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    Fourier Transform by Distribution Function in Statistics
    (2024) Yalaz, Seçil
    The Fourier transform is one of the most important methods, which has the ability to transform complex integral equations into simple algebraic equations and is frequently used in both mathematics and statistics. Although the Fourier transform is valid for every function in mathematics under certain conditions, this situation can become more complicated in statistics because of the fact that statistics are very different from mathematics. While in statistics, different observation values, that is, different x values, are considered for each situation, in mathematics for each x a function is defined. Because in statistics, random variables are concerned rather than functions, and the density functions of the observed values of interest should also be known. In statistics, it is seen that the Fourier transform is used in non-parametric models in which asymptotic properties are examined. In the Fourier transform, which can be performed using both distribution and density functions, it is not possible to use the density function when there are unknown or non-integrable density functions or very slow convergence rate (considering asymptotic properties). In such cases, it would be more appropriate to perform the Fourier transform with the distribution function. In this study, suggestions are presented on under which conditions it would be more appropriate to perform the Fourier transform with the distribution function.
  • [ X ]
    Öğe
    Fourier Transform by Distribution Function in Statistics
    (Osmaniye Korkut Ata Üniversitesi, 2024) Yalaz, Seçil
    The Fourier transform is one of the most important methods, which has the ability to transform complex integral equations into simple algebraic equations and is frequently used in both mathematics and statistics. Although the Fourier transform is valid for every function in mathematics under certain conditions, this situation can become more complicated in statistics because of the fact that statistics are very different from mathematics. While in statistics, different observation values, that is, different x values, are considered for each situation, in mathematics for each x a function is defined. Because in statistics, random variables are concerned rather than functions, and the density functions of the observed values of interest should also be known. In statistics, it is seen that the Fourier transform is used in non-parametric models in which asymptotic properties are examined. In the Fourier transform, which can be performed using both distribution and density functions, it is not possible to use the density function when there are unknown or non-integrable density functions or very slow convergence rate (considering asymptotic properties). In such cases, it would be more appropriate to perform the Fourier transform with the distribution function. In this study, suggestions are presented on under which conditions it would be more appropriate to perform the Fourier transform with the distribution function.
  • [ X ]
    Öğe
    Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method
    (2016) Yalaz, Seçil; Atay, Arife
    Regresyon ve sınıflandırma üzerine yaptığımız bu çalışma, yıllardır birçok alanda kullanılan zaman serileri analizine yeni bir katkı sağlamaktadır. Zaman serileri için regresyon uygulamasında karşılaşılan otokorelasyonun kaldırılması aşamasında çoğu kez ya uyum sağlanamadığından başarıya ulaşılamamakta ya da modelin derecesinin değiştirilmesi zorunluluğuyla karşı karşıya kalınmaktadır. Modelin derecesinin değiştirilmesi ise her zaman istenilen bir durum olmayabilir. Böyle durumlarda kullanılmak üzere önerilen çalışmamızda, zamana bağlı veriler basit üyelik fonksiyonu ve bulanıklık kuralı üretim tekniği (SMRGT) ile bulanıklaştırılmış ve elde edilen değişkenler için bulanık en küçük kareler (Bulanık EKK) modeli ile basit doğrusal regresyon yöntemi uygulanarak geleceğe yönelik tahmine ilişkin bir denklem oluşturulmuştur. SMRGT açık kanallarda debi akışını belirlemede başarılı olmasına ve açık kanallarda debi akışını modellemede güvenle kullanılabilmesine rağmen bu tekniğin bulanık doğrusal regresyon modellemesinde de başarılı olacağı hakkında hiçbir ip ucu yoktur. Bu nedenle bu tür bir modellemenin eksikliği adres gösterilerek yeni bir hibrit model bu çalışma kapsamında tarif edilmiştir. Sonuç olarak yöntemin geçerliliğinin ölçülebilmesi bakımından zaman serileri için doğrusal regresyon ve bulanık zaman serileri için doğrusal regresyon iki ayrı veri setine uygulanmış ve bu iki yaklaşımın performansları çeşitli ölçüm kriterleri kullanılarak karşılaştırılmıştır
  • Küçük Resim
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    Henderson's method approach to Kernel prediction in partially linear mixed models
    (Sivas Cumhuriyet Üniversitesi Fen Fakültesi, 2020) Kuran, Özge; Yalaz, Seçil
    In this article, we propose Kernel prediction in partially linear mixed models by usingHenderson's method approach. We derive the Kernel estimator and the Kernel predictor viathe mixed model equations (MMEs) of Henderson's that they give the best linear unbiasedestimation (BLUE) of the fixed effects parameters and the nonparametric functioncomputationally easier and the best linear unbiased prediction (BLUP) of the random effectsparameters as by-products. Additionally, asymptotic property of the Kernel estimator isinvestigated. A Monte Carlo simulation study is supported to illustrate the performance ofKernel prediction in partially linear mixed models and then, we finalize the article with thehelp of conclusion and discussion part to summarize the findings.
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    Kernel Liu prediction approach in partially linear mixed measurement error models
    (Taylor and Francis Ltd., 2022) Kuran, Özge; Yalaz, Seçil
    In this paper, we put forward ‘kernel Liu prediction approach’ instead of ‘kernel prediction approach’ under multicollinearity case in partially linear mixed measurement error model. We obtain the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the Liu biasing parameter via the Conceptual Prediction ((Formula presented.)) criterion. The asymptotic normality condition is examined and the unknown covariance matrix of measurement errors circumstance is derived. We study a numerical example together with a Monte Carlo simulation study to evaluate the performance of the kernel Liu prediction approach at the end of this paper.
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    Kernel mixed and Kernel stochastic restricted ridge predictions in the partially linear mixed measurement error models: an application to COVID-19
    (Taylor & Francis Ltd, 2023) Kuran, Özge; Yalaz, Seçil
    In this article, we define mixed predictor and stochastic restricted ridge predictor of partially linear mixed measurement error models by taking advantage of Kernel approximation. Under matrix mean square error criterion, we make the comparison of the superiorities the linear combinations of the new defined predictors. Then we investigate the asymptotic normality characteristics and the situation of the unknown covariance matrix of measurement errors. Finally, the study is ended with a Monte Carlo simulation study and COVID-19 data application.
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    Kernel ridge prediction method in partially linear mixed measurement error model
    (Taylor & Francis, 2022) Kuran, Özge; Yalaz, Seçil
    In this article, a new kernel prediction method by using ridge regression approach is suggested to combat multicollinearity and the impacts of its existence on various views of partially linear mixed measurement error model. We derive the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the ridge biasing parameter. The asymptotic normality condition is investigated and the unknown covariance matrix of measurement errors circumstance is handled. A real data analysis together with a Monte Carlo simulation study is made to assess endorsement of the kernel ridge prediction method.
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    Partially linear multivariate regression in the presence of measurement error
    (Korean Statistical Society, 2020) Yalaz, Seçil; Tez, Müjgan
    In this paper, a partially linear multivariate model with error in the explanatory variable of the nonparametric part, and an m dimensional response variable is considered. Using the uniform consistency results found for the estimator of the nonparametric part, we derive an estimator of the parametric part. The dependence of the convergence rates on the errors distributions is examined and demonstrated that proposed estimator is asymptotically normal. In main results, both ordinary and super smooth error distributions are considered. Moreover, the derived estimators are applied to the economic behaviors of consumers. Our method handles contaminated data is founded more effectively than the semiparametric method ignores measurement errors
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    Öğe
    Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis
    (2024) Kuran, Özge; Yalaz, Seçil
    In this article we describe new predictors under multicollinearity situation in the partially linear mixed measurement error models. In order to achieve this aim, we refer to some preliminary information and use it in order to suggest the modified Kernel ridge predictors in the partially linear mixed measurement error models. In addition, we also attain some mean square error comparisons between our new described modified Kernel ridge predictors and predictors previously described in literature for the partially linear mixed measurement error model. In conclusion, the article showcases real data analysis and a simulation study to illusrate our theoretical findings.
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    Semiparametric EIV regression model with unknown errors in all variables
    (Bitlis Eren Üniversitesi, 2019) Yalaz, Seçil; Tez, Müjgan
    Bu makale ile değişkenleri hatalı ölçülmüş yarı parametrik kısmi doğrusal regresyon modelinde hataların yoğunlukları bilinmediğinde kullanılabilecek bir yöntem geliştirilmektedir. Bağımsız değişkenlerin hata bulaşmış iki ölçümünün mevcudiyeti tanımlamayı sağlamak için kullanılır. Bu yöntem, ölçüm hataları yoğunluklarının bilindiği varsayımına dayanan kernel dekonvolüsyon yöntemine benzetilir. Bununla birlikte, bu dekonvolüsyon yönteminde, süper düzgün hataların varlığında bir regresyon fonksiyonunun tahmin edilmesi, yakınsama oranları çok yavaş olduğu için son derece zordur. Bu durum nedeniyle, literatürde yazarlar sadece hatanın olağan düzgün dağılıma sahip olduğu durumlarda çalışmışlardır. Bu problemi Nadaraya-Watson tahmin edicisinin Fourier temsiliyle çözebiliriz, çünkü bu yöntem hem süper düzgün hem de olağan düzgün dağılımların üstesinden gelebilir. Literatürde asimptotik normallik gösteriminde de aynı düzleştirme probleminden dolayı zorluk çekilmektedir. Bu çalışma ile parametrik kısmın asimptotik normalliğinin gösterimi de sağlanabilinmiştir. Uygulama bölümünde, Monte Carlo simülasyon denemeleri ile .....)'nin performansları incelenmiştir.
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    Wavelet estimation in nonparametric linear mixed-effects errors in variables model
    (Yildiz Technical University, 2022) Yalaz, Seçil; Kuran, Özge
    Nonparametric linear mixed effects models are preferred due to overcome the restrictions of linear models which need to satisfy distributional assumptions. In these models, smoothing approaches are needed to handle nonparametric part and chosen according to the type of data. When there is a measurement error in the nonparametric part, these smoothing techniques become more complicated. In this paper, we propose wavelet approach to smooth nonparametric function under known measurement error in nonparametric linear mixed effects model and then, we predict random effects pa ra meter. Fu rt hermore, as imu lation study is done to demonstrate the theoretical findings b y c omparing w ith t he c ase i gnoring measurement error. The performances are much better for the proposed model than the no measurement error case.
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    Wavelet estimation of semiparametric errors in variables model
    (Ankara University, 2019) Yalaz, Seçil
    Most of the work on wavelet estimation when the variables aremeasured with errors have centered around nonparametric approaches whichcause curse of dimensionality. In this paper it is aimed to avoid this complexityusing wavelet semiparametric errors in variables regression model. Using theoretical arguments for nonparametric wavelet estimation a wavelet approachis represented to estimate partially linear errors in variables model which is asemiparametric model when explanatory variable of nonparametric part hasmeasurement error. Assuming that the measurement error has a known distribution we derive an estimator of the linear partsíparameter. In simulationstudy derived method is compared with no measurement error case.