Model Estimation in Nonlinear Regression Under Shape Invariance

Kneip, Aloïs; Engel, Joachim

doi:10.1214/aos/1176324535

Cited by 51 publications

(60 citation statements)

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“…Hanewald (2011) found that the LC mortality index k t correlates significantly with macroeconomic fluctuations in some periods, which provides a good reference with which to connect the mortality trends between China and Japan. The research from Härdle and Marron (1990) on semiparametric comparison of regression curves and also the one from Kneip and Engel (1995) suggest one potential way to analyse demographic common trend between two countries and even among multi-countries. …”

Section: Literature Reviewmentioning

confidence: 99%

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A Mortality Model for Multi-Populations: A Semi-Parametric Approach

2016

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractMortality is different across countries, states and regions. Several empirical research works however reveal that mortality trends exhibit a common pattern and show similar structures across populations. The key element in analyzing mortality rate is a time-varying indicator curve. Our main interest lies in validating the existence of the common trends among these curves, the similar gender differences and their variability in location among the curves at the national level. Motivated by the empirical findings, we make the study of estimating and forecasting mortality rates based on a semi-parametric approach, which is applied to multiple curves with the shape-related nonlinear variation. This approach allows us to capture the common features contained in the curve functions and meanwhile provides the possibility to characterize the nonlinear variation via a few deviation parameters. These parameters carry an instructive summary of the time-varying curve functions and can be further used to make a suggestive forecast analysis for countries with barren data sets. In this research the model is illustrated with mortality rates of Japan and China, and extended to incorporate more countries. All numerical procedures are transparent and reproduced on www.quantlet.de.JEL classification: C14, C32, C38, J11, J13

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Section: Literature Reviewmentioning

confidence: 99%

“…The model in Equ. (3) is commonly known as shape invariant model (SIM), firstly proposed by Lawton et al (1972) and further studied by Kneip and Engel (1995) and provides an extension of the model in Equ. (2) to multiple curves.…”

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confidence: 99%

A Mortality Model for Multi-Populations: A Semi-Parametric Approach

2016

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“…Given m, we maximize the profile likelihood over the remaining parameters to get (8) Since this is linear in h, we may choose various h in the score to obtain a series of equations. In particular, letting h(r) = δ t (r), the Dirac function, in the score equation …”

Section: Appendix a Derivations Of The Npmle Estimates In The One-samentioning

confidence: 99%

“…The selfmodelling method is an automatic alignment procedure without using such landmark registration (Lawton et al, 1972;Ramsay and Silverman, 2005;Ronn, 2001;Gervini and Gasser, 2004;Ramsay and Li, 1998;Wang and Gasser, 1999). Other methods include shape invariant modelling (Kneip and Engel, 1995), local regression (Kneip et al, 2000), among others. All the above mentioned methods assume that the shifting effect is deterministic.…”

Section: Introductionmentioning

confidence: 99%

Alignment of protein mass spectrometry data by integrated Markov chain shifting method

Feng

Wang

et al. 2009

Statistics and Its Interface

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Mass spectrometers such as SELDI-TOF (surface enhanced laser desorption/ionization time-of-flight) and MALDI-TOF (matrix assisted laser desorption and ionization time-of-flight) measure the relative abundance of different protein ions or protein fragments (peptides) indexed by the mass-to-charge ratio (m/z). A special characteristic of the MS spectra is its variabilities in both m/z values and intensity magnitudes. We propose modelling the logintensities by a semiparametric model and the m/z by the integrated Markov chain shifting (IMS) model, for which the second-order differences of the random effects are assumed to follow a second-order Markov chain. Alignment of spectra is done through averaging over the random shifts conditional on the observed intensity information. The unknown parameters are estimated by an iterative nonparametric maximum profile likelihood method and a Gaussian kernel approximation. The bandwidths in kernel approximation are taken to be 0.04%-0.08% of the m/z values. Simulation results show that the proposed approach can achieve satisfactory alignment by reducing the intensity variations of the misalignment spectra by a factor of around 75%. Most alignment algorithms align spectra by clustering neighboring peaks and do not incorporate peak height information. Our semiparametric random shifting method builds a model taking into consideration of both the random shift effects of neighboring m/z values and similarity of the intensity magnitudes of common peaks within the ranges of about 50% of the intensity values.AMS 2000 subject classifications: Primary 62P10, 62G99; secondary 92F05. Keywords and phrases: MS spectra, semiparametric model, markov chain, integrated markov chain shifting, profile likelihood. BACKGROUNDThe field of proteomics is an evolving area, which may shed light on the proteins associated with diseases and tumors. A powerful tool for proteomic profiling is the mass spectrometer (MS). It produces high throughput relative * Corresponding author. abundance of protein ions or peptides (fragment of proteins) of the studied sample, in the form of spectrum. Screening multiple MS spectra can provide insight into the protein ion composition of different samples under different conditions.Mass spectrometers such as SELDI-TOF (surface enhanced laser desorption/ionization time-of-flight) and MALDI-TOF (matrix assisted laser desorption and ionization time-of-flight) measure the relative abundance of different protein ions or peptides indexed by the mass-to-charge ratio (m/z). MS spectra can reveal proteomic patterns or features (e.g. biomarker ions) which may be related to specific characteristics of biological samples and can be used for diagnostic purposes. They can also be used for prognosis and for monitoring disease progression and evaluating treatment or intervention. Other applications of MS spectrum include pharmaceutical analysis, biomolecule characterization, environmental assessment and forensic analysis.High throughput MS spectra data have raised challenging issues such as...

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“…in the sense that there exists an average curve, see Kneip and Engel (1995). This is not restriction at all and can be replaced by any appropriate combination of parameters.…”

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confidence: 99%

Shape Invariant Modelling Pricing Kernels and Risk Aversion

2009

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Pricing kernels play a major role in quantifying risk aversion and investors' preferences. Several empirical studies reported that pricing kernels exhibit a common pattern across different markets. Mostly visual inspection and occasionally numerically summarise are used to make comparison. With increasing amount of information updated every day, the empirical pricing kernels can be viewed as an object evolving over time. We propose a systematic modelling approach to describing the evolution of the empirical pricing kernels. The approach is based on shape invariant models. It captures the common features contained in the shape of the functions and at the same time characterises the variability between the pricing kernels based on a few interpretable parameters. The method is demonstrated with the European options and returns values of DAX index.

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Model Estimation in Nonlinear Regression Under Shape Invariance

Cited by 51 publications

References 0 publications

A Mortality Model for Multi-Populations: A Semi-Parametric Approach

A Mortality Model for Multi-Populations: A Semi-Parametric Approach

Alignment of protein mass spectrometry data by integrated Markov chain shifting method

Shape Invariant Modelling Pricing Kernels and Risk Aversion

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