in this study, we introduced the non-parametric kernel regression method to estimate the 2013~2014 religious giving amount of Taiwan. We compared the results of multiple linear regression, Tobit regression and non-parametric kernel regression and found that the kernel regression model shows the best fitting and the smallest RSE. Also, the significance of each coefficients in kernel regression is quite different from that in multiple regression and Tobit regression.
Chih-Lung, Lu, and 陸治隆. "Double Smoothing of Kernel Estimator in Nonparametric Regression." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/88736964907361472522.
Full text淡江大學
數學學系
90
In the nonparametric regression model﹐to ideally estimate the regression function on the whole support of the design density﹐the kernel estimate of the regression function value at each point on the support of the design density needs to be calculated﹒The resulting regression estimate is called the ideal regression function estimate in this paper. In practice﹐the regression function estimate is produced by joining every two consecutive kernel estimates of regression function values by a straight line segment﹒Here the regression function values are estimated on a sequence of equally spaced partition points of real line﹒Hence such regression function estimate is one of the polygon type﹒This type has been addressed by Jones(1989)﹐Deng and Chu(1999)﹐in which it is called interpolated kernel regression estimate﹒The asymptotic bias of the polygon is worse than ideal regression function estimate and the IMSE is also worse than ideal regression function estimate﹒To improve the disadvantage, Yen、Wu and Cheng(2001)proposed a quadratic interpolated regression estimate with three points to estimate the regression function and they also to structure a new estimator with the quadratic interpolated regression estimate which is better than local linear kernel estimate﹒In this paper﹐we propose two new version of the Yen、Wu and Cheng in which that is to fit a piece of quadratic cure with four points and the other is moving quadratic kernel estimate﹒And we prove that the asymptotic bias of the piece of quadratic cure with four points is the same as the ideal regression function estimate, and the asymptotic variance is better than ideal regression function estimate. Simulation studies show that the resulting performance of the moving quadratic kernel estimate with four points is better than two-order kernel estimate and moving quadratic kernel estimate with three points﹒When samples small than 200﹐our method is also better than four-order kernel estimate﹒
Schindler, Anja. "Bandwidth Selection in Nonparametric Kernel Estimation." Thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-0006-AFD4-4.
Full textLin, Yung-Li, and 林永立. "The Application of Fourier Series And Kernel Estimators in Nonparametric Regression Analysis." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/52714711274185599593.
Full text國立中興大學
農藝學系
87
One of the objective of regression analysis is to investigate the relationship between the design points tj and expected value of response variable yj on the data set {(tj,yj)},j=1,…,n . In general, the analysis could be classified as parametric and nonparametric models. The main distinction is whether the functional form of μ is known. A parametric regression model assume that the form of μ is known. In nonparametric regression analysis, the information of observations yj on the neighborhood of design point t are used to estimate μ(t) . The simplest way is to calculate the weighted average of these observations. Both classical Fourier series and kernel estimators are the kind of weighted average. When the observed data exhibit periodic behavior, usually a linear model including sines and cosines is employed to estimate the regression function μ. The classical Fourier series estimator is of this type. However, if the regression function μ does not satisfy periodic boundary conditions, the criterion based on the mean squared error, i.e. CV or GCV, to choose the number of trigonometric functions in the regression would yield too many terms and the chosen function performs wiggly. A combination of low-order polynomial and trigonometric terms could alleviate the above problem and achieve a smooth curve. As the data set on the interval [0,1] , kernel estimator may also be used to estimate the regression function. The kernel estimator is biased. Under a specified kernel function, smaller bandwidth will cause small bias, but large variance, hence the estimator will be undersmoothing. On the contrary, large bandwidth will cause large bias, but small variance, so the estimator will be oversmoothing. When the σ2 is known, the risk function criteria can be employed to trade-off the biasness and variance and used to decide a suitable smoothing parameter value. However, when the σ2 is unknown, CV and GCV criteria can be used to choose a smoothing parameter value. Beside using on the fitting of data, kernel estimation was also applicable for the estimation of median effective dose (ED50), and constructed the approximate confidence interval for the dose-response curve in bioassay. Finney(1978) had used the data of insulin, 9 doses of s preparation with a dose of insulin were treated to mice, then recorded the numbers of mice showing the symptoms of convulsions. The fitness of probit and logit models of the data set was examined by Pearson's chi-squares test, and the ED50 estimate and 95% confidence interval using parametric method and kernel estimation were compared. The ED50 estimate using kernel estimation is larger than using parametric method, and the width of confidence interval constructed by kernel estimation is wider. Additionally, on the data of treating carbofuran to Meloidogyne incognita, after lack of fit test, it was shown should that both the probit and logit models were not appropriate. The estimate of the ED50 using trimmed Spearman-Karber method was compared with the result using kernel estimate. There is little difference between these two ED50 estimates, and the width of confidence interval of ED50 using kernel estimation is narrower.
Mao, Kai. "Nonparametric Bayesian Models for Supervised Dimension Reduction and Regression." Diss., 2009. http://hdl.handle.net/10161/1581.
Full textWe propose nonparametric Bayesian models for supervised dimension
reduction and regression problems. Supervised dimension reduction is
a setting where one needs to reduce the dimensionality of the
predictors or find the dimension reduction subspace and lose little
or no predictive information. Our first method retrieves the
dimension reduction subspace in the inverse regression framework by
utilizing a dependent Dirichlet process that allows for natural
clustering for the data in terms of both the response and predictor
variables. Our second method is based on ideas from the gradient
learning framework and retrieves the dimension reduction subspace
through coherent nonparametric Bayesian kernel models. We also
discuss and provide a new rationalization of kernel regression based
on nonparametric Bayesian models allowing for direct and formal
inference on the uncertain regression functions. Our proposed models
apply for high dimensional cases where the number of variables far
exceed the sample size, and hold for both the classical setting of
Euclidean subspaces and the Riemannian setting where the marginal
distribution is concentrated on a manifold. Our Bayesian perspective
adds appropriate probabilistic and statistical frameworks that allow
for rich inference such as uncertainty estimation which is important
for measuring the estimates. Formal probabilistic models with
likelihoods and priors are given and efficient posterior sampling
can be obtained by Markov chain Monte Carlo methodologies,
particularly Gibbs sampling schemes. For the supervised dimension
reduction as the posterior draws are linear subspaces which are
points on a Grassmann manifold, we do the posterior inference with
respect to geodesics on the Grassmannian. The utility of our
approaches is illustrated on simulated and real examples.
Dissertation
Chang, Po-Jen, and 張博仁. "A Nonparametric Approach to Pricing and Hedging MBS Via Kernel-Density Regression Model." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/34145936749136671434.
Full text國立中正大學
財務金融研究所
90
The Financial Asset Securitization Law was just passed by Taiwan’s legislature in June, 2002. The law is expected to address stagnancy in Taiwan''s capital markets, it could potentially reinvigorate domestic banks by allowing their asset-backed loans to be packaged into securities. Hence, this new law facilitates the mechanism whereby banks can re-package collateral and sell it to investors as securities, helping to increase the "liquidity of banks" and also diversifying their risks. Financial assets such as mortgages, car loans or credit card receivable accounts can be repackaged into small values in the form of securities certificates or beneficiary certificates for sales to investors. Among all kinds of financial asset products, mortgage-backed security is the most popular in US market. The current way of solving this valuation problems has been to assume a stochastic process for term structure movements and to employ either a simulation/forecasting pricing approach or an empirical/statistical approach for prepayment behavior and price process. In this article, we propose a nonparametric pricing method, kernel-density regression approach, to price weekly TBA (to be announced) GNMA securities. Here we have three goals: the first is to find out what is the best way to reduce the number of independent variables to use for the kernel model and other model and what is the remaining inputs, the second is to assess the pricing effect of kernel-density regression approach versus other pricing models. Finally, we want to recognize the hedging effectiveness of kernel-density regression approach and other models. For comparison, we use another two popular pricing approaches: ordinary least squares (OLS) and a parametric model (proprietary practitioner model). According empirical results, we find that kernel-density regression model perform more effectively on estimating MBS price than the other two models mentioned in this article, except in out-of-sample of time-series sampling. Moreover, kernel-density regression model have better pricing effect on random sampling than on time-series sampling, especially in out-of-sample. In addition, SAS MAXR procedure and principal component analysis can effectively reduce the number of independent variables used for both kernel-density regression model and OLS model. In regard to the hedging effect, the results of in-of-sample are approximately the same with pricing effect analysis. But, in contrast with in-of-sample, Kernel(3-month rate) is the best way to hedge the MBS in out-of-sample, especially on random sampling.
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