ON THE ASYMPTOTIC NORMALITY FOR NONPARAMETRIC SEQUENTIAL DENSITY ESTIMATION

Sequential nonparametric density estimation

On asymptotic normality of sequential

For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting distribution of the sequential LSE is shown to be normal for the parameter vector lying both inside the stability region and on some part of its boundary in contr...

Asymptotic Normality in Density Support Estimation

Estimation Gérard BIAU a,∗, Benôıt CADRE b, David M. MASON c and Bruno PELLETIER d a LSTA & LPMA Université Pierre et Marie Curie – Paris VI Bôıte 158, 175 rue du Chevaleret 75013 Paris, France [email protected] b IRMAR, ENS Cachan Bretagne, CNRS, UEB Campus de Ker Lann Avenue Robert Schuman 35170 Bruz, France [email protected] c University of Delaware Food and Resource Econ...

Asymptotic Normality for Deconvolving Kernel Density Estimators

Suppose that we have 11 observations from the convolution model Y = X + £, where X and £ are the independent unobservable random variables, and £ is measurement error with a known distribution. We will discuss the asymptotic normality for deconvolving kernel density estimators of the unknown density f x 0 of X by assuming either the tail of the characteristic function of £ behaves as II I~Oexp(...

On Nonparametric Sequential Point Estimation