Optimal generalized ridge estimator under the generalized cross-validation criterion in linear regression

Given the noise-corrupted seismic recordings, blind deconvolution simultaneously solves for the reflectivity series and the wavelet. Blind deconvolution can be formulated as a fully perturbed linear regression model and solved by the total least-squares (TLS) algorithm. However, this algorithm performs poorly when the data matrix is a structured matrix and ill-conditioned. In blind deconvolution, the data matrix has a Toeplitz structure and is ill-conditioned. Accordingly, we develop a fully automatic single-channel blind-deconvolution algorithm to improve the performance of the TLS method. The proposed algorithm, called Toeplitz-structured sparse TLS, has no assumptions about the phase of the wavelet. However, it assumes that the reflectivity series is sparse. In addition, to reduce the model space and the number of unknowns, the algorithm benefits from the structural constraints on the data matrix. Our algorithm is an alternating minimization method and uses a generalized cross validation function to define the optimum regularization parameter automatically. Because the generalized cross validation function does not require any prior information about the noise level of the data, our approach is suitable for real-world applications. We validate the proposed technique using synthetic examples. In noise-free data, we achieve a near-optimal recovery of the wavelet and the reflectivity series. For noise-corrupted data with a moderate signal-to-noise ratio (S/N), we found that the algorithm successfully accounts for the noise in its model, resulting in a satisfactory performance. However, the results deteriorate as the S/N and the sparsity level of the data are decreased. We also successfully apply the algorithm to real data. The real-data examples come from 2D and 3D data sets of the Teapot Dome seismic survey.

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ESTIMASI PARAMETER REGRESI SPLINE DENGAN METODE PENALIZED SPLINE

Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya ◽

10.26418/bbimst.v8i2.31532 ◽

2019 ◽

Vol 8 (2) ◽

Author(s):

Wahyu Kurniasari, Dadan Kusnandar, Evy Sulistianingsih

Keyword(s):

Cross Validation ◽

Generalized Cross Validation ◽

Penalized Spline

Regresi spline merupakan suatu pendekatan ke arah pencocokan data dengan tetap memperhitungkan kemulusan kurva. Salah satu bentuk estimator dari regresi spline ialah penalized spline. Tujuan dari penelitian ini adalah untuk mengestimasi parameter regresi spline dengan metode penalized spline untuk data yang tidak memiliki pola tertentu. Data penelitian ini menggunakan data sekunder yang diperoleh dari Badan Pusat Statistik Indonesia pada tahun 2015 yaitu indeks pembangunan manusia, gini rasio, harapan lama sekolah, penduduk miskin, dan kepadatan penduduk. Hasil regresi spline yang diperoleh untuk model terbaik yaitu model spline linier pada setiap variabel dengan nilai Generalized Cross Validation (GCV) minimum. Hasil penelitian menunjukkan bahwa regresi spline dengan metode penalized spline menghasilkan estimasi parameter yang signifikan dan memperoleh nilai koefisien determinasi terkoreksi sebesar 76,66% serta nilai MAPE untuk model regresi spline sebesar 1,415%. Kata Kunci: regresi nonparametrik, regresi spline, penalized spline.

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