{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T07:16:57Z","timestamp":1781162217031,"version":"3.54.1"},"reference-count":18,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,4]],"date-time":"2021-11-04T00:00:00Z","timestamp":1635984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.<\/jats:p>","DOI":"10.3390\/sym13112094","type":"journal-article","created":{"date-parts":[[2021,11,4]],"date-time":"2021-11-04T22:25:54Z","timestamp":1636064754000},"page":"2094","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0492-488X","authenticated-orcid":false,"given":"Ni Putu Ayu Mirah","family":"Mariati","sequence":"first","affiliation":[{"name":"Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia"},{"name":"Universitas Mahasaraswati Denpasar, Bali 80233, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6572-4083","authenticated-orcid":false,"given":"I. Nyoman","family":"Budiantara","sequence":"additional","affiliation":[{"name":"Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vita","family":"Ratnasari","sequence":"additional","affiliation":[{"name":"Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Eubank, R.L. (1999). Nonparametric Regression and Spline Smoothing, Marcel Dekker, Inc.. [2nd ed.].","DOI":"10.1201\/9781482273144"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Akram, T., Abbas, M., Iqbal, A., Baleanu, D., and Asad, J.H. (2020). Novel numerical approach based on modified extended cubic B-spline functions for solving non-linear time-fractional telegraph equation. 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Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/2094\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:26:03Z","timestamp":1760167563000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/2094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,4]]},"references-count":18,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["sym13112094"],"URL":"https:\/\/doi.org\/10.3390\/sym13112094","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,4]]}}}