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1 edition of Nonparametric estimators of actuarial values found in the catalog.

Nonparametric estimators of actuarial values

Jens Praestgaard

# Nonparametric estimators of actuarial values

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Published by University of Copenhagen in Copenhagen .
Written in English

Edition Notes

The Physical Object ID Numbers Series Working Paper ; vol. 80 Pagination 30 p. Number of Pages 30 Open Library OL24686001M

Next, in section 2 we describe the kernel density estimator and the transformed kernel den-sity estimator. In section 3 we present diﬀerent measures of goodness of ﬁt for non-parametric estimations. Then, in section 4 we describe the data set used in our application. Finally, we present the results and conclusions. The ﬁrst nonparametric regression estimate of local averaging type was proposed by J. W. Tukey in The partitioning regression es-timate he introduced, by analogy to the classical partitioning (histogram) density estimate, can be regarded as a special least squares estimate. Some aspects of nonparametric estimation had already appeared.   These actuarial tables do not apply to valuations under Chapter 1, Subchapter D, (relating to qualified retirement arrangements), nor to sect (relating to computations for exclusion ratios for annuities), and for certain other limited purposes as provided by regulations at (a), (a), and (a). Volume 1 Description. Volume 1 will lay out the foundations of predictive modeling. Beginning with reviews of regression and time series methods, this book will provide step-by-step introductions to advanced predictive modeling techniques that are particularly useful in actuarial practice.

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### Nonparametric estimators of actuarial values by Jens Praestgaard Download PDF EPUB FB2

Nonparametric estimates do not depend on any particular distribution. Therefore, these estimates are useful when no distribution adequately fits the data. ) is a resistant statistic because outliers and the tails in a skewed distribution do not significantly affect its values.

actuarial estimation method. Missing and Modified Data in Nonparametric Estimation: With R Examples (Chapman & Hall/CRC Monographs on Statistics and Applied Probability Book ) - Kindle edition by Efromovich, Sam.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Missing and Modified Data in Nonparametric 5/5(1).

1 Nonparametric models and parameters The discussion of in nite dimensional (or non-regular, or parameters falling outside the parametric framework) began with the early work of Fix and Hodges (), followed by the introduction of kernel estimators of density functions by Rosenblatt () and Parzen () in the ’s.

HereFile Size: KB. Note that as mentioned above, the median of the capital distribution, if sampled from a distribution centered on the true parameter values, is an unbiased estimator of true capital, as shown below. The actuarial-simple method is an easy-to-use form of non-parametric data analysis that can be used for multiple censored data that are arranged in intervals.

This method is based on calculating the number of failures in a time interval, versus the number of operating units in that time period. Abstract: The paper deals with the problem of estimating the actuarial present value of the continuous whole life and n-year term life annuities.

We synthesize nonparametric estimators of these statuses of life annuity. The main parts of their asymptotic mean square errors for these estimators and their limit distributions are found.

(). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association: Vol. 53, No.pp. () Non-parametric estimation for a pure-jump Lévy process. Annals of Actuarial Science() Parametric inference for ruin probability in the classical risk model.

The meaning of \nonparametric" for now is density estimate and estimation of conditional expectations. Han Hong Basic Nonparametric Estimation. Density Estimate: Motivation One motivation is to rst use the histogram to estimate the density: 1 2h # of x i in (x h;x + h) n = 1 2h 1 n Xn t=1 1(x h x.

() Improved Estimators in Nonparametric Regression Problems. Journal of the American Statistical Association() Kernel estimation in transect sampiing withoyt the shoulder condition. Actuarial estimation method for Nonparametric Distribution Analysis median is a resistant statistic because outliers and the tails in a skewed distribution do not significantly affect its value.

Nonparametric estimates do not depend on any particular distribution and therefore are good to use when no distribution adequately fits the data. After defining Aalen–Johansen integral estimators, we derive in Section 3 three versions of the non-parametric estimators of the quantities under study.

Their asymptotic properties are discussed, as well as the inclusion of left-truncation. Section 4 is devoted to a Nonparametric estimators of actuarial values book analysis to assess the performance of our non-parametric.

opinion of the nonparametric estimate, please look one more time at the data and you may notice that this conclusion has merit. The bottom diagram in Figure 1 presents monthly housing starts from January to December ; this is the R test data.

An interesting discussion of actuarial values of housing markets can be found in Wang and Chen. Makeham's formula: A = K+p(I-t)(C-K) g where: A is the present value of capital and net interest payments; K is the present value of capital payments; C is the total capital to be repaid (at redemption price); g is the rate of interest expressed per unit of the redemption price; t is the rate of tax on interest.

Value of annuity certain net of tax: a;-- tg (a& - 03 where. Let us begin with the log-likelihood function. This function is not appropriate for evaluating the performance of non-parametric density estimates.

The log-likelihood depends on the values of the density exclusively at sample points. Lett. 12 () –; P. Hall, N. Tajvidi, Distribution and dependence-function estimation for bivariate extreme-value distributions, Bernoulli 6 () –; P.

Capéraà, A.-L. Nonparametric maximum likelihood estimators (NPMLEs) of the cumulative incidence for competing risks data were pioneered by Aalen () and Kalbfleisch and Prentice (). Subsequently, Dinse () proposed an NPMLE for right-censored and masked competing risks data to be computed with the explicit use of a Dempster et al.

() Expectation. In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random density estimation is a fundamental data smoothing problem where inferences about the population are made, based on a finite data some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method.

JWSTfm JWSTPromislow Printer:YettoCome Trimmm×mm October13, viii CONTENTS ∗ Changeofdiscountfunction 27 Internalratesofreturn 28 ∗ Forwardpricesandtermstructure 30 Standardnotationandterminology In addition, the book covers: Extremes in samples of random size Methods of estimating extreme quantiles and tail probabilities Self-normalized sums of random variables Measures of market risk Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over exercises.

86 Non-parametric Empirical Bayes Estimation for the Buhlmann Actuarial Modeling This book is concerned with the construction and evaluation of actuarial models.

The purpose of this chapter is to de ne models in the actuarial pension fund actuaries use models to estimate the. This can be formalized with the breakdown point of an estimator. The breakdown point of an estimator is defined as the minimum proportion of data points to be changed in order to change the value of the estimator.

This in essence measures what we were discussing just now. The breakdown point of the nonparametric estimator is obviously 1/n. the number of sample values less than the argument t.

Besides describing the sample, this F(t) is also a nonparametric estimate of the population distribution, in the sense indicated in below.

When the observations are incomplete, the corresponding estimate is still a. The Kaplan-Meier Estimator The Kaplan-Meier estimator (Kaplan and Meier, ) was originally derived as an NP maximum likeli-hood estimator of F and as a limit of the actuarial esti-mator as the time axis is partitioned into fine intervals.

Because of the latter method of derivation, it is also known as the product-limit (PL) estimator. In this section we formulate two nonparametric estimators of p. Let Y(r) is the r-th order statistic of the original negative log returns and ^p = Y([n(1 p)]+1) be the sample quantile estimator of p, which is called the historical VaR estimator in empirical nance.

The rst nonparametric estimator of p considered in this paper is a simple conditional. However, there are a number of alternative nonparametric approaches that can be used, each with its own advantages and disadvantages. In this paper we compare nonparametric volatility function estimators based on kernel estimators and on neural networks in terms of their accuracy to fit the true unknown volatility function.

Downloadable. We design a system for calculating the quantile of a random variable that allows us combining parametric and non-parametric estimation methods. This approach is applicable to evaluate the severity of potential losses from existing data records; therefore, it is useful in many areas of economics and risk evaluation.

The procedure is based on an initial parametric model assumption. percentages of total values that could be lost in one event or an aggregation of events over some time period—usually a year.

Total insured values3 obviously represent the upper bound of loss potential. Scenario testing is another method used to estimate. Nonparametric estimation of distribution functions and quantiles (notes and Ch.

2 of Wasseman All of Nonparametric Statistics). Goodness of t (notes). Permutation tests (article + notes). Bootstrapping Kernel density estimator Smoothing: general concepts (Ch. 4 of Wasserman). Nonparametric regression (Ch.

5 of Wasserman). Extreme value theory. Extreme values modelling and estimation are an important challenge in various domains of application, such as environment, hydrology, finance, actuarial science, just to name a few.

The restriction to the analysis of extreme values may be justified since the extreme. probability-value and power of a test. Apply basic tests for the one-sample and two-sample situations involving the normal, binomial and Poisson distributions, and apply basic tests for paired data.

Apply the permutation approach to non-parametric hypothesis tests. Many of the non-parametric procedures require a simple rank transformation of the data (Conover, ; Sprent, ). This involves pooling the data from all subjects, regardless of treatment group, and ranking in ascending order based on the value of the dependent variable.

The subject with the lowest value is assigned the rank of 1. Actuarial Appraisal Value One of the primary goals of the actuarial appraisal is to provide enough information for potential investors to make informed judgments as to the potential value of a property.

The components of value typically presented in an actuarial appraisal include: • the adjusted book value. Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data.

Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the model estimates.

The KM estimator is also an MLE You can read in Cox and Oakes book Section Here we need to think of the distribution function F(t) as an (in nite dimensional) parameter, and we try to nd the F^ (or S^ = 1 F^) that maximizes a nonparametric likelihood.

Such a MLE is called a NPMLE. As it turns out, such a F^(t) has to be discrete in order. Nonparametric Methods for Right-Censored Data: The LIFETEST Procedure The LIFETEST procedure computes nonparametric estimates of the survival distribution function.

You can request either the product-limit (Kaplan and Meier) or the life-table (actuarial) estimate of the. Nonparametric estimation tools for model selection (graphical methods, goodness of fit statistics) Nonparametric estimation using modified data (ogive, Kaplan-Meier, Nelson-Aalen) Parametric (likelihood-based) estimation (with data that are individual and complete, grouped, censored, and/or truncated), including starting values based on method.

I posted a query about nonparametric effect size estimators on EDSTAT-L and got a few responses, which I provide here. Leech () suggested to report nonparametric effect size indices, such as Vargha & Delaney's A or Cliff's d. (Leech (). A Call for Greater Use of Nonparametric.

Non-parametric and parametric bootstrap techniques for age-to-age development factor methods in stochastic claims reserving. Scandinavian Actuarial Journal, (4), – Björkwall, S., Hössjer, O., and Ohlsson, E. To build intuition, another way to view the kernel estimator in (3) is the following: at each input x, it employs the estimate f^(x) = ^, where ^ is the minimizer of Xn i=1 K x xi h (yi)2: Instead we could consider forming the local estimate f^(x) = ^ + x^, where ^ ; ^ minimize Xn i=1 K x xi h (yi xi)2: This is called local linear regression 4.

In this paper we suggest several nonparametric quantile estimators based on Beta kernel. They are applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte Carlo based study has shown that those estimators improve the efficiency of the traditional ones, not only for light tailed distributions, but also for heavy tailed, when the probability.Nonparametric curves are driven by structure in the data and are broadly applicable.

Parametric curves rely on model building and prior knowledge of the equations underlying the data. In the nonparametric world, an estimator may be optimal for one purpose and noticeably suboptimal for another.Introduction and definition. Here we discuss the non-parametric estimation of a pdf $$f$$ of a distribution on the real line.

The kernel density estimator is a non-parametric estimator because it is not based on a parametric model of the form $$\{ f_{\theta}, \theta \in \Theta \subset {\mathbb R}^d\}$$. What makes the latter model 'parametric' is the assumption that the parameter space.