## Single index model statistics

SPLINE ESTIMATION OF SINGLE-INDEX MODELS Li Wang and Lijian Yang University of Georgia and Michigan State University Abstract: For the past two decades, the single-index model, a special case of pro-jection pursuit regression, has proven to be an eﬃcient way of coping with the high-dimensional problem in nonparametric regression. 8 Semiparametric Single Index Models 8.1 Index Models A object of interest such as the conditional density f (y j x) or conditional mean E(y j x) is a single index model when it only depends on the vector x through a single linear combination x0 : Most parametric models are single index, including Normal regression, Logit, Probit, Tobit, Abstract. A single index model (SIM) summarizes the effects of the explanatory variables X 1, , X d within a single variable called the index. As stated at the beginning of Part II, the SIM is one possibility for generalizing the GLM or for restricting the multidimensional regression E(Y|X) to overcome the curse of dimensionality and the lack of interpretability.

Single-index models have been studied extensively in the econometrics and statistics literature in the past thirty years or so and cover many classic parametric   15 Jul 2016 We use a multivariate single-index model to ascertain the best functional form for Journal of the American Statistical Association, 84, 986–95. In Section 2, we construct a. Cramér-von Mises test statistic and give its asymptotic distribution. In Section 3, we propose some bootstrap test statistics and show  To circumvent this difficulty, we consider the single-index model estimation problem from a sparsity Mathematical Methods of Statistics, 17:279-304, 2008. Learning Single-Index Models in Gaussian Space. Rishabh Dudeja. RD2714@ COLUMBIA.EDU. Department of Statistics, Columbia University. Daniel Hsu. 31 Mar 2010 Ann Inst Stat Math (2011) 63:1277–1293. DOI 10.1007/s10463-010-0287-4. Variable selection in a class of single-index models. Li-Ping Zhu

## Semiparametric Single Index Model Parameter and Bandwidth Selection Description. npindexbw computes a npindexbw bandwidth specification using the model Y = G(XB) + epsilon.The bandwidth object contains parameters for the single index model and the (scalar) bandwidth for the index function.

A single index model (SIM) summarizes the effects of the explanatory variables X1,, Xdwithin a Part of the Springer Series in Statistics book series (SSS)  Estimating and testing the model index coefficients β is one of the most important objectives in the statistical analysis. However, the commonly used assumption  Single index models are natural extensions of linear models and overcome the The mode is an important feature of a statistical distribution or data set. Estimating and testing the model index coefficients β is one of the most important objectives in the statistical analysis. However, the commonly used assumption on

### A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION - Volume 28 Issue 4 Journal of Statistical Planning and Inference 136, 730–769.

A single index model (SIM) summarizes the effects of the explanatory variables X1,, Xdwithin a Part of the Springer Series in Statistics book series (SSS)  Estimating and testing the model index coefficients β is one of the most important objectives in the statistical analysis. However, the commonly used assumption

### 5 Jan 2016 In this paper, the authors study the partially linear single-index model when the covariate X is measured with additive error and the response

An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed.

## The Single Index Model (SIM) is an asset pricing model, according to which the returns on a security can be represented as a linear relationship with any economic variable relevant to the security. In case of stocks, this single factor is the market return. The SIM for stock returns can be represented as follows:

In Section 2, we construct a. Cramér-von Mises test statistic and give its asymptotic distribution. In Section 3, we propose some bootstrap test statistics and show  To circumvent this difficulty, we consider the single-index model estimation problem from a sparsity Mathematical Methods of Statistics, 17:279-304, 2008.

FUNCTIONAL SINGLE INDEX MODELS FOR LONGITUDINAL DATA By Ci-Ren JiangandJane-LingWang1 University of California, Berkeley and University of California, Davis A new single-index model that reﬂects the time-dynamic eﬀects of the single index is proposed for longitudinal and functional response data, possibly measured with errors, for both { Single Index Model (Review) { Multi Index Models { Capital Asset Pricing Model 1 The Single Index Model (Review) One possible model for the returns is R i = i + iR m + i where i,and i are constants, R m is the return of a market index and i is a random variable with mean 0 and variance ˝2 i. If the 2 i, i and ˝ Single-Index Model 2 / 25. Correlation Structure of Security Returns is a Key Input Recall from Mean-Variance Portfolio: Z = 1 (R RF1) (1) This implies that correlation structure of security returns, 1, is a We can use historical or past time-series data on security Rit and summary features of the data contribute to the actual knowledge discovery. The DSI model has connections to several familiar multivariate models. For example, in the special case when q D 1, the DSI model in (1) reduces to the familiar single index model (Ichimura, 1993; Härdle et al., 1993). In addition, DSI is an extension and gener- single index model when it only depends on the vector x through a single linear combination x0 : Most parametric models are single index, including Normal regression, Logit, Probit, Tobit, and Poisson regression. In a semiparametric single index model, the object of interest depends on x through the function g(x0 ) where 2 Rk and g : R ! R are Single-index model A model of stock returns that decomposes influences on returns into a systematic factor, as measured by the return on the broad market index, and firm specific factors. Related: Market Model Single-Index Model The relationship between a security's performance and the performance of a portfolio containing it. The market model states Estimating the Single Index Model Eric Zivot August 15, 2013. Estimating the Single Index Model Sharpe’s Single (SI) model: Assuming the SI model generates the observed data, the estimators