# hierband.path: Solves main optimization problem over a grid of lambda values In hierband: Convex Banding of the Covariance Matrix

## Description

See `hierband` for the problem this is solving. If `lamlist` not provided, then grid will be constructed starting at lambda_max, the smallest value of lam for which the solution (with `delta=NULL`) is diagonal.

## Usage

 ```1 2``` ```hierband.path(Sighat, nlam = 20, flmin = 0.01, lamlist = NULL, w = NULL, delta = NULL, maxiter = 100, tol = 1e-07) ```

## Arguments

 `Sighat` The sample covariance matrix `nlam` Number of lambda values to include in grid. `flmin` Ratio between the smallest lambda and largest lambda in grid. (Default: 0.01) Decreasing this gives less sparse solutions. `lamlist` A grid of lambda values to use. If this is non-NULL, then `nlam` and `flmin` are ignored. `w` `(p-1)`-by-`(p-1)` lower-triangular matrix (above diagonal ignored). `w[l,]` gives the `l` weights for g_l. Defaults to `w[l,m]=sqrt(2 * l)/(l - m + 1)` for `m <= l` `delta` Lower bound on eigenvalues. If this is NULL (which is default), then no eigenvalue constraint is included. `maxiter` Number of iterations of blockwise coordinate descent to perform. `tol` Only used when `delta` is non-NULL. When no eigenvalue changes by more than `tol` in BCD, convergence is assumed.

## Value

Returns a sequence of convex banded estimates of the covariance matrix.

P:

A `nrow(Sighat)`-by-`nrow(Sighat)`-by-`nlam` array where `P[, , i]` gives the `i`th estimate of the covariance matrix.

lamlist:

Grid of lambda values used.

w:

Value of w used.

delta:

Value of delta used.

`hierband` `hierband.cv`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```set.seed(123) p <- 100 n <- 50 K <- 10 true <- ma(p, K) x <- matrix(rnorm(n*p), n, p) %*% true\$A Sighat <- cov(x) path <- hierband.path(Sighat) cv <- hierband.cv(path, x) fit <- hierband(Sighat, lam=cv\$lam.best) ```