Least Squares Estimators of the Mode of a Unimodal Regression Function
نویسنده
چکیده
where m = f f is a unimodal function with mode m . In this paper, we establish almost sure convergence of (1.2) with optimal convergence rates up to a logarithmic factor, under the assumption of the exponential tail for the error distributions. Suppose throughout the sequel that Xi are iid random variables from a continuous distribution GX such that the density G ′ X exists in a neighborhood of the unknown mode m0 and G ′ X is positive and continuous at m0. Consider smoothness condition
منابع مشابه
A robust least squares fuzzy regression model based on kernel function
In this paper, a new approach is presented to fit arobust fuzzy regression model based on some fuzzy quantities. Inthis approach, we first introduce a new distance between two fuzzynumbers using the kernel function, and then, based on the leastsquares method, the parameters of fuzzy regression model isestimated. The proposed approach has a suitable performance to<b...
متن کاملFuzzy Robust Regression Analysis with Fuzzy Response Variable and Fuzzy Parameters Based on the Ranking of Fuzzy Sets
Robust regression is an appropriate alternative for ordinal regression when outliers exist in a given data set. If we have fuzzy observations, using ordinal regression methods can't model them; In this case, using fuzzy regression is a good method. When observations are fuzzy and there are outliers in the data sets, using robust fuzzy regression methods are appropriate alternatives....
متن کاملAdaptive Risk Bounds in Unimodal Regression
We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal regression has not been as extensively studied. We show that the unimodal least squares estimator is adaptive in the sense that the risk scales as a function of the number of values in the true underlying sequence. Such adaptivity properti...
متن کاملبرآورد ناپارامتریک و شبهپارامتریک تابع تولید صنعت خودرو با تاکید بر نهاده انرژی: معرفی روش اولی - پاکس (OP) در برآورد الگوی دادههای ترکیبی
Unobservable productivity shocks cause selection and simultaneity problems in firm’s decisions and these problems cause estimators such as ordinary least squares, have biased estimation for coefficients of production function inputs. In this study, data of five automaker companies in the period of 1383-1387 have been used and production function of car industry have been estimated by ordinary l...
متن کاملEfficient Estimation of the Density and Cumulative Distribution Function of the Generalized Rayleigh Distribution
The uniformly minimum variance unbiased (UMVU), maximum likelihood, percentile (PC), least squares (LS) and weighted least squares (WLS) estimators of the probability density function (pdf) and cumulative distribution function are derived for the generalized Rayleigh distribution. This model can be used quite effectively in modelling strength data and also modeling general lifetime data. It has...
متن کامل